CN114002996B - A smoothing method for continuous five-axis path transfer of hybrid robot C3 - Google Patents

Abstract

The invention discloses a continuous five-axis path smoothing method for hybrid robot C3, which includes the following steps: the tool tip point position path is defined in the Cartesian coordinate system; the tool axis direction path is defined on the surface of the unit sphere; the tool tip The point position path and the tool axis direction path both use spline curve segments for smoothing. The smoothed paths are composed of inserted spline curve segments and remaining path segments. The transfer between the two is deduced respectively. The necessary and sufficient conditions for the continuous differential curvature at the point are established, and then the relationship functions between the path smoothing length at the tool tip point position, the path smoothing angle in the tool axis direction and the respective smoothing errors are established; combined with the constraints introduced by parameter synchronization, the tool tip point position is determined The smoothing curve of the path and the tool axis direction path; the parameter synchronization curve is introduced to ensure that the third-order derivative of the geometrically smoothed five-axis path with respect to time is continuous. The invention can realize accurate prediction and control of smoothing errors, and at the same time improve the calculation efficiency of the smoothing method.

Description

A smoothing method for continuous five-axis path transfer of hybrid robot C3

Technical Field

The present invention relates to the field of robot numerical control machining, and in particular to a hybrid robot C3 continuous five-axis path switching and smoothing method.

Background Art

At present, with the rapid development of aviation, aerospace, railway and shipping, the demand for processing large-sized complex parts is increasing. Manufacturing super-large machine tools with serial stroke is a common solution for processing large-sized parts. However, when the processing features are scattered in different areas on large parts, such as hole making on aircraft wing skin, the above processing solution is not an economical and efficient choice. Considering the five-degree-of-freedom hybrid robot as a "plug-and-play" module, combined with a long-stroke guide rail, large-sized parts can be processed in situ. Robot processing technology is a combination of CNC processing technology and robot motion control technology. Among them, the processing path is usually measured in the operating space, and high-order continuous path planning technology is an important guarantee for realizing robot motion control. In order to solve the problem of frequent acceleration and deceleration of the robot caused by the non-high-order continuity of the processing path at the connection point, improve processing efficiency and improve accuracy, it is necessary to transfer and smooth the linear path of the hybrid robot. By inserting spline curves to replace the corners of the original path, the smoothed path is guaranteed to achieve curvature differential continuity (G3 continuity).

Patent CN111230864 discloses a "Hybrid Robot Parallel Robot Tool Path Planning" that divides the original path into multiple long straight line segments and multiple short straight line segments, performs transition smoothing on the breakpoints, and performs fitting smoothing on the straight line segment groups. Although this method focuses on path transition smoothing and uses a direct smoothing method to process the tool direction path, it does not provide a specific construction method for the control points of the smoothing curve, and does not establish a smoothing curve solution model under the smoothing error limit.

Patent CN112506139 discloses a method for smoothing local corners of short straight line segments of hybrid robots. It provides a real-time corner smoothing method based on asymmetric PH curves and third-order continuity. Although this method focuses on the smoothing of linear path transitions of hybrid robots, it does not involve the case where the tool tip position path contains arc segments. In addition, this method maps the tool axis direction path into a linear path, which makes it difficult to improve the tool axis motion performance near the connection point.

There are two types of problems that need to be solved for path smoothing of hybrid robots: (1) smoothing error control; (2) parameter synchronization of position and directional paths. In terms of directional error control, existing methods can be divided into two categories. One is to directly control the directional error using a numerical iteration method, which will greatly increase the amount of calculation; the other is to indirectly control the directional error by using the directional deviation at the midpoint of the spline curve as a predicted value. However, in certain circumstances, there will be a large deviation between the actual value and the predicted value, which will deteriorate the error control ability. Therefore, there is an urgent need for a directional path smoothing method that can not only improve the computational efficiency but also accurately predict and control the smoothing error.

There are two solutions for parameter synchronization. One is to achieve parameter synchronization by re-parameterizing the residual path. This method ignores the geometric characteristics of the position and direction paths, which will lead to large tool axis angular acceleration and angular jump near the path transition point. The second is to ensure parameter synchronization by establishing a constraint relationship between the smoothing length of the position path and the smoothing angle of the direction path. However, this method requires mapping the direction path into a series of intermediate paths composed of straight line segments, and will reduce the error control capability. Therefore, there is an urgent need for a parameter synchronization method that is suitable for the direction path smoothing of the unit sphere surface and can improve the smoothness of the tool axis motion.

Considering the multi-branch coupling characteristics of the hybrid robot, in order to avoid the inertial forced vibration of the robot, the motion trajectory is usually required to meet C3 continuity. In addition, in order to avoid the singularity caused by the indirect smoothing method, the direct smoothing method should be used to process the tool axis direction path on the unit sphere surface.

Summary of the invention

The present invention provides a hybrid robot C3 continuous five-axis path transition smoothing method to solve the technical problems existing in the known technology.

The technical solution adopted by the present invention to solve the technical problems existing in the known technology is: a hybrid robot C3 continuous five-axis path transition smoothing method, the method comprising the following steps: setting the end point trajectory of the tool axis unit vector as the tool axis direction path; setting the tool tip point position trajectory as the tool tip point position path; the tool tip point position path is defined in a Cartesian coordinate system; the tool axis direction path is defined on the surface of a unit sphere; both the tool tip point position path and the tool axis direction path are transition smoothed using spline curve segments, and the smoothed paths of both are composed of inserted spline curve segments and remaining path segments, wherein the inserted spline curve segments each contain an odd number of control The control point is set, and it is assumed that the deviation between the middle control point of the inserted spline curve and the original path is the largest; the necessary and sufficient conditions for the continuity of the curvature differential of the tool tip point position path and the tool axis direction path at the transition point are derived respectively, and then the relationship functions between the smoothing length of the tool tip point position path and the smoothing angle of the tool axis direction path and their respective smoothing errors are established respectively; based on the process requirements, the corresponding smoothing error limit values of the tool tip point position path and the tool axis direction path are determined, and combined with the constraints introduced by parameter synchronization, the smoothing length of the tool tip point position path and the smoothing angle of the tool axis direction path are determined, and then the smoothing curves of the tool tip point position path and the tool axis direction path are determined.

Furthermore, the method also includes the following steps: introducing a parameter synchronization curve, reconstructing the analytical expressions of the tool tip position path and the tool axis direction path; selecting a seventh-order B-spline with eight control points as the parameter synchronization curve, and setting the node vector to (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1) ^T ; wherein, the first control point of the parameter synchronization curve = 0 and the eighth control point = 1; obtaining the h-1th path C _h-1 (u), the hth path C _h (u), and the h+1th path C _h+1 (u) from the smoothed tool tip position path; obtaining the h-1th path Q _h-1 (u), the hth path Q _h (u), and the h+1th path Q _h+1 (u) from the smoothed tool axis direction path; then the necessary and sufficient conditions for C3 continuity at the connection point of the two paths are as follows:

C′ _h (u)| _u＝1 ＝C′ _h+1 (u)| _u＝0 ；C″ _h (u)| _u＝1 ＝C″ _h+1 (u)| _u＝0 ；C″ ′ _h (u)| _u＝1 =C″′ _h+1 (u)| _u＝0 ;

Q′ _h (u)| _u＝1 ＝Q′ _h+1 (u)| _u＝0 ；Q″ _h (u)| _u＝1 ＝Q″ _h+1 (u)| _u＝0 ；Q″ ′ _h (u)| _u＝1 ＝Q″′ _h+1 (u)| _u＝0 ;

Wherein, u represents the B-spline curve parameter; h represents the path segment number of the tool tip position path and the tool axis direction path after smoothing; “′”, “″” and “″′” represent the first-order, second-order and third-order derivatives of the curve with respect to parameter u, respectively; according to the necessary and sufficient conditions for the continuity of the tool axis angular velocity, the values of the second and seventh control points of the parameter synchronization curve are determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular acceleration, the values of the third and sixth control points are determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular jump, the values of the fourth and fifth control points are determined.

Furthermore, the method also includes the following steps: after completing the smoothing of the tool tip position path and the tool axis direction path, a tool tip velocity curve with continuous jumps is generated by correcting the jump curve in the S acceleration and deceleration motion; according to the tool tip velocity curve, parameter interpolation is performed in combination with the estimation-correction method to generate the interpolation point sequence required in the robot machining process.

Furthermore, the method also includes the following steps: determining the joint variables of each driving joint of the robot at each moment according to the interpolation point sequence and based on the kinematic model of the hybrid robot; controlling the movement of the hybrid robot according to the joint variables of each driving joint of the robot at each moment; and collecting the following errors of each joint during the robot movement in real time based on the PMAC motion control card, and evaluating the smoothness effectiveness of the tool tip position path and the tool axis direction path.

Furthermore, the inserted spline curve segment is a quintic B-spline.

