CN112828359A - Robot milling attitude planning method and system based on multiple constraints of potential field method - Google Patents

Robot milling attitude planning method and system based on multiple constraints of potential field method Download PDF

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CN112828359A
CN112828359A CN202110111578.4A CN202110111578A CN112828359A CN 112828359 A CN112828359 A CN 112828359A CN 202110111578 A CN202110111578 A CN 202110111578A CN 112828359 A CN112828359 A CN 112828359A
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robot
potential field
end effector
bcs
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CN112828359B (en
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彭芳瑜
李泽鹏
孙朝阳
唐小卫
闫蓉
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Huazhong University of Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23C—MILLING
    • B23C3/00—Milling particular work; Special milling operations; Machines therefor
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J11/00—Manipulators not otherwise provided for
    • B25J11/005—Manipulators for mechanical processing tasks
    • B25J11/0055—Cutting
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention discloses a multi-constraint robot milling attitude planning method and system based on a potential field method, and belongs to the field of milling manufacturing. According to the invention, the geometric physical constraint is converted into the virtual potential field, so that the constrained quantity is far away from the constraint boundary under the action of the repulsive torque generated by the virtual potential field, and the generated attitude track meets the geometric physical constraint. The invention comprehensively considers the redundant angle of the robot and the front inclination angle of the end effector, thereby further improving the processing quality. After the factor is considered, the generated track is applied to milling, and the processing precision is obviously improved. The invention provides a new potential field function, which is characterized in that a virtual kinetic equation is calculated through numerical integration to solve an attitude track, and the obtained solution is a numerical value in a continuous domain, so that the joint motion C3 continuity of the robot track is ensured all the time in the motion process, and the smoothness of the generated attitude track is ensured.

Description

Robot milling attitude planning method and system based on multiple constraints of potential field method
Technical Field
The invention belongs to the field of milling machining and manufacturing, and particularly relates to a potential field method multi-constraint robot milling machining attitude planning method and system.
Background
Industrial robots are widely used in various automated productions due to their advantages of high flexibility, programmability, competitive cost, etc., and trajectory planning for different production task demands has become a very important requirement for robot operations. Aiming at the milling of the robot, the requirements on the precision of a processing track and the mechanical performance of the processing are higher, and the robot provides greater challenges compared with other operation tasks such as stacking, carrying and the like; compared with the traditional five-axis machining, the robot milling machining has the advantages that besides the front inclination angle and the side inclination angle, redundant angles also affect the machining mechanical property, and the planning difficulty is higher. Therefore, it is necessary to develop a posture trajectory planning technique suitable for multi-axis milling of a robot.
In the field of current machine tool and robot attitude planning, an algorithm based on sampling and graph theory is mainly adopted to disperse the reachable space of the whole robot and perform traversal calculation on indexes such as machining performance, operating performance and the like, so that the calculation cost is high. And due to the dispersion of the reachable space, the planning result needs to be smoothened. The scholars such as Khatib of Stanford University in the United states, published on Autonomous Robot Vehicles, Real-Time Obstacle Avoidance for Robots and Mobile Robots propose a Robot Obstacle Avoidance track planning algorithm based on a potential field method, interference in a space is endowed with repulsive force, an attraction force is set at a target point, and the Robot is planned from an initial point to a terminal point without interference track through the action of two forces. The stress condition of the position of the robot is only calculated, so that the traversal of the whole reachable space is avoided; and the generated track smoothness is ensured through continuous calculation. Cho et al, National University, in Seoul, Korea, published on the International Journal of Advanced Manufacturing technologies, introduced the potential field method into machine tool milling tool pose trajectory planning. Lacharnay et al scholaray of University of Paris, France, published an article A physical-based model for global alignment in 5-axis point milling on Computer-aid Design, and endowing obstacles of global interference with a virtual repulsive force field, endowing pre-planned tool attitude trajectories with an attractive force field, and endowing the tool with virtual modal parameters, so that the tool realizes efficient, global interference-free and smooth tool attitude planning through the action of attractive force and repulsive force in a rule of moving along a planned path. Related researches only apply a potential field method to robot obstacle avoidance and machine tool attitude planning, and corresponding planning algorithms are less in application to multi-axis milling attitude trajectory planning of robots.