Furthermore, the specific steps of establishing the relationship function between the smoothing length of the tool tip position path and its smoothing error include:

Step A1, assuming that the i-1th tool tip point Pi _-1 , the i-th tool tip point _Pi and the i+1th tool tip point _Pi+1 are three tool tip points connected in sequence in the original tool tip point position path; a quintic B-spline curve with seven control points is used as a spline curve segment inserted when the three tool tip points are transferred and smoothed; the expression of the inserted spline curve segment is as follows:

Where, _Ci (u) represents the spline curve inserted at point _Pi ; Bj _,i represents the control point of the spline curve _Ci (u), where i represents the number of the original tool position point, j=0,1,…,6 represents the number of the control point; u∈[0,1] represents the spline curve parameter; Nj _,5 (u) represents the fifth-order B-spline basis function;

Step A2, the necessary and sufficient conditions for establishing the curvature differential continuity of the tool tip position path at the connection point are as follows:

In the formula, m _e,i represents the unit direction vector from point _Pi to point _Pi+1 , where “e” is the sign bit; s represents the cumulative arc length of the tool tip position path;

Step A3, assuming that the path segment The length of satisfies ||B _0,i B _1,i ||＝c ₁ ||B _0,i B _3,i ||, where c ₁ ∈(0,1) is a preset constant; assuming that the path segment The length of satisfies ||B _1,i B _2,i ||＝c ₂ ||B _0,i B _3,i ||, where c ₂ ∈(0,1) is a preset constant; to avoid the curve from crossing itself, it should be ensured that 0＜c ₁ +c ₂ ＜1; based on the above assumptions, the functional relationship between each control point of the position spline curve _Ci (u) and the tool tip point _Pi is established;

Step A4, according to the fact that the arc length of the remaining path segment monotonically increases with the curve parameter, the lower limit of the length of the remaining path segment is determined; based on the functional relationship between the control points of the tool tip position path curve, the relationship function between the smoothing length of the tool tip position path and its smoothing error is established as follows:

||B _0,i B _3,i ||＝||B _3,i B _6,i ||;

In the formula,

ε _pos,max represents the smoothing error limit value of the set tool tip position path;

φ _i represents the angle between the unit vectors m _s,i and m _e,i , where m _s,i represents the unit vector from point P _i to point P _i-1 , and m _e,i represents the unit vector from point P _i to point P _i+1 ;

_Li represents the original path segment Length;

Li ₊₁ represents the original path segment Length;

Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _6,i-1 represents the last control point of the spline curve inserted at point Pi _-1 ;

Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _0,i+1 represents the first control point of the spline curve inserted at point Pi ₊₁ .

Furthermore, the specific steps of establishing the relationship function between the smoothing angle of the tool axis path and its smoothing error include:

Step B1, the original tool axis direction path is composed of a series of concentric arcs on the surface of a unit sphere, and the center of the unit sphere is set to W; the i-1th tool axis unit vector endpoint O _i-1 , the i-th tool axis unit vector endpoint O _i and the i+1th tool axis unit vector endpoint O _i+1 are set as three consecutive tool axis unit vector endpoints in the original tool axis direction path; based on the constant modulus of the tool axis unit vector being 1, a quintic B-spline curve including seven control points is used as the spline curve segment inserted when the tool axis direction path is converted and smoothed; _Qi (u) is set as the spline curve of the tool axis direction path inserted at point O _i : the expression of _Qi (u) is as follows:

Wherein, Φ _i (u) represents the initial spline curve constructed at point O _i according to the differential continuity condition of the path curvature in the tool axis direction; “||WΦ _i (u)||” represents the distance from point W to the point corresponding to parameter u on the curve Φ _i (u); D _k,i represents the control point of the spline curve _Qi (u), where i represents the number of the original tool position point, k = 0, 1, ..., 6 represents the number of the control point; u∈[0,1] represents the spline curve parameter;

Step B2, establish the necessary and sufficient conditions for the continuity of the curvature differential of the tool axis path at the connection point:

In the formula, s _o represents the cumulative arc length of the path in the tool axis direction; Represents an arc The unit tangent vector at D _6,i on the upper right corner, where “e” is the sign; d _6,i represents the vector from the center W of the unit sphere to the point D _6,i ;

Step B3, based on the necessary and sufficient conditions for the continuity of curvature differential and the derivative characteristics of the B-spline curve, establish the functional relationship between each control point of the curve _Qi (u) and the end point of the unit vector of the original tool axis; assume that the control points of the curve _Qi (u) satisfy the following relationship: With line segment The length ratio is 1:h, 2≤h≤8; according to the necessary and sufficient conditions for the differential continuity of the curvature of the path in the tool axis direction, determine the control point D _3,i of the smoothing curve _Qi (u); according to the necessary and sufficient conditions for the continuity of the curvature of the path in the tool axis direction and the center angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the transition segment, determine the control points D _2,i and D _4,i of the curve _Qi (u); according to the necessary and sufficient conditions for the tangential continuity of the path in the tool axis direction and the center angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the transition segment, determine the control points D _1,i and D _5,i of the curve _Qi (u);

Let {R _s,i } represent the arc segment The Frenet coordinate system is constructed at the upper point O _i. Represents an arc segment The unit tangent vector at point O _i is Represents an arc segment The principal normal unit vector at point O _i is Represents an arc segment The binormal unit vector at point O _i ;

Let {R _e,i } represent the arc segment The Frenet coordinate system is constructed at the upper point O _i. Represents an arc segment The unit tangent vector at point O _i is Represents an arc segment The principal normal unit vector at point O _i is Represents an arc segment The binormal unit vector at point O _i ;

Assume d _3,i = o _i ; then:

In the formula,

o _i represents the unit vector of the tool axis corresponding to the i-th tool position point;

Represents an arc The unit tangent vector at D _0,i , where "s" is the sign bit;

represents the angle ∠D _0,i WD _3,i , where “s” represents the sign bit;

represents the angle ∠D _3,i WD _6,i , where “e” represents the sign bit;

d _0,i represents the vector from point W to point D _0,i ;

d _1,i represents the vector from point W to point D _1,i ;

d _2,i represents the vector from point W to point D _2,i ;

d _3,i represents the vector from point W to point D _3,i ;

d _4,i represents the vector from point W to point D _4,i ;

d _5,i represents the vector from point W to point D _5,i ;

d _6,i represents the vector from point W to point D _6,i ;

Step B4, according to the functional relationship between each control point of the curve _Qi (u) and the end point of the original tool axis unit vector, derive the analytical expression of the tool axis direction path smoothing error and the smoothing angle; the tool axis direction path smoothing error is expressed as and θ _n,i, where θ _n,i represents the unit vector and By drawing the global variation trend diagram of the smoothing error in the tool axis direction, the smoothing error in the tool axis direction is obtained as a function of the smoothing angle. Monotonically increasing; Based on the smoothing error of the tool axis path and the constraints of parameter synchronization, a numerical method is used to solve the smoothing angle and

Further, step B4 includes the following sub-steps:

Step B4-1, determine the smoothing angle considering the following constraints Upper limit value:

1) To avoid the intersection of path curves at adjacent tool tip points, the smoothing angle should not exceed half of the original center angle;

2) according to the fact that the arc length of the remaining path segment increases monotonically with the curve parameter, determine the lower limit values of the central angles ∠D _{0, i} WD _3,i and ∠D _3,i WD _6,i of the remaining path segment;

Then we have:

In the formula, Indicates the smoothing angle The upper limit value of δ _i represents the arc segment The central angle of the circle; δ _i+1 represents the arc segment The central angle of a circle; Indicates the lower limit of the center angle ∠D _6,i-1 WD _0,i of the remaining path segment; Indicates the lower limit of the center angle ∠D _6,i WD _0,i+1 of the remaining path segment;

Step B4-2, according to the smoothing angle The upper limit value of the tool axis path is calculated to calculate the smoothing error of the tool axis path; determine whether the smoothing error of the tool axis path meets the following conditions:

(1-ε _t )ε _ori,max ≤ε _ori,i ≤ε _ori,max ;

Where, ε _t represents the control accuracy of the smoothing error of the tool axis path, ε _ori,i represents the smoothing error of the tool axis path at point O _i ; ε _ori,max is the predefined limit value of the smoothing error of the tool axis path;

If the path smoothing error in the tool axis direction meets the condition, then

If the path smoothing error in the tool axis direction does not meet the conditions, the smoothing angle is solved by the binary search method. According to the binary search strategy, the value of the smoothing angle is continuously updated until the constraint conditions are met.

Step B4-3, further completely determine the smoothing curve of the tool axis direction path based on the calculated smoothing angle.

Furthermore, the tool axis motion performance of the hybrid robot is improved by adjusting the smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path. The method for adjusting the smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path includes:

Step D1, based on the planned hybrid robot machining path, determine whether the path smoothing length of the tool tip position and the path smoothing angle of the tool axis direction meet the following conditions:

If the conditions are met, then

If the condition is not met, then

Step D2, based on the planned machining path, determine whether the path smoothing length of the tool tip position and the path smoothing angle of the tool axis direction meet the following conditions:

If the conditions are met, then

If the condition is not met, then

Step D3, after the smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path are adjusted, the tool tip position path smoothing curve _Ci (u) and the tool axis direction path smoothing curve _Qi (u) are recalculated according to the updated smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path;

Step D4, a global C3 continuous hybrid robot machining path after tool planning is formed by the C3 continuous tool tip point position path and the C3 continuous tool axis direction path.

The advantages and positive effects of the present invention are as follows: according to the constraint condition of curvature differential continuity, the present invention proposes an analytical construction method for control points of a smooth curve for transition between a straight line segment and an arc segment.

The present invention realizes direct smoothing of directional paths on the surface of a unit sphere without mapping the directional paths into linear paths, thus avoiding the singularity caused by indirect methods, ensuring accurate prediction and control of directional smoothing errors, improving the computational efficiency of the smoothing method, and further improving the motion performance of the hybrid robot.

The present invention realizes geometric smooth path parameter synchronization by re-parameterizing the remaining path segment, and can determine the control points of the synchronization curve and the length or angle margin of the remaining path segment without iterative calculation. In order to improve the motion performance of the tool axis, the present invention proposes a method for adjusting the smooth length or angle.

The smoothing method proposed in the present invention is not only applicable to five-axis linear paths, but also to tool tip position paths containing arc segments. Therefore, based on the present invention, a universal five-axis path smoothing method can be further obtained, and the relevant algorithm can be used as a pre-processing module independent of the robot numerical control system.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1: Flow chart of continuous transfer and smoothing of hybrid robot processing path C3.

Figure 2: Schematic diagram of tool tip position path transition and smoothing.

Figure 3: Schematic diagram of path smoothing in tool axis direction.

Figure 4: Direction error change trend graph.

Figure 5: Flowchart of calculating the directional path smoothing angle using the binary method.

Figure 6: S-shaped path C3 continuous transition smoothing result.

FIG. 7 : Processing results of an S-shaped test piece according to the present invention.

In Figure 1:

C3 continuity means that the third-order derivative of the parameter curve with respect to time is continuous;

G3 continuity means that the third-order derivative of the parametric curve with respect to the arc length of the curve is continuous, that is, the curvature differential is continuous;

CAD stands for Computer Aided Design, which means computer-aided design;

CAM stands for Computer Aided Manufacturing.

In Figure 2:

_Pi represents the tool tip position corresponding to the i-th tool position point;

P _i-1 represents the position of the tool tip corresponding to the i-1th tool position point;

Pi ₊₁ represents the position of the tool tip corresponding to the i+1th tool position point;

_Ci (u) represents the position smoothing curve inserted at point _Pi ;

B _6,i-1 represents the seventh control point of the position smoothing curve Ci _-1 (u), where Ci _-1 (u) represents the position smoothing curve inserted at the point _Pi-1 ;

B _0,i represents the first control point of the position smoothing curve C _i (u);

B _3,i represents the fourth control point of the position smoothing curve C _i (u);

B _6,i represents the seventh control point of the position smoothing curve C _i (u);

B _0,i+1 represents the first control point of the position smoothing curve Ci ₊₁ (u), where Ci ₊₁ (u) represents the position smoothing curve inserted at the point _Pi+1 ;

_Li represents the original location path segment Length;

Li ₊₁ represents the original position path segment Length;

l _r,i represents the remaining position path segment The length of , where the subscript "r" is the sign bit;

l _r,i+1 represents the remaining position path segment The length of , where the subscript "r" is the sign bit;

φ _i represents the angle between vectors m _s,i and m _e,i , where m _s,i represents the unit vector from P _i to P _i-1 , with the subscript "s" being the sign, and m _e,i represents the unit vector from P _i to P _i+1 , with the subscript "e" being the sign;

In Figure 3:

W represents the origin of the workpiece coordinate system;

O _i represents the end point of the unit vector of the tool axis corresponding to the i-th tool position point;

O _i-1 represents the end point of the tool axis unit vector corresponding to the i-1th tool position point;

O _i+1 represents the end point of the tool axis unit vector corresponding to the i+1th tool position point;

_Qi (u) represents the directional smoothing curve inserted at point _Oi ;

D _6,i-1 represents the seventh control point of the directional smoothing curve Qi _-1 (u), wherein Qi _-1 (u) represents the directional smoothing curve inserted at the point O _i-1 ;

D _0,i represents the first control point of the directional smoothing curve _Qi (u);

D _3,i represents the fourth control point of the directional smoothing curve _Qi (u);

D _6,i represents the seventh control point of the directional smoothing curve _Qi (u);

D _0,i+1 represents the first control point of the directional smoothing curve Qi ₊₁ (u), where Qi ₊₁ (u) represents the directional smoothing curve inserted at point O _i+1 ;

{R _s,i } represents the arc segment The Frenet coordinate system constructed at the upper point O _i , the subscript "s" is the sign, where represents the unit tangent vector, represents the principal normal vector, represents the binormal vector;

{R _e,i } represents the arc segment The Frenet coordinate system constructed at the upper point O _i , the subscript "e" is the sign, where represents the unit tangent vector, represents the principal normal vector, represents the binormal vector;

θ _n,i represents two binormal vectors and The angle of , where the subscript "n" is a sign;

δ _i represents the arc segment The central angle of a circle;

δ _i+1 represents an arc segment The central angle of a circle;

Represents an arc The unit tangent vector at D _0,i , where the subscript "s" is a flag;

Represents an arc The unit tangent vector at D _6,i , where the subscript "e" is a flag;

Figure 4

ε _ori,i represents the directional smoothing error at point O _i ;

In Figure 5:

Indicates the angle determined by considering constraints such as non-intersection of the directional smoothing curve itself and parameter synchronization The upper limit value of Represents the angle ∠D _3,i WD _6,i , where i represents the index value of the tool position point;

ε _t represents the control accuracy of directional smoothing error, where the subscript "t" is a flag, for example, ε _t = 0.1%;

b _s indicates the use of intermediate variables in the iterative algorithm, where the subscript "s" is a flag bit;

b _e indicates the use of intermediate variables in the iterative algorithm, where the subscript "e" is a flag;

DETAILED DESCRIPTION

In order to further understand the content, features and effects of the present invention, the following embodiments are listed and described in detail with reference to the accompanying drawings:

Please refer to Figures 1 to 7, a hybrid robot C3 continuous five-axis path transition smoothing method, the method includes the following steps: set the end point trajectory of the tool axis unit vector as the tool axis direction path; set the tool tip point position trajectory as the tool tip point position path; the tool tip point position path is defined in the Cartesian coordinate system; the tool axis direction path is defined on the unit sphere surface; both the tool tip point position path and the tool axis direction path are transition smoothed using spline curve segments, and the smoothed paths of both are composed of inserted spline curve segments and remaining path segments, wherein the inserted spline curve segments contain an odd number of control points, and it is assumed that the inserted spline curve segments have an odd number of control points. The deviation between the middle control point of the curve and the original path is the largest; the necessary and sufficient conditions for the continuity of the curvature differential of the tool tip point position path and the tool axis direction path at the transition point are derived respectively, and then the relationship functions between the smoothing length of the tool tip point position path and the smoothing angle of the tool axis direction path and their respective smoothing errors are established respectively; based on the process requirements, the corresponding smoothing error limit values of the tool tip point position path and the tool axis direction path are determined, and combined with the constraints introduced by parameter synchronization, the smoothing length of the tool tip point position path and the smoothing angle of the tool axis direction path are determined, and then the smoothing curves of the tool tip point position path and the tool axis direction path are determined.

The starting point of the tool axis unit vector is the origin of the workpiece coordinate system.

Smoothing length of tool tip location path: the length of the part of the tool tip location path that is replaced by the spline curve.

Smoothing angle of the tool axis path: the center angle of the part of the tool axis path that is replaced by the spline curve.

The smoothing error refers to the maximum deviation between the spline curve and the original path. For example, the position smoothing error refers to the Hausdorff distance between the spline curve and the original path.

Preferably, the method may further include the following steps: introducing a parameter synchronization curve, reconstructing the analytical expressions of the tool tip position path and the tool axis direction path; selecting a seventh-order B-spline with eight control points as the parameter synchronization curve, and setting the node vector to (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1) ^T ; wherein, the first control point of the parameter synchronization curve = 0 and the eighth control point = 1; obtaining the h-1th path C _h-1 (u), the hth path C _h (u), and the h+1th path C _h+1 (u) from the smoothed tool tip position path; obtaining the h-1th path Q _h-1 (u), the hth path Q _h (u), and the h+1th path Q _h+1 (u) from the smoothed tool axis direction path; then the necessary and sufficient conditions for the continuity of C3 at the connection point of the two paths are as follows: C′ _h (u)| _u＝1 ＝C′ _h+1 (u)| _u＝0 ；C″ _h (u)| _u＝1 ＝C″ _h+1 (u)| _u＝0 ；C″′ _h (u)| _u＝1 ＝C″′ _h+1 (u)| _u＝0 ;

Q′ _h (u)| _u＝1 ＝Q′ _h+1 (u)| _u＝0 ；Q″ _h (u)| _u＝1 ＝Q″ _h+1 (u)| _u＝0 ；Q″ ′ _h (u)| _u＝1 =Q″′ _h+1 (u)| _u＝0 ;

Wherein, u represents the B-spline curve parameter; h represents the path segment number of the tool tip position path and the tool axis direction path after smoothing; “′”, “″” and “″′” represent the first-order, second-order and third-order derivatives of the curve with respect to parameter u, respectively; according to the necessary and sufficient conditions for the continuity of the tool axis angular velocity, the values of the second and seventh control points of the parameter synchronization curve are determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular acceleration, the values of the third and sixth control points are determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular jump, the values of the fourth and fifth control points are determined.

The parameter synchronization curve refers to the curve used to achieve synchronization of tool tip position path and tool axis direction path parameters.

Preferably, the method may also include the following steps: after completing the smoothing of the tool tip position path and the tool axis direction path, generating a tool tip velocity curve with continuous jumps by correcting the jump curve in the S acceleration and deceleration motion; performing parameter interpolation based on the tool tip velocity curve in combination with the estimation-correction method to generate the interpolation point sequence required in the robot machining process.