Disclosure of Invention
Aiming at the defects and improvement requirements of the prior art, the invention provides a multi-constraint robot milling attitude planning method and system based on a potential field method, aiming at comprehensively considering the influence of tool attitude and redundant angles on the processing precision in the milling process, realizing the efficient generation of the smooth robot attitude track moving along a tool path and being beneficial to improving the processing precision of a workpiece.
In order to achieve the above object, according to a first aspect of the present invention, there is provided a potential field method multi-constraint-based robot milling attitude planning method, including the following steps:
s1, acquiring a cutter path;
s2, initializing a virtual rotational inertia M of the robot end effector and a virtual rotational damping C of the robot end effector, initializing the posture of the robot end effector at a first knife position, and initializing constraint values theta of each joint angle of the robotlimAnd a threshold value theta0The constraint value of the rake angle of the toollimAnd a threshold value l0The roll angle constraint value tlimAnd a threshold value t0And an error index constraint value deltalimSum threshold δ0；
S3, for each tool location point in the tool path, performing the following processing until the gesture planning of the robot end effector on the tool location point on the whole tool path is completed:
(1) taking the tool position point in the tool path as the origin of coordinates and the normal vector direction of the workpiece design surface as ZECSAxis, with tangent direction of tool path as XECSAxis, establishing Y by right hand ruleECSAxes, thereby establishing an ECS coordinate system;
(2) calculating the joint angle theta of the robot based on the relation between the TCS and the BCS coordinate system and the kinematics of the robot; calculating a tool rake angle l and a side rake angle t based on the relation of TCS and ECS coordinate systems; calculating a machining error index delta based on the relation among TCS, BCS and ECS coordinate systems and the rigidity and the milling mechanics of the robot;
(3) respectively calculating absolute values of difference values of the actual value and the constraint value to obtain theta ', l', t ', delta';
(4) respectively substituting the calculated theta ', l', t ', delta' into a repulsion torque function, summing the calculated repulsion torques, and calculating to obtain the total repulsion torque applied to the end effector at the knife position, wherein the repulsion torque function is obtained by performing partial derivation on a potential field function, and the potential field function must simultaneously meet the following limitations:
1) when any of θ ', l', t ', δ' tends to 0, the potential field tends to infinity;
2) when any of θ ', l', t ', δ' is greater than the corresponding threshold, the potential field is constantly equal to 0;
3) at least ensuring the second order partial derivative to be continuous;
(5) substituting the obtained total repulsive torque into a virtual dynamic equation, and solving to obtain the robot end effector posture at the next knife position, wherein the virtual dynamic equation is as follows:
Figure BDA0002919099070000031
wherein M is the virtual moment of inertia of the robot end effector, C is the virtual rotational damping, P (t) is the total potential field function, alphaiIs the TCS coordinate systemThe Euler angle of rotation about the X, Y or Z axis of the BCS,
Figure BDA0002919099070000032
is total repulsive torque, omega (t) is the rotation speed of the TCS corresponding to the robot end effector under the BCS coordinate system,
Figure BDA0002919099070000033
is the rotation acceleration of the TCS corresponding to the robot end effector in the BCS coordinate system.
Has the advantages that: according to the method, constraint conditions in the robot milling process are converted into potential field functions, after the posture of the robot end effector on a first cutter location point is given, the repulsion moments corresponding to different constraint conditions are calculated through the potential field functions, a virtual dynamic equation is solved, and therefore the planning of the posture track of the robot end effector on the whole cutter path is achieved.
Preferably, the tool side rake angle t is calculated as follows:
Figure BDA0002919099070000041
the calculation formula of the cutter rake angle l is as follows:
Figure BDA0002919099070000042
Figure BDA0002919099070000043
wherein the content of the first and second substances,
Figure BDA0002919099070000044
is a rotation matrix of TCS to ECS,
Figure BDA0002919099070000045
is an intermediate matrix and the subscripts represent the number of rows and columns corresponding to the matrix.
Has the advantages that: according to the invention, the front inclination angle and the side inclination angle are defined in the robot milling process, so that the redundant angle planning in the existing robot processing is expanded to the common planning of the front inclination angle, the side inclination angle and the redundant angle. Thereby further improving the milling capacity of the robot.