Preferably, the method may also include the following steps: determining the joint variables of each driving joint of the robot at each moment according to the interpolation point sequence and based on the kinematic model of the hybrid robot; controlling the movement of the hybrid robot according to the joint variables of each driving joint of the robot at each moment; and collecting the following errors of each joint during the movement of the robot in real time based on the PMAC motion control card, and evaluating the smoothness effectiveness of the tool tip position path and the tool axis direction path.

Preferably, the inserted spline curve segment may be a quintic B-spline.

Preferably, the specific steps of establishing the relationship function between the smoothing length of the tool tip position path and its smoothing error may include:

In step A1, the i-1th tool tip point Pi _-1 , the i-th tool tip point _Pi and the i+1th tool tip point _Pi+1 are three tool tip points connected in sequence in the original tool tip point position path; a quintic B-spline curve with seven control points can be used as the spline curve segment inserted when the three tool tip points are smoothed; the expression of the inserted spline curve segment is as follows:

Where, _Ci (u) represents the spline curve inserted at point _Pi ; Bj _,i represents the control point of the spline curve _Ci (u), where i represents the number of the original tool position point, j=0,1,…,6 represents the number of the control point; u∈[0,1] represents the spline curve parameter; Nj _,5 (u) represents the fifth-order B-spline basis function;

Step A2, the necessary and sufficient conditions for the continuity of the curvature differential of the tool tip position path at the connection point can be established as follows:

In the formula, m _e,i represents the unit direction vector from point _Pi to point _Pi+1 , where “e” is the sign bit; s represents the cumulative arc length of the tool tip position path;

Step A3, it can be assumed that the path segment The length of satisfies ||B _0,i B _1,i ||＝c ₁ ||B _0,i B _3,i ||, where c ₁ ∈(0,1) is a preset constant; assuming that the path segment The length of satisfies ||B _1,i B _2,i ||＝c ₂ ||B _0,i B _3,i ||, where c ₂ ∈(0,1) is a preset constant; to avoid the curve from crossing itself, it should be ensured that 0＜c ₁ +c ₂ ＜1; based on the above assumptions, the functional relationship between each control point of the position spline curve _Ci (u) and the tool tip point _Pi is established;

In step A4, the lower limit of the length of the remaining path segment can be determined according to the fact that the arc length of the remaining path segment increases monotonically with the curve parameter; based on the functional relationship between the control points of the tool tip position path curve, the relationship function between the smoothing length of the tool tip position path and its smoothing error is established as follows:

||B _0,i B _3,i ||＝||B _3,i B _6,i ||;

In the formula,

ε _pos,max represents the smoothing error limit value of the set tool tip position path;

φ _i represents the angle between the unit vectors m _s,i and m _e,i , where m _s,i represents the unit vector from point P _i to point P _i-1 , and m _e,i represents the unit vector from point P _i to point P _i+1 ;

_Li represents the original path segment Length;

Li ₊₁ represents the original path segment Length;

Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _6,i-1 represents the last control point of the spline curve inserted at point Pi _-1 ;

Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _0,i+1 represents the first control point of the spline curve inserted at point Pi ₊₁ .

Preferably, the specific steps of establishing the relationship function between the smoothing angle of the tool axis path and its smoothing error may include:

Step B1, the original tool axis direction path is composed of a series of concentric arcs on the surface of the unit sphere. The tool axis direction path is a three-dimensional path formed by the end point of the tool axis unit vector on the surface of the unit sphere during the hybrid robot machining process.

The center of the unit sphere can be set as W; the i-1th tool axis unit vector endpoint O _i-1 , the i-th tool axis unit vector endpoint O _i and the i+1th tool axis unit vector endpoint O _i+1 can be set as three consecutive tool axis unit vector endpoints in the original tool axis direction path; based on the constant modulus of the tool axis unit vector being 1, a quintic B-spline curve including seven control points can be used as the spline curve segment inserted when the tool axis direction path is converted and smoothed; let _Qi (u) be the spline curve of the tool axis direction path inserted at point O _i : the expression of _Qi (u) can be as follows:

Wherein, Φ _i (u) represents the initial spline curve constructed at point O _i according to the differential continuity condition of the path curvature in the tool axis direction; “||WΦ _i (u)||” represents the distance from point W to the point corresponding to parameter u on the curve Φ _i (u); D _k,i represents the control point of the spline curve _Qi (u), where i represents the number of the original tool position point, k = 0, 1, ..., 6 represents the number of the control point; u∈[0,1] represents the spline curve parameter;

Step B2, the following necessary and sufficient conditions for the continuity of the curvature differential of the tool axis path at the connection point can be established:

In the formula, s _o represents the cumulative arc length of the path in the tool axis direction; Represents an arc The unit tangent vector at D _6,i on the upper right corner, where “e” is the sign; d _6,i represents the vector from the center W of the unit sphere to the point D _6,i ;

Step B3, according to the necessary and sufficient conditions for the continuity of curvature differential and the derivative characteristics of the B-spline curve, the functional relationship between each control point of the curve _Qi (u) and the end point of the original tool axis unit vector can be established; it can be assumed that the control points of the curve _Qi (u) satisfy the following relationship: With line segment The length ratio is 1:h, 2≤h≤8; the control point D _3,i of the smoothing curve _Qi (u) can be determined according to the necessary and sufficient conditions for the differential continuity of the curvature of the path in the tool axis direction; the control points D 2,i and D 4,i of the curve _Qi (u) can be determined according to the necessary and sufficient conditions for the continuity of the curvature of the path in the tool axis direction and the center angles ∠D _0,i WD _3,i and ∠D 3 _,i WD _6,i of the transition segment; the control points D 1 _{,i and} D _{5 ,i} of the curve _Qi (u) can be determined according to the necessary and sufficient conditions for the tangential continuity of the path in the tool axis direction and the center angles ∠D _0,i WD ₃ ,i and ∠D _3,i WD _6,i of the transition segment;

{R _s,i } can be set to represent the arc segment The Frenet coordinate system is constructed at the upper point O _i. Represents an arc segment The unit tangent vector at point O _i is Represents an arc segment The principal normal unit vector at point O _i is Represents an arc segment The binormal unit vector at point O _i ;

{R _e,i } can be set to represent the arc segment The Frenet coordinate system is constructed at the upper point O _i. Represents an arc segment The unit tangent vector at point O _i is Represents an arc segment The principal normal unit vector at point O _i is Represents an arc segment The binormal unit vector at point O _i ;

We can assume d _3,i = o _i ; then we have:

In the formula,

o _i represents the unit vector of the tool axis corresponding to the i-th tool position point;

Represents an arc The unit tangent vector at D _0,i , where "s" is the sign bit;

represents the angle ∠D _0,i WD _3,i , where “s” represents the sign bit;

represents the angle ∠D _3,i WD _6,i , where “e” represents the sign bit;

d _0,i represents the vector from point W to point D _0,i ;

d _1,i represents the vector from point W to point D _1,i ;

d _2,i represents the vector from point W to point D _2,i ;

d _3,i represents the vector from point W to point D _3,i ;

d _4,i represents the vector from point W to point D _4,i ;

d _5,i represents the vector from point W to point D _5,i ;

d _6,i represents the vector from point W to point D _6,i ;

Step B4, according to the functional relationship between each control point of the curve _Qi (u) and the end point of the original tool axis unit vector, derive the analytical expression of the tool axis direction path smoothing error and the smoothing angle; the tool axis direction path smoothing error is expressed as and θ _n,i, where θ _n,i represents the unit vector and By drawing the global variation trend diagram of the smoothing error in the tool axis direction, the smoothing error in the tool axis direction is obtained as a function of the smoothing angle. Monotonically increasing; Based on the smoothing error of the tool axis path and the constraints of parameter synchronization, a numerical method is used to solve the smoothing angle and

The Frenet coordinate system refers to a coordinate system consisting of three mutually orthogonal unit vectors defined at a point on a space curve.

Preferably, step B4 may include the following sub-steps:

Step B4-1, the following constraints can be considered to determine the smoothing angle Upper limit value:

1) To avoid the intersection of path curves at adjacent tool tip points, the smoothing angle should not exceed half of the original center angle;

2) According to the fact that the arc length of the remaining path segment increases monotonically with the curve parameters, determine the center angle ∠D _{0, i} WD _{3, i} of the remaining path segment

and the lower limit of ∠D _3,i WD _6,i ;

Then we have:

In the formula, Indicates the smoothing angle The upper limit value of δ _i represents the arc segment The central angle of the circle; δ _i+1 represents the arc segment The central angle of a circle; Indicates the lower limit of the center angle ∠D _6,i-1 WD _0,i of the remaining path segment; Indicates the lower limit of the center angle ∠D _6,i WD _0,i+1 of the remaining path segment;

Step B4-2, according to the smoothing angle The upper limit value of the tool axis path is calculated to calculate the smoothing error of the tool axis path; determine whether the smoothing error of the tool axis path meets the following conditions:

(1-ε _t )ε _ori,max ≤ε _ori,i ≤ε _ori,max ;

Where, ε _t represents the control accuracy of the smoothing error of the tool axis path, ε _ori,i represents the smoothing error of the tool axis path at point O _i ; ε _ori,max is the predefined limit value of the smoothing error of the tool axis path;

If the path smoothing error in the tool axis direction meets the conditions, then

If the path smoothing error in the tool axis direction does not meet the conditions, the smoothing angle can be solved by the binary method. According to the binary method solution strategy, the value of the smoothing angle is continuously updated until the constraint conditions are met.

In step B4-3, the smoothing curve of the tool axis path can be further completely determined based on the calculated smoothing angle.

Preferably, the motion performance of the tool axis of the hybrid robot can be improved by adjusting the smoothing length of the position segment and the smoothing angle of the direction segment. The method of adjusting the smoothing length of the position segment and the smoothing angle of the direction segment may include:

Step D1, based on the planned hybrid robot machining path, determines whether the path smoothing length of the tool tip position and the path smoothing angle of the tool axis direction meet the following conditions:

If the conditions are met, then

If the conditions are not met,

Step D2, based on the planned machining path, determines whether the path smoothing length of the tool tip position and the path smoothing angle of the tool axis direction meet the following conditions:

If the conditions are met, then

If the conditions are not met,

Step D3, after the smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path are adjusted, the tool tip position path smoothing curve _Ci (u) and the tool axis direction path smoothing curve _Qi (u) can be recalculated according to the updated tool tip position path smoothing length and tool axis direction path smoothing angle;

In step D4, a global C3 continuous hybrid robot machining path after tool planning may be formed by the C3 continuous tool tip point position path and the C3 continuous tool axis direction path.

The working process and principle of the present invention are further described below with a preferred embodiment of the present invention:

Step 1, obtain the original posture information of the tool from the tool location file, including the tool tip position information and the tool axis direction information; determine the original processing path according to the original posture of the tool; the tool tip position is defined in the Cartesian coordinate system, given the position vectors of two adjacent tool tip points, the intermediate position vector is generated by linear and circular interpolation respectively; the tool axis direction is defined on the surface of the unit sphere, given the unit vectors of two adjacent tool axes, the intermediate direction vector is generated by spherical linear interpolation;

Step 2, the original linear tool tip point position path generated by linear interpolation only achieves position continuity or tangential continuity; by inserting parametric curves such as fifth-order B-spline curves at the corners of the original tool tip point position path, the curvature differential continuity of the tool tip point position path, that is, G3 continuity, is achieved; by limiting the smoothing error of the tool tip point position path, it is ensured that the smoothed tool tip point position path meets the actual processing requirements; by constructing the functional relationship between the control points of the tool tip point position path smoothing curve, under the restriction conditions of tool tip point position path smoothing error and parameter synchronization, the efficient solution of the tool tip point position path smoothing curve is achieved.

Based on the necessary and sufficient conditions for curvature continuity and the derivative characteristics of the fifth-order B-spline curve, the functional relationship between the control points of the tool tip position path curve is established, which specifically includes the following steps:

Step 2.1, assuming that the i-1th tool tip point P _i-1 , the i-th tool tip point P _i and the i+1th tool tip point P _i+1 are three tool tip points connected in sequence in the original tool tip point position path; a quintic B-spline curve including seven control points is used as a spline curve segment inserted when the three tool tip points are transferred and smoothed;

Where, _Ci (u) represents the spline curve inserted at point _Pi ; Bj _,i represents the control point of the spline curve _Ci (u), where i represents the number of the original tool position point, j=0,1,…,6 represents the number of the control point; u∈[0,1] represents the spline curve parameter; Nj _,5 (u) represents the fifth-order B-spline basis function;

Step 2.2, based on the i-1th tool tip point _Pi-1 , the i-th tool tip point _Pi and the i+1th tool tip point _Pi+1 , derive the necessary and sufficient conditions for the continuity of the curvature differential of the remaining path segment and the spline curve segment at the connection point. To ensure the continuity of the tool tip position path, the control point _B0,i of the tool tip position path smoothing curve should be located on the straight line segment To ensure the continuity of the tool tip position path, the smoothing curve control point B _6,i of the tool tip position path should be located on the straight line segment Furthermore, the remaining path segment of the tool tip position path It can be described by control point B _6,i and control point B _0,i+1 , where B _0,i+1 represents the control point of the tool tip position path smoothing curve inserted at point Pi ₊₁ . It can be described by control point B _6,i-1 and control point B _0,i , where B _6,i-1 represents the control point of the tool tip position path smoothing curve inserted at point P _i-1 .

The necessary and sufficient conditions for establishing the curvature differential continuity of the tool tip position path at the connection point are as follows:

Where, m _e,i represents the unit direction vector from point _Pi to point _Pi+1 ; s represents the cumulative arc length of the curve;

Step 2.3, assuming the path segment The length of satisfies ||B _0,i B _1,i ||＝c ₁ ||B _0,i B _3,i ||, where c ₁ ∈(0,1) is a preset constant; assuming that the path segment The length of satisfies ||B _1,i B _2,i ||＝c ₂ ||B _0,i B _3,i ||, where c ₂ ∈(0,1) is a preset constant. To avoid the curve from crossing itself, it should be ensured that 0＜c ₁ +c ₂ ＜1;

According to the above necessary and sufficient conditions for curvature continuity and the derivative characteristics of the fifth-order B-spline curve, the functional relationship between the control points of the smoothing curve of the tool tip position path is established. Specifically, according to the necessary and sufficient conditions for curvature differential continuity, the control point B _3,i of the smoothing curve C _i (u) can be determined; according to the necessary and sufficient conditions for curvature continuity and the smoothing lengths ||B _0,i B _3,i || and ||B _3,i B _6,i ||, the control points B _2,i and B _4,i of the smoothing curve C _i (u) can be determined; according to the necessary and sufficient conditions for tangential continuity and the smoothing lengths ||B _0,i B _3,i || and ||B _3,i B _6,i ||, the control points B _1,i and B _5,i of the smoothing curve C _i (u) can be determined;

Step 3, based on the functional relationship between the control points of the tool tip position path smoothing curve, considering the tool tip position path smoothing error and parameter synchronization constraints, determine the smoothing lengths ||B _0,i B _3,i || and ||B _3,i B _6,i ||. To ensure that the tool tip position path smoothing error is located at parameter u = 0.5, it can be assumed that ||B _0,i B _3,i || = ||B _3,i B _6,i ||, and then the tool tip position path smoothing error expression can be derived based on the Hausdorff distance. The tool tip position path smoothing error can be expressed analytically by the smoothing length. Furthermore, the value of the smoothing length can be determined from the following three aspects: (1) To avoid the intersection of smoothing curves at adjacent positions, the smoothing length should not exceed half of the original path length; (2) the path smoothing error at the tool tip position should be less than the predefined error limit; (3) the remaining path segment lengths ||B _6,i-1 B _0,i || and ||B _6,i B _0,i+1 || should meet the subsequent parameter synchronization requirements.

Based on the functional relationship between the control points of the tool tip position path curve, the tool tip position path smoothing error and parameter synchronization constraints, the following smoothing length is determined:

||B _0,i B _3,i ||＝||B _3,i B _6,i ||;

In the formula,

ε _pos,max represents the smoothing error limit value of the set tool tip position path;

φ _i represents the angle between the unit vectors m _s,i and m _e,i , where m _s,i represents the unit vector from point P _i to point P _i-1 , and m _e,i represents the unit vector from point P _i to point P _i+1 ;

_Li represents the original path segment Length;

Li ₊₁ represents the original path segment Length;

Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _6,i-1 represents the last control point of the spline curve inserted at point Pi _-1 ;

Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _0,i+1 represents the first control point of the spline curve inserted at point Pi ₊₁ ;

Step 4: The original tool axis direction path is composed of a series of concentric arcs on the surface of the unit sphere. The original direction path generated by arc interpolation only achieves position continuity or tangential continuity. The original tool axis direction path is smoothed on the surface of the unit sphere to achieve differential continuity of the curvature of the tool axis direction path. The necessary and sufficient conditions for differential continuity of the curvature of the direction path are derived to analytically construct the mathematical relationship between each control point of the direction smoothing curve and the end point of the unit vector of the original tool axis.

Assume that the center of the unit sphere is W; Assume that the i-1th tool axis unit vector endpoint O _i-1 , the i-th tool axis unit vector endpoint O _i and the i+1th tool axis unit vector endpoint O _i+1 are three successively connected tool axis unit vector endpoints in the original tool axis direction path; Based on the necessary and sufficient conditions for the differential continuity of the curvature of the tool axis direction path, the functional relationship between each control point of the inserted spline curve of the tool axis direction path and the original tool axis unit vector endpoint is analytically constructed; Specifically, the following steps are included:

Step 4.1, based on the i-1th tool axis unit vector endpoint, the i-th tool axis unit vector endpoint, and the i+1th tool axis unit vector endpoint, derive the necessary and sufficient conditions for the continuity of the directional path curvature differential. To ensure the continuity of the tool axis directional path, the control point D _0,i of the tool axis directional path smoothing curve should be located on the arc segment To ensure the continuity of the tool axis path, the control point D _6,i of the tool axis path smoothing curve should be located on the arc segment Furthermore, the remaining path segments in the tool axis direction It can be described by the control point D _6,i and the control point D _0,i+1 , where D _0,i+1 represents the control point of the smoothing curve inserted at point O _i+1 . It can be described by control point D _6,i and control point D _0,i+1 , where D _0,i+1 represents the control point of the smoothing curve inserted at point O _i+1 .