Preferably, the machining error index is defined as: when the average milling force acts on a cutter of the robot end effector, the component of the generated deformation in the normal vector direction of the surface of the workpiece is calculated as follows:
(1) rotation matrix by TCS to BCS
Figure BDA0002919099070000046
Converting milling force to BCSBCSF；
Figure BDA0002919099070000047
Wherein f isforce(l, t) is a calculated function of the average milling force in TCS at the rake angle l and the roll angle t of the tool;
(2) calculating a robot tail end rigidity matrix K based on the robot joint angle theta;
K＝fstiffness(θ)
wherein f isstiffness(theta) is a calculation function of a robot terminal stiffness matrix K;
(3) calculating the machining error index delta
δ＝|BCSZECS(CLi)K-1 BCSF|
Wherein, CLiIs the position coordinate of the ith knife location point in the BCS coordinate system,BCSZECS(CLi) Is the vector coordinate of the Z-axis of the ECS at the ith knife location under the BCS.
Has the advantages that: according to the method, the influence of different robot postures on the rigidity of the tail end of the robot and the milling force is considered by defining the machining error index delta of the robot. By means of constraint on machining error indexes and combination of the proposed potential field algorithm, milling attitude trajectory planning of the high-precision robot is achieved.
Preferably, the potential field function with r as a constraint is as follows:
Figure BDA0002919099070000051
where η is a control parameter, and r ═ θ 'or l' or t 'or δ'.
Has the advantages that: the invention provides a robot end effector attitude trajectory planning potential field function model considering multiple constraints. When the potential field function approaches to 0, the potential energy approaches to infinity, so that the generated track is ensured to meet the constraint condition. Since the potential field function is greater than the threshold r at any of θ ', l ', t ', δ0And the potential energy is constantly equal to 0, so that the influence of the repulsive torque on the tail end posture of the robot when the distance from the constraint boundary is far is avoided, and the motion stability of the robot tail end actuator is ensured. As the potential field function at least ensures the continuity of second-order partial derivatives, the operation C of the robot end effector is ensured3Continuity.
Preferably, the step (5) is solved by adopting a Longge Kutta to obtain
Figure BDA0002919099070000052
Figure BDA0002919099070000053
Wherein the content of the first and second substances,
Figure BDA0002919099070000054
Figure BDA0002919099070000055
Figure BDA0002919099070000056
Figure BDA0002919099070000061
Figure BDA0002919099070000062
Figure BDA0002919099070000063
Figure BDA0002919099070000064
wherein alpha ispre，
Figure BDA0002919099070000065
The Euler angle and angular velocity, alpha, of the robot end effector corresponding to the position of the previous knife point1,α2,α3Is an intermediate variable, tgapIs the time interval between adjacent tool positions,
Figure BDA0002919099070000066
is the total repulsive torque, tpreIs the time corresponding to the previous knife location point, and CL (t) is the knife location point at time t.
Has the advantages that: the method converts the robot attitude trajectory planning problem into the solution of a virtual dynamic equation, realizes the planning of the robot end effector attitude on the subsequent tool location point by a Runge-Kutta numerical integration method on the given initial tool location point.
Preferably, the constraint values of step S3 further include at least one of robot pose singularity condition number, singular point, vibration, and energy.
Has the advantages that: the method converts the constraint into potential energy through the potential field function to generate repulsive torque, so that the gesture track of the robot end effector is planned. The potential field function has universality, and can be applied to constraints such as robot attitude singularity condition number, singular points, vibration, energy and the like, so that robot end effector attitude trajectory planning under different constraints under different working conditions is realized.
In order to achieve the above object, according to a second aspect of the present invention, there is provided a multi-constraint robot milling processing attitude planning system based on a potential field method, including: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is configured to read executable instructions stored in the computer-readable storage medium, and execute the potential field method-based multi-constraint robot milling machining attitude planning method according to the first aspect.
Generally, by the above technical solution conceived by the present invention, the following beneficial effects can be obtained:
(1) according to the invention, the geometric physical constraint is converted into the virtual potential field, and the corresponding potential energy at the constraint limit value is infinite, so that the constrained quantity is far away from the boundary under the action of the repulsive force generated by the virtual potential field, and the generated attitude track meets the geometric-physical constraint.
(2) The forward tilt angle of the end effector also affects the mechanical properties of the robot, and thus the machining accuracy. The invention comprehensively considers the redundant angle of the robot and the front inclination angle of the end effector, thereby further improving the processing quality. After the factor is considered, the generated track is applied to milling, and the corresponding processing precision is obviously improved.
(3) The invention provides a new potential field function, which is characterized in that a virtual kinetic equation is calculated through numerical integration to solve an attitude track, the obtained solution is a numerical value in a continuous domain, so that the continuity of C3 of a robot track is always ensured in the motion process, and the smoothness of the generated attitude track is ensured.