Based on the constant modulus of the unit vector in the tool axis direction being 1, a standardized quintic B-spline curve _Qi (u) including seven control points is used as the transition smoothing curve;

Wherein, Φ _i (u) represents the initial spline curve constructed at point O _i according to the differential continuity condition of the path curvature in the tool axis direction; “||WΦ _i (u)||” represents the distance from point W to the point corresponding to parameter u on the curve Φ _i (u); D _k,i represents the control point of the spline curve _Qi (u), where i represents the number of the original tool position point, k = 0, 1, ..., 6 represents the number of the control point; u∈[0,1] represents the spline curve parameter;

Step 4.2, establish the necessary and sufficient conditions for the continuity of the curvature differential of the tool axis path at the connection point:

In the formula, s _o represents the cumulative arc length of the path in the tool axis direction; Represents an arc The unit tangent vector at D _6,i on the sphere; d _6,i represents the vector from the center of the unit sphere to the point D _6,i ;

Step 4.2, according to the necessary and sufficient conditions for the continuity of curvature differential and the derivative characteristics of the B-spline curve, establish the function of each control point of the curve _Qi (u) and the end point of the unit vector of the original tool axis; assume that the control points of the curve _Qi (u) satisfy the following relationship: With line segment The length ratio is 1:5; according to the necessary and sufficient conditions for curvature differential continuity, the control point D _3,i of the curve _Qi (u) is determined; according to the necessary and sufficient conditions for curvature continuity and the center angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the transition segment, the control points D _2,i and D _4,i of the curve _Qi (u) are determined; according to the necessary and sufficient conditions for tangential continuity and the center angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the transition segment, the control points D _1,i and D _5,i of the directionally smooth curve _Qi (u) are determined; let d _3,i =o _i ; then:

In the formula,

o _i represents the unit vector of the tool axis direction corresponding to the i-th tool position point;

Represents an arc The unit tangent vector at D _0,i , where "s" is the sign bit;

represents the angle ∠D _0,i WD _3,i , where “s” represents the sign bit;

represents the angle ∠D _3,i WD _6,i , where “e” represents the sign bit;

d _0,i represents the vector from point W to point D _0,i ;

d _1,i represents the vector from point W to point D _1,i ;

d _2,i represents the vector from point W to point D _2,i ;

d _3,i represents the vector from point W to point D _3,i ;

d _4,i represents the vector from point W to point D _4,i ;

d _5,i represents the vector from point W to point D _5,i ;

d _6,i represents the vector from point W to point D _6,i ;

{R _s,i } represents the arc segment The Frenet coordinate system constructed at the upper point O _i , where Represents an arc segment The unit tangent vector at point O _i , Represents an arc segment The principal normal vector at point O _i is, Represents an arc segment The binormal vector at point O _i ;

{R _e,i } represents the arc segment The Frenet coordinate system constructed at the upper point O _i , where Represents an arc segment The unit tangent vector at point O _i , Represents an arc segment The principal normal vector at point O _i is, Represents an arc segment The binormal vector at point O _i ;

Step 5: By limiting the smoothing error of the tool axis direction path, ensure that the smoothed direction path meets the processing requirements; according to the mathematical relationship between each control point of the tool axis direction path smoothing curve and the end point of the direction vector, under the constraints of smoothing error and parameter synchronization, realize the efficient solution of the direction smoothing curve;

Step 5.1, according to the function of each control point of the curve _Qi (u) and the end point of the original tool axis unit vector, derive the analytical expression of the tool axis path smoothing error and the smoothing angle; suppose the parameter u corresponding to the maximum tool axis path smoothing error is u＝0.5, then Then the analytical expression of the path smoothing error in the tool axis direction is obtained; the path smoothing error in the tool axis direction is expressed as and θ _n,i, where θ _n,i represents the unit vector and By drawing the global variation trend diagram of the smoothing error in the tool axis direction, it is found that the smoothing error in the tool axis direction changes with the smoothing angle. Monotonically increasing; thus achieving the solution of the smoothing angle under the smoothing error limit;

Step 5.2: Based on the smoothing error of the tool axis path and the constraints of parameter synchronization, a numerical method is used to quickly solve the smoothing angle. and

(1) Determine the smoothing angle The upper limit value of the smoothing angle is used as the basis for solving the smoothing angle under error constraints. To determine the upper limit value of the smoothing angle, the following constraints are considered: 1) To avoid the intersection of the path curves of adjacent tool tip points, the smoothing angle should not exceed half of the original center angle; 2) The center angles of the remaining path segments ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the tool axis path should meet the subsequent parameter synchronization requirements;

In the formula, Indicates the smoothing angle The upper limit value of δ _i represents the arc segment The central angle of the circle; δ _i+1 represents the arc segment The central angle of a circle; It represents the lower limit of the center angle ∠D _6,i-1 WD _0,i of the remaining direction segment; Indicates the lower limit of the center angle ∠D _6,i WD _0,i+1 of the remaining direction segment;

(2) According to the upper limit of the smoothing angle, the smoothing angle solution under error limit is realized; Calculate the directional smoothing error of the tool axis path; determine whether the directional smoothing error of the tool axis path meets the following conditions:

(1-ε _t )ε _ori,max ≤ε _ori,i ≤ε _ori,max ;

Wherein, ε _t represents the control accuracy of the smoothing error of the tool axis direction path, for example, ε _t = 0.1%; ε _ori,i represents the directional smoothing error at the end point O _i of the directional vector; ε _ori,max is the predefined directional smoothing error limit value.

If the directional smoothing error satisfies the condition, then let

If the directional smoothing error does not meet the conditions, the bisection method is used to solve the smoothing angle. According to the bisection solution strategy, the value of the smoothing length is continuously updated until the constraint conditions are met.

According to the smoothing angle, the directional smoothing curve is further fully determined.

Step 6: To improve the motion performance of the tool axis of the hybrid robot, the smooth length of the tool tip position path and the smooth angle of the tool axis direction path need to satisfy a specific mathematical relationship. To achieve a specific mathematical relationship, the smooth length of the position segment and the smooth angle of the direction segment need to be adjusted. Specifically, it includes:

(1) According to the planned hybrid robot machining path, determine whether the path smoothing length of the tool tip position and the path smoothing angle in the tool axis direction meet the following conditions:

If the conditions are met, then

If the condition is not met, then

(2) Based on the planned machining path, determine whether the path smoothing length at the tool tip position and the path smoothing angle in the tool axis direction meet the following conditions:

If the conditions are met, then

If the condition is not met, then

After the smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path are adjusted, the tool tip position path smoothing curve _Ci (u) and the tool axis direction path smoothing curve _Qi (u) are recalculated according to the updated tool tip position path smoothing length and tool axis direction path smoothing angle. The G3 continuous tool tip position path and the G3 continuous tool axis direction path constitute the global G3 continuous hybrid robot machining path after tool planning.

Step 7: For the inserted smoothing curve, it is assumed that the tool tip position path and the tool axis direction path share the same parameter; for the remaining path segment, if the tool tip position path and the tool axis direction path share the same parameter, the third-order derivative of the planned tool axis direction path with respect to time is not continuous; in order to achieve the C3 continuity of the planned hybrid robot machining path, that is, the continuity of the third-order derivative of the tool axis direction path with respect to time, the remaining path segment re-parameterization strategy is adopted. The remaining path segment re-parameterization strategy refers to reconstructing the analytical expressions of the remaining path segment of the tool tip position path and the remaining path segment of the tool axis direction path by introducing a parameter synchronization curve.

A seventh-order B-spline with eight control points is selected as the parameter synchronization curve, and the node vector is set to (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1) ^T. In order to ensure the continuity of the smooth curve segment and the remaining path segment at the connection point after parameter synchronization, the control points should satisfy the first control point = 0 and the eighth control point = 1.

Step 7.1 Assume that the smoothed paths of the tool tip position path and the tool axis direction path are composed of the inserted B-spline smoothing curve and the remaining path alternately. Obtain the h-1th path segment C _h-1 (u), the hth path segment C _h (u), and the h+1th path segment C _h+1 (u) from the smoothed tool tip position path; obtain the h-1th path segment Q _h-1 (u), the hth path segment Q _h (u), and the h+1th path segment Q _h+1 (u) from the smoothed tool axis direction path; according to the C3 continuity requirements of the planned hybrid robot processing path, the necessary and sufficient conditions for C3 continuity at the connection point can be further derived as follows:

C′ _h (u)| _u＝1 ＝C′ _h+1 (u)| _u＝0 , C″ _h (u)| _u＝1 ＝C″ _h+1 (u)| _u＝0 , C″ ′ _h (u)| _u＝1 ＝C″′ _h+1 (u)| _u＝0

Q′ _h (u)| _u＝1 ＝Q′ _h+1 (u)| _u＝0 ，Q″ _h (u)| _u＝1 ＝Q″ _h+1 (u)| _u＝0 ，Q″ ′ _h (u)| _u＝1 ＝Q″′ _h+1 (u)| _u＝0

Where u represents the curve parameter; h represents the path segment number in the tool tip position path and the tool axis direction path after smoothing; in order to achieve the synchronization of the tool tip position path and the tool axis direction path parameters, the division and numbering of their path segments are consistent; “′”, “″” and “″′” respectively represent the first-order, second-order and third-order derivatives of the curve with respect to the parameter u.

Step 7.2 For the remaining path segment of the tool tip position path, determine the control points of the synchronization curve v(u) according to the necessary and sufficient conditions for C3 continuity. Note that the solution process does not require the use of an iterative solution algorithm. According to the necessary and sufficient conditions for the continuity of the tool axis angular velocity, the values of the second control point and the seventh control point can be determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular acceleration, the values of the third control point and the sixth control point can be determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular jump, the values of the fourth control point and the fifth control point can be determined, see the following formula:

Where {v ₁ ,v ₂ ,v ₃ ,v ₄ ,v ₅ ,v ₆ } represents the values of the second to seventh control points of the parameter synchronization curve v(u). _{v 1} represents the value of the second control point of the parameter synchronization curve v(u); v ₂ represents the value of the third control point of the parameter synchronization curve v(u); and so on.

Furthermore, in order to ensure that the arc length of the re-parameterized curve increases monotonically with the curve parameter, the first-order derivative of the synchronous curve v(u) with respect to the curve parameter u should be always greater than 0. Then, the length of the remaining path segment of the tool tip position path can be derived. The lower limit of is as follows:

In the formula, Indicates the remaining path segment length of the tool tip position path The lower limit value of the path segment, the subscript "r" is the flag bit; Li ₊₁ represents the original path segment Length;

The remaining path segment length according to the tool tip position path The lower limit value of , combined with step 2 and step 3, can further completely determine the smoothing curve of the tool tip position path inserted at point _Pi .

Step 7.3 For the remaining path segments in the tool axis direction, determine the control points of the synchronization curve w(u) according to the necessary and sufficient conditions for C3 continuity. Note that the solution process does not require the use of an iterative solution algorithm. According to the necessary and sufficient conditions for the continuity of the tool axis angular velocity, the values of the second control point and the seventh control point can be determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular acceleration, the values of the third control point and the sixth control point can be determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular jump, the values of the fourth control point and the fifth control point can be determined, see the following formula:

Represents the angle ∠D _3,i WD _6,i ;

represents the angle ∠D _0,i+1 WO _i+1 , where D _0,i+1 represents the first control point of the directional smoothing curve inserted at point O _i+1 ;

Indicates the angle ∠D _6,i WD _0,i+1 ;

{w ₁ ,w ₂ ,w ₃ ,w ₄ ,w ₅ ,w ₆ } represents the values of the second control point to the seventh control point of the parameter synchronization curve w(u). _{w 1} represents the value of the second control point of the parameter synchronization curve w(u); w ₂ represents the value of the third control point of the parameter synchronization curve w(u); and so on.

To ensure that the arc length of the re-parameterized curve increases monotonically with the curve parameter, the first-order derivative of the synchronous curve with respect to the curve parameter w(u) should always be greater than 0. Then, the lower limit of the center angle ∠D _6,i WD _0,i+1 of the residual direction path can be derived;

In the formula, Indicates the lower limit of the center angle ∠D _6,i WD _0,i+1 of the remaining path segment in the tool axis direction. The subscript "r" is a flag; δ _i+1 indicates an arc segment The central angle of a circle;

According to the lower limit value of the center angle ∠D _6,i WD _0,i+1 of the remaining path segment in the tool axis direction, the tool axis direction path smoothing curve inserted at point O _i can be further fully determined in combination with step 4 and step 5.

Step 8: Based on the planned C3 continuous hybrid robot processing path, a tool tip velocity curve with continuous jumps is planned by correcting the jump curve in the S acceleration and deceleration motion law. According to the tool tip velocity curve, parameter interpolation is carried out in combination with the estimation-correction method to generate the interpolation point sequence required in the robot processing process.

Step 9: According to the interpolation point sequence and the kinematic model of the hybrid robot, determine the joint variables of each driving joint of the robot at each moment; control the movement of the hybrid robot according to the joint variables of each driving joint of the robot at each moment; based on the PMAC motion control card, collect the following errors of each joint during the robot movement in real time to verify the effectiveness of the smoothness of the tool tip position path and the tool axis direction path.

The above embodiments of the tool tip point position path are only used to illustrate the technical ideas and features of the present invention, and their purpose is to enable technicians in this field to understand the contents of the present invention and implement them accordingly. The patent scope of the present invention cannot be limited only by this embodiment, that is, any equivalent changes or modifications made to the spirit disclosed by the present invention still fall within the patent scope of the present invention.

Claims (9)