Drawings
FIG. 1 is a general flow chart of a multi-constraint robot milling attitude planning method based on a potential field method provided by the invention;
FIG. 2 is a schematic diagram of a six-axis milling process of a robot and BCS, TCS and ECS provided by the present invention;
FIG. 3 is a rotation transformation relationship between a base coordinate system BCS of a robot and a tool coordinate system TCS provided by the present invention;
fig. 4 is a rotation transformation relation diagram of a robot coordinate system provided by the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in FIG. 1, the invention provides a multi-constraint robot milling attitude trajectory planning method based on a potential field method. Based on a kinematics and mechanics model of the robot, corresponding constraint conditions are given, and a robot attitude trajectory planning model under a given tool path is established; then, in order to ensure that the generated attitude track meets the geometric physical constraint and has C3 smoothness, a potential field model is provided, and an algorithm of virtual repulsive torque generated by the potential field is provided; combining the repulsion torque with the virtual modal parameters endowed to the robot end effector to construct a dynamic equation of the robot end effector posture; and finally, planning the posture track of the robot is realized through a numerical integration algorithm.
1. Robot attitude trajectory planning model
For convenience of describing the robot milling process, as shown in fig. 2, relevant coordinate systems in the robot milling process are established, including a robot Base Coordinate System (BCS), a process coordinate system (ECS), and a robot end effector coordinate system (TCS). Wherein, BCS is a coordinate system fixed on the robot; TCS with robotic tipThe center of the cutter on the actuator is the original point, and the axial direction of the cutter is ZTCSAxis, YTCSWith axis perpendicular to the tool axis and feed direction, and establishing X by right hand ruleTCSA shaft. The ECS is defined according to the tool path, the tool position point in the machining is taken as the origin of coordinates, and the normal vector of the designed surface of the workpiece is taken as ZECSAxis, with tangent direction of tool path as XECSAxis, establishing Y by right hand ruleECSA shaft.
Robotic multi-axis milling, as shown in fig. 2, may be viewed as a translational movement of a tool tip point along a given tool path while a robotic end effector rotates about the tool tip point. The tool path is made up of a series of tool location points CL, which can be generated by CAM software. The tool attitude, namely the attitude of the robot end effector is a planning object, and the mathematical relation of the attitude of the robot end effector under the base coordinate system BCS is described through the Euler angle alpha. The relationship between BCS and TCS is shown in FIG. 3. The pose of the TCS under the BCS is described by a homogeneous transformation matrix of Euler angles alpha as follows:
Figure BDA0002919099070000081
αx、αyand alphazIs Euler angle of rotation about X, Y and Z axes of BCS, CLx、CLyAnd CLzThe position of the tool location point relative to the base coordinate system.
In order to generate a machining attitude track of the robot multi-axis milling, the constraints of a joint angle range, a tool attitude angle and a machining error index need to be comprehensively met. On the other hand, the smoothness is required to ensure the dynamic characteristics of the robot and the motion performance of the tool during operation, so that the track is required to ensure C3And (4) continuous. The planning model for the trajectory is therefore:
Figure BDA0002919099070000091
in the formula, i refers to the serial number of a cutter point on a cutter path track; and theta, l, t and delta are indexes of a joint angle of the robot, a tool posture forward inclination angle, a side inclination angle and a machining error respectively.
2 robot end effector pose constraints
2.1 Joint Angle constraint
Because the motion range of each joint angle theta of the robot is fixed, the reachable space of the posture of the robot end effector is restrained in order to avoid the situation that the planned robot posture is unreachable.
For a given euler angle alphax,αy,αzThe attitude of the end effector of the robot can obtain an end effector pose matrix of the robot
Figure BDA0002919099070000092
Calculating a function f by inverse kinematics of a robotikinThen, the joint angle θ of the robot can be obtained, namely:
Figure BDA0002919099070000093
joint angle theta range (theta) of combined robotmin,θmax) Obtaining the constraint conditions of the attitude of the robot end effector, namely:
θ＝f1(αx,αy,αz)∈(θmin,θmax) (4)
2.2 tool attitude Angle constraints
In the field of five-axis milling, concepts of a front rake angle and a side rake angle are used for describing the tool posture. The forward inclination angle and the side inclination angle are limited within a certain range to avoid interference collision. Meanwhile, in the milling process of cutters such as a ball-end cutter and the like, the linear velocity of a cutter point is zero, which is not beneficial to cutting, so that the forward inclination angle of the cutter needs to be ensured to be larger than zero to avoid the cutter point from participating in cutting.