1. A hybrid robot C3 continuous five-axis path transition smoothing method, characterized in that the method comprises the following steps: setting the end point trajectory of the tool axis unit vector as the tool axis direction path; setting the tool tip point position trajectory as the tool tip point position path; the tool tip point position path is defined in a Cartesian coordinate system; the tool axis direction path is defined on a unit sphere surface; both the tool tip point position path and the tool axis direction path are transition smoothed using spline curve segments, and both smoothed paths are composed of inserted spline curve segments and remaining path segments, wherein the inserted spline curve segments contain an odd number of control points, and it is assumed that the inserted spline curve segments have an odd number of control points. The deviation between the middle control point of the curve and the original path is the largest; the necessary and sufficient conditions for the continuity of the curvature differential of the tool tip point position path and the tool axis direction path at the transition point are derived respectively, and then the relationship functions between the smoothing length of the tool tip point position path and the smoothing angle of the tool axis direction path and their respective smoothing errors are established respectively; based on the process requirements, the corresponding smoothing error limit values of the tool tip point position path and the tool axis direction path are determined, and combined with the constraints introduced by parameter synchronization, the smoothing length of the tool tip point position path and the smoothing angle of the tool axis direction path are determined, and then the smoothing curves of the tool tip point position path and the tool axis direction path are determined. 2. The hybrid robot C3 continuous five-axis path transition and smoothing method according to claim 1 is characterized in that the method further comprises the following steps: introducing a parameter synchronization curve to reconstruct the analytical expressions of the tool tip point position path and the tool axis direction path; selecting a seventh-order B-spline with eight control points as the parameter synchronization curve, and setting the node vector to (0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1) ^T ; wherein, the first control point of the parameter synchronization curve = 0 and the eighth control point = 1; obtaining the h-1th path C _h-1 (u), the hth path C _h (u), and the h+1th path C _h+1 (u) from the tool tip point position path after smoothing; obtaining the h-1th path Q _h-1 (u), the hth path Q _h (u), and the h+1th path Q _h+1 (u) from the tool axis direction path after smoothing; then the necessary and sufficient conditions for C3 continuity at the connection point of the two paths are as follows: C′ _h (u)| _u＝1 ＝C′ _h+1 (u)| _u＝0 ；C″ _h (u)| _u＝1 ＝C″ _h+1 (u)| _u＝0 ；C″ ′ _h (u)| _u＝1 =C″′ _h+1 (u)| _u＝0 ; Q′ _h (u)| _u＝1 ＝Q′ _h+1 (u)| _u＝0 ；Q″ _h (u)| _u＝1 ＝Q″ _h+1 (u)| _u＝0 ；Q″ ′ _h (u)| _u＝1 ＝Q″′ _h+1 (u)| _u＝0 ; Wherein, u represents the B-spline curve parameter; h represents the path segment number of the tool tip position path and the tool axis direction path after smoothing; "'", """ and ""'" respectively represent the first-order, second-order and third-order derivatives of the curve with respect to parameter u; according to the necessary and sufficient conditions for the continuity of the tool axis angular velocity, the values of the second and seventh control points of the parameter synchronization curve are determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular acceleration, the values of the third and sixth control points are determined; according to the necessary and sufficient conditions for the continuity of the tool axis angular jump, the values of the fourth and fifth control points are determined. 3. The hybrid robot C3 continuous five-axis path transition smoothing method according to claim 1 is characterized in that the method also includes the following steps: after completing the smoothing of the tool tip position path and the tool axis direction path, by correcting the jump curve in the S acceleration and deceleration motion, a tool tip velocity curve with continuous jump is generated; according to the tool tip velocity curve, parameter interpolation is performed in combination with the estimation-correction method to generate the interpolation point sequence required in the robot processing process. 4. The hybrid robot C3 continuous five-axis path transition smoothing method according to claim 3 is characterized in that the method also includes the following steps: determining the joint variables of each driving joint of the robot at each moment based on the interpolation point sequence and the kinematic model of the hybrid robot; controlling the movement of the hybrid robot based on the joint variables of each driving joint of the robot at each moment; and based on the PMAC motion control card, collecting the following errors of each joint during the robot movement in real time to evaluate the smoothing effectiveness of the tool tip position path and the tool axis direction path. 5. The hybrid robot C3 continuous five-axis path transition and smoothing method according to claim 1 is characterized in that the inserted spline curve segment is a quintic B-spline. 6. The hybrid robot C3 continuous five-axis path transition smoothing method according to claim 1 is characterized in that the specific steps of establishing the relationship function between the smoothing length of the tool tip position path and its smoothing error include: Step A1, assuming that the i-1th tool tip point Pi _-1 , the i-th tool tip point _Pi and the i+1th tool tip point _Pi+1 are three tool tip points connected in sequence in the original tool tip point position path; a quintic B-spline curve with seven control points is used as a spline curve segment inserted when the three tool tip points are transferred and smoothed; the expression of the inserted spline curve segment is as follows: Where, _Ci (u) represents the spline curve inserted at point _Pi ; Bj _,i represents the control point of the spline curve _Ci (u), where i represents the number of the original tool position point, j=0,1,…,6 represents the number of the control point; u∈[0,1] represents the spline curve parameter; Nj _,5 (u) represents the fifth-order B-spline basis function; Step A2, the necessary and sufficient conditions for establishing the curvature differential continuity of the tool tip position path at the connection point are as follows: In the formula, m _e,i represents the unit direction vector from point _Pi to point _Pi+1 , where “e” is the sign bit; s represents the cumulative arc length of the tool tip position path; Step A3, assuming that the path segment The length of satisfies ||B _0,i B _1,i ||＝c ₁ ||B _0,i B _3,i ||, where c ₁ ∈(0,1) is a preset constant; assuming that the path segment The length of satisfies ||B _1,i B _2,i ||＝c ₂ ||B _0,i B _3,i ||, where c ₂ ∈(0,1) is a preset constant; to avoid the curve from crossing itself, it should be ensured that 0＜c ₁ +c ₂ ＜1; based on the above assumptions, the functional relationship between each control point of the position spline curve _Ci (u) and the tool tip point _Pi is established; Step A4, according to the fact that the arc length of the remaining path segment monotonically increases with the curve parameter, the lower limit of the length of the remaining path segment is determined; based on the functional relationship between the control points of the tool tip position path curve, the relationship function between the smoothing length of the tool tip position path and its smoothing error is established as follows: ||B _0,i B _3,i ||＝||B _3,i B _6,i ||; In the formula, ε _pos,max represents the smoothing error limit value of the set tool tip position path; φ _i represents the angle between the unit vectors m _s,i and m _e,i , where m _s,i represents the unit vector from point P _i to point P _i-1 , and m _e,i represents the unit vector from point P _i to point P _i+1 ; _Li represents the original path segment Length; Li ₊₁ represents the original path segment Length; Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _6,i-1 represents the last control point of the spline curve inserted at point Pi _-1 ; Indicates the remaining position path length determined by parameter synchronization The lower limit value of , where B _0,i+1 represents the first control point of the spline curve inserted at point Pi ₊₁ . 7. The hybrid robot C3 continuous five-axis path transition smoothing method according to claim 6 is characterized in that the specific steps of establishing the relationship function between the tool axis direction path smoothing angle and its smoothing error include: Step B1, the original tool axis direction path is composed of a series of concentric arcs on the surface of a unit sphere, and the center of the unit sphere is set to W; the i-1th tool axis unit vector endpoint O _i-1 , the i-th tool axis unit vector endpoint O _i and the i+1th tool axis unit vector endpoint O _i+1 are set as three consecutive tool axis unit vector endpoints in the original tool axis direction path; based on the constant modulus of the tool axis unit vector being 1, a quintic B-spline curve including seven control points is used as the spline curve segment inserted when the tool axis direction path is converted and smoothed; _Qi (u) is set as the spline curve of the tool axis direction path inserted at point O _i : the expression of _Qi (u) is as follows: Wherein, Φ _i (u) represents the initial spline curve constructed at point O _i according to the differential continuity condition of the path curvature in the tool axis direction; “||WΦ _i (u)||” represents the distance from point W to the point corresponding to parameter u on the curve Φ _i (u); D _k,i represents the control point of the spline curve _Qi (u), where i represents the number of the original tool position point, k = 0, 1, ..., 6 represents the number of the control point; u∈[0,1] represents the spline curve parameter; Step B2, establish the necessary and sufficient conditions for the continuity of the curvature differential of the tool axis path at the connection point: In the formula, s _o represents the cumulative arc length of the path in the tool axis direction; Represents an arc The unit tangent vector at D _6,i on the upper right corner, where “e” is the sign; d _6,i represents the vector from the center W of the unit sphere to the point D _6,i ; Step B3, based on the necessary and sufficient conditions for the continuity of curvature differential and the derivative characteristics of the B-spline curve, establish the functional relationship between each control point of the curve _Qi (u) and the end point of the unit vector of the original tool axis; assume that the control points of the curve _Qi (u) satisfy the following relationship: With line segment The length ratio is 1:h, 2≤h≤8; according to the necessary and sufficient conditions for the differential continuity of the curvature of the path in the tool axis direction, determine the control point D _3,i of the smoothing curve _Qi (u); according to the necessary and sufficient conditions for the continuity of the curvature of the path in the tool axis direction and the center angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the transition segment, determine the control points D _2,i and D _4,i of the curve _Qi (u); according to the necessary and sufficient conditions for the tangential continuity of the path in the tool axis direction and the center angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the transition segment, determine the control points D _1,i and D _5,i of the curve _Qi (u); Let {R _s,i } represent the arc segment The Frenet coordinate system is constructed at the upper point O _i. Represents an arc segment The unit tangent vector at point O _i is Represents an arc segment The principal normal unit vector at point O _i is Represents an arc segment The binormal unit vector at point O _i ; Let {R _e,i } represent the arc segment The Frenet coordinate system is constructed at the upper point O _i. Represents an arc segment The unit tangent vector at point O _i is Represents an arc segment The principal normal unit vector at point O _i is Represents an arc segment The binormal unit vector at point O _i ; Assume d _3,i = o _i ; then: In the formula, o _i represents the unit vector of the tool axis corresponding to the i-th tool position point; Represents an arc The unit tangent vector at D _0,i , where "s" is the sign bit; represents the angle ∠D _0,i WD _3,i , where “s” represents the sign bit; represents the angle ∠D _3,i WD _6,i , where “e” represents the sign bit; d _0,i represents the vector from point W to point D _0,i ; d _1,i represents the vector from point W to point D _1,i ; d _2,i represents the vector from point W to point D _2,i ; d _3,i represents the vector from point W to point D _3,i ; d _4,i represents the vector from point W to point D _4,i ; d _5,i represents the vector from point W to point D _5,i ; d _6,i represents the vector from point W to point D _6,i ; Step B4, according to the functional relationship between each control point of the curve _Qi (u) and the end point of the original tool axis unit vector, derive the analytical expression of the tool axis direction path smoothing error and the smoothing angle; the tool axis direction path smoothing error is expressed as and θ _n,i, where θ _n,i represents the unit vector and By drawing the global variation trend diagram of the smoothing error in the tool axis direction, the smoothing error in the tool axis direction is obtained as a function of the smoothing angle. Monotonically increasing; Based on the smoothing error of the tool axis path and the constraints of parameter synchronization, a numerical method is used to solve the smoothing angle and 8. The hybrid robot C3 continuous five-axis path transition and smoothing method according to claim 7, characterized in that step B4 includes the following sub-steps: Step B4-1, determine the smoothing angle considering the following constraints Upper limit value: 1) To avoid the intersection of path curves at adjacent tool tip points, the smoothing angle should not exceed half of the original center angle; 2) According to the fact that the arc length of the remaining path segment increases monotonically with the curve parameter, the lower limit values of the central angles ∠D _0,i WD _3,i and ∠D _3,i WD _6,i of the remaining path segment are determined; Then we have: In the formula, Indicates the smoothing angle The upper limit value of δ _i represents the arc segment The central angle of the circle; δ _i+1 represents the arc segment The central angle of a circle; Indicates the lower limit of the center angle ∠D _6,i-1 WD _0,i of the remaining path segment; Indicates the lower limit of the center angle ∠D _6,i WD _0,i+1 of the remaining path segment; Step B4-2, according to the smoothing angle The upper limit value of the tool axis path is calculated to calculate the smoothing error of the tool axis path; determine whether the smoothing error of the tool axis path meets the following conditions: (1-ε _t )ε _ori,max ≤ε _ori,i ≤ε _ori,max ; Where, ε _t represents the control accuracy of the smoothing error of the tool axis path, ε _ori,i represents the smoothing error of the tool axis path at point O _i ; ε _ori,max is the predefined limit value of the smoothing error of the tool axis path; If the path smoothing error in the tool axis direction meets the condition, then If the path smoothing error in the tool axis direction does not meet the conditions, the smoothing angle is solved by the binary search method. According to the binary search strategy, the value of the smoothing angle is continuously updated until the constraint conditions are met. Step B4-3, further completely determine the smoothing curve of the tool axis direction path based on the calculated smoothing angle. 9. The hybrid robot C3 continuous five-axis path transition smoothing method according to claim 7 is characterized in that the tool axis motion performance of the hybrid robot is improved by adjusting the tool tip point path smoothing length and the tool axis direction path smoothing angle, and the method for adjusting the tool tip point path smoothing length and the tool axis direction path smoothing angle comprises: Step D1, based on the planned hybrid robot machining path, determine whether the path smoothing length of the tool tip position and the path smoothing angle of the tool axis direction meet the following conditions: If the conditions are met, then If the condition is not met, then Step D2, based on the planned machining path, determine whether the path smoothing length of the tool tip position and the path smoothing angle of the tool axis direction meet the following conditions: If the conditions are met, then If the condition is not met, then Step D3, after the smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path are adjusted, the tool tip position path smoothing curve _Ci (u) and the tool axis direction path smoothing curve _Qi (u) are recalculated according to the updated smoothing length of the tool tip position path and the smoothing angle of the tool axis direction path; Step D4, a global C3 continuous hybrid robot machining path after tool planning is formed by the C3 continuous tool tip point position path and the C3 continuous tool axis direction path.