Unlike conventional machine tool milling, industrial robots have redundant degrees of freedom. In order to characterize the attitude characteristic of the robot, a forward tilt angle and a redundant angle of the multi-axis milling of the industrial robot are specified. As shown in FIG. 4, initially the TCS coincides with the ECS, with the TCS surrounding the ECThe Z axis of S is rotated by a redundancy angle S, then the TCS is rotated by a forward inclination angle l around the Y axis of the ECS, and finally the TCS is rotated by a side inclination angle t around the X axis of the ECS. Homogeneous transformation matrix
Figure BDA0002919099070000101
The expression is as follows:
Figure BDA0002919099070000102
after the attitude Euler angle and the tool location point coordinates of the robot end effector are given, the attitude Euler angle and the tool location point coordinates can be obtained by the formula (1)
Figure BDA0002919099070000103
And (3) according to the geometric relation, carrying out inverse operation on the formula:
the calculation formula of the side inclination angle t of the cutter is as follows:
Figure BDA0002919099070000104
the calculation formula of the cutter rake angle l is as follows:
Figure BDA0002919099070000105
Figure BDA0002919099070000106
wherein the content of the first and second substances,
Figure BDA0002919099070000107
is a rotation matrix of TCS to ECS,
Figure BDA0002919099070000108
is an intermediate matrix and the subscripts represent the number of rows and columns corresponding to the matrix. Mapping function f of forward inclination and roll redundancy angle from attitude Euler angle of robot end effector2Comprises the following steps:
Figure BDA0002919099070000109
thus, the constraint of the tool pose angle and the redundant angle is converted into an implicit constraint on the euler angle, namely:
[t,l,s]＝f2(αx,αy,αz)∈([tmin,tmax],[lmin,lmax]) (10)
2.3 machining error constraint
In order to characterize the machining precision, a component of deformation generated when an average cutting force acts on the robot end tool in a normal vector direction of a workpiece surface is defined as a machining error index.
(1) Rotation matrix by TCS to BCS
Figure BDA0002919099070000111
Converting milling force to BCSBCSF；
Figure BDA0002919099070000112
Wherein f isforce(l, t) is a calculated function of the average milling force in TCS at the rake angle l and the roll angle t of the tool;
(2) calculating a robot tail end rigidity matrix K based on the robot joint angle theta;
K＝fstiffness(θ) (12)
wherein f isstiffness(theta) is a calculation function of a robot terminal stiffness matrix K;
(3) calculating the machining error index delta
δ＝|BCSZECS(CLi)K-1 BCSF| (13)
Wherein, CLiIs the position coordinate of the ith knife location point in the BCS coordinate system, BCSZECS(CLi) Is the vector coordinate of the Z-axis of the ECS at the ith knife location under the BCS.
The coupling formulas (3), (9), (11), (12) and (13) are as followsFormula is converted into function f of Euler angle of robot end effector posture3：
δ＝|ZECS(CL)K-1(f1(αx,αy,αz))BCSF(f3(αx,αy,αz))|＝f3(αx,αy,αz)
In order to ensure the machining precision, the error index is limited as follows:
δ＝f3(αx,αy,αz)∈[0，δmax)
3. potential field algorithm
The potential field algorithm is used for converting absolute values theta ', l', t ', delta' of differences between indexes theta, l, t, delta and constraint limit values under different postures into virtual potential energy to construct a potential field. The repelling torque generated by the potential field acts on the attitude of the robot end effector, so that the tool point at the tail end of the robot automatically leaves away from a constraint limit value in the process of moving along a tool path, and the attitude track of the robot end effector meeting the constraint is generated.
In order to realize the method, on one hand, a potential field function and a repulsive moment function suitable for multi-axis milling of the robot are provided, on the other hand, a multi-axis machining attitude virtual dynamic equation of the robot is provided, and a solving method process is provided.
3.1 construction of potential field function and repulsive moment function
The generated gesture track should ensure that: (1) ensuring that the postures of the robot end effector on any tool position point meet constraint conditions; (2) the motion trail of the joint angle of the robot is smooth.
In order to guarantee the condition (1), the virtual potential energy tends to be infinite when the potential energy function is at the extreme position of the robot attitude area.
In order to ensure that the condition (2) is to avoid the generated robot track from oscillating, the robot posture is required to be larger than a threshold value r in distance0When the potential energy is zero; requirement that the generated trajectory have C3Continuity of (i.e. jerk θ of joint angle at all positions)(3)Continuity should be ensured.
Thus, the potential field function must simultaneously satisfy the following definitions:
1) when any of θ ', l', t ', δ' tends to 0, the potential field tends to infinity;
2) at any one of θ ', l', t ', δ' being greater than the threshold value r0When the potential field is constantly equal to 0;
3) at least ensuring the second order partial derivative to be continuous;
namely:
Figure BDA0002919099070000121
where r ═ θ 'or l' or t 'or δ'. This yields the potential field function:
Figure BDA0002919099070000122
the potential field repulsive moment is the derivative of the virtual potential energy with respect to the Euler angle of the robot end effector attitude. For robotic multi-axis milling, since the euler angle has three dimensions, the repulsive moment is:
Figure BDA0002919099070000123
through the calculation, the joint angle, the attitude angle and the error index are converted into the repulsive torque to act on the robot end effector, and the Euler angle corresponding to the attitude of the end effector is influenced.
3.2 virtual kinetic equation modeling and solving
According to the foregoing description about the potential field method, by giving virtual modal parameters to the robot end effector, under the action of the virtual repulsive torque generated by the constraint, a corresponding virtual dynamic equation can be established, that is:
Figure BDA0002919099070000131
wherein M is the virtual moment of inertia of the robot end effector, C is the virtual rotational damping, P (t) is the total potential field function, alphaiIs the Euler angle of the TCS coordinate system rotating around the X axis, the Y axis or the Z axis of the BCS in turn,
Figure BDA0002919099070000132
is total repulsive torque, omega (t) is the rotation speed of the TCS corresponding to the robot end effector under the BCS coordinate system,
Figure BDA0002919099070000133
is the rotation acceleration of the TCS corresponding to the robot end effector in the BCS coordinate system.
And solving the three directions respectively by a Longge Kutta method so as to plan the track.
Obtained by the Longge Kutta method
Figure BDA0002919099070000134
Figure BDA0002919099070000135
Wherein the content of the first and second substances,
Figure BDA0002919099070000136
Figure BDA0002919099070000137
Figure BDA0002919099070000138
Figure BDA0002919099070000141
Figure BDA0002919099070000142
Figure BDA0002919099070000143
Figure BDA0002919099070000144
wherein alpha ispre，
Figure BDA0002919099070000145
The Euler angle and angular velocity, alpha, of the robot end effector corresponding to the position of the previous knife point1,α2,α3Is an intermediate variable, tgapIs the time interval between adjacent tool positions,
Figure BDA0002919099070000146
is the total repulsive torque, tpreIs the time corresponding to the previous knife location point, and CL (t) is the knife location point at time t.
Therefore, when the robot conducts multi-axis milling, the robot end effector can automatically plan the attitude track of the tool along the given tool route initial tool position point in the process of moving to the tail end of the path.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1. A multi-constraint robot milling attitude planning method based on a potential field method is characterized by comprising the following steps:
s1, acquiring a cutter path;
s2, initializing a virtual rotational inertia M of the robot end effector and a virtual rotational damping C of the robot end effector, initializing the posture of the robot end effector at a first knife position, and initializing constraint values theta of each joint angle of the robotlimAnd a threshold value theta0The constraint value of the rake angle of the toollimAnd a threshold value l0The roll angle constraint value tlimAnd a threshold value t0And an error index constraint value deltalimSum threshold δ0；
S3, for each tool location point in the tool path, performing the following processing until the gesture planning of the robot end effector on the tool location point on the whole tool path is completed:
(1) taking the tool position point in the tool path as the origin of coordinates and the normal vector direction of the workpiece design surface as ZECSAxis, with tangent direction of tool path as XECSAxis, establishing Y by right hand ruleECSAxes, thereby establishing an ECS coordinate system;
(2) calculating the joint angle theta of the robot based on the relation between the TCS and the BCS coordinate system and the kinematics of the robot; calculating a tool rake angle l and a side rake angle t based on the relation of TCS and ECS coordinate systems; calculating a machining error index delta based on the relation among TCS, BCS and ECS coordinate systems and the rigidity and the milling mechanics of the robot;
(3) respectively calculating absolute values of difference values of the actual value and the constraint value to obtain theta ', l', t ', delta';
(4) respectively substituting the calculated theta ', l', t ', delta' into a repulsion torque function, summing the calculated repulsion torques, and calculating to obtain the total repulsion torque applied to the end effector at the knife position, wherein the repulsion torque function is obtained by performing partial derivation on a potential field function, and the potential field function must simultaneously meet the following limitations:
1) when any of θ ', l', t ', δ' tends to 0, the potential field tends to infinity;
2) when any of θ ', l', t ', δ' is greater than the corresponding threshold, the potential field is constantly equal to 0;
3) at least ensuring the second order partial derivative to be continuous;
(5) substituting the obtained total repulsive torque into a virtual dynamic equation, and solving to obtain the robot end effector posture at the next knife position, wherein the virtual dynamic equation is as follows:
Figure FDA0002919099060000021
wherein M is the virtual moment of inertia of the robot end effector, C is the virtual rotational damping, P (t) is the total potential field function, alphaiIs the Euler angle of the TCS coordinate system rotating around the X axis, the Y axis or the Z axis of the BCS in turn,
Figure FDA0002919099060000022
is total repulsive torque, omega (t) is the rotation speed of the TCS corresponding to the robot end effector under the BCS coordinate system,
Figure FDA0002919099060000023
is the rotation acceleration of the TCS corresponding to the robot end effector in the BCS coordinate system.
2. The method of claim 1, wherein the tool roll angle t is calculated as follows:
Figure FDA0002919099060000024
the calculation formula of the cutter rake angle l is as follows:
Figure FDA0002919099060000025
Figure FDA0002919099060000026
wherein the content of the first and second substances,
Figure FDA0002919099060000027
is a rotation matrix of TCS to ECS,
Figure FDA0002919099060000028
is an intermediate matrix and the subscripts represent the number of rows and columns corresponding to the matrix.
3. The method according to claim 1 or 2, wherein the machining error indicator is defined as: when the average milling force acts on a cutter of the robot end effector, the component of the generated deformation in the normal vector direction of the surface of the workpiece is calculated as follows:
(1) rotation matrix by TCS to BCS
Figure FDA0002919099060000029
Converting milling force to BCSBCSF；
Figure FDA00029190990600000210
Wherein f isforce(l, t) is a calculated function of the average milling force in TCS at the rake angle l and the roll angle t of the tool;
(2) calculating a robot tail end rigidity matrix K based on the robot joint angle theta;
K＝fstiffness(θ)
wherein f isstiffness(theta) is a calculation function of a robot terminal stiffness matrix K;
(3) calculating the machining error index delta
δ＝|BCSZECS(CLi)K-1BCSF|
Wherein, CLiIs the position coordinate of the ith knife location point in the BCS coordinate system,BCSZECS(CLi) Is the vector coordinate of the Z-axis of the ECS at the ith knife location under the BCS.
4. A method according to any one of claims 1 to 3, wherein the potential field function with r as a constraint is as follows:
Figure FDA0002919099060000031
where η is a control parameter, and r ═ θ 'or l' or t 'or δ'.
5. The method of claim 4, wherein step (5) is solved using a Runge Kutta to obtain
Figure FDA0002919099060000032
Figure FDA0002919099060000033
Wherein the content of the first and second substances,
Figure FDA0002919099060000034
Figure FDA0002919099060000035
Figure FDA0002919099060000036
Figure FDA0002919099060000037
Figure FDA0002919099060000038
Figure FDA0002919099060000041
Figure FDA0002919099060000042
wherein alpha ispre，
Figure FDA0002919099060000043
The Euler angle and angular velocity, alpha, of the robot end effector corresponding to the position of the previous knife point1，α2，α3Is an intermediate variable, tgapIs the time interval between adjacent tool positions,
Figure FDA0002919099060000044
is the total repulsive torque, tpreIs the time corresponding to the previous knife location point, and CL (t) is the knife location point at time t.
6. The method of claim 1, wherein the constraint values of step S3 further include at least one of robot pose singularity condition number, singular points, vibration, and energy.
7. A multi-constraint robot milling attitude planning system based on a potential field method is characterized by comprising the following steps: a computer-readable storage medium and a processor;
the computer-readable storage medium is used for storing executable instructions;
the processor is used for reading executable instructions stored in the computer-readable storage medium and executing the potential field method-based multi-constraint robot milling machining attitude planning method according to any one of claims 1 to 6.
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