CN113084821A - Spraying robot time optimal trajectory planning method based on dynamics - Google Patents

Spraying robot time optimal trajectory planning method based on dynamics Download PDF

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CN113084821A
CN113084821A CN202110482412.3A CN202110482412A CN113084821A CN 113084821 A CN113084821 A CN 113084821A CN 202110482412 A CN202110482412 A CN 202110482412A CN 113084821 A CN113084821 A CN 113084821A
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constraints
acceleration
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孔民秀
邓晗
李昂
刘霄朋
姬一明
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Harbin Institute of Technology
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    • 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
    • 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
    • B25J11/0075—Manipulators for painting or coating
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses

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Abstract

A spraying robot time optimal trajectory planning method based on dynamics relates to a robot trajectory planning method. Giving a Cartesian space path; calculating interpolation point related parameters: the method comprises the following steps of (1) interpolating point number, Cartesian space parameters, joint space parameters and kinetic equation coefficients, wherein the Cartesian space parameters comprise positions, postures, linear velocities, Euler angular velocities, linear accelerations and Euler angular accelerations, and the joint space parameters comprise joint angles, joint velocities and joint accelerations; calculating a speed range; calculating an optimal speed value; smoothing the track; and outputting the joint parameters. The method has the advantages that kinematic constraint is considered, a dynamic model is introduced to consider the dynamic constraint, the method has obvious advantages in time compared with the traditional trajectory planning method, at least one joint motor reaches the limit running state in the running process, the driving performance is fully exerted, and each joint parameter does not exceed the limit value, so that the working efficiency is improved, and the method has universality.

Description

Spraying robot time optimal trajectory planning method based on dynamics
Technical Field
The invention relates to a robot trajectory planning method, in particular to a spraying robot time optimal trajectory planning method based on dynamics, and belongs to the technical field of robot control.
Background
The application and development of industrial robots promote social progress, but with the continuous development of social economy, higher requirements are put on industrial automation technology. When the robot performs a painting operation, in order to improve the production efficiency of the painting robot and create a greater economic value, it is necessary to make the robot move faster, more accurately, and more safely. Therefore, intensive research into trajectory planning of the spray robot is required.
However, the conventional trajectory planning method only considers the kinematic constraint, does not fully utilize the driving performance of the joint motor, and has a problem that the planning speed exceeds the limited area, and the obtained trajectory is not a time-optimal trajectory, as shown in fig. 2. To overcome these disadvantages and achieve time-optimal results, trajectory planning needs to be performed in consideration of dynamic constraints.
In the prior art, there are methods for time-optimal planning, such as numerical integration, convex optimization. However, the numerical integration method is not universal and is not suitable for all kinetic models, and the convex optimization method has large calculation amount and low efficiency. Therefore, a method for planning a trajectory of a painting robot with optimal time is needed.
Disclosure of Invention
The invention aims to provide a spraying robot time optimal trajectory planning method based on dynamics, which considers kinematic constraints and introduces a dynamics model to consider dynamics constraints and has obvious advantages in time.
In order to achieve the purpose, the invention adopts the following technical scheme: a spraying robot time optimal trajectory planning method based on dynamics comprises the following steps:
step 1, giving a Cartesian space path: giving a teaching point by using a teaching device of the spraying robot, and determining a path through the teaching point;
step 2, calculating relevant parameters of the interpolation points: introducing a path parameter s, s representing the path length from a starting point to an interpolation point, setting the path length as l, s belonging to [0, l ], calculating the number of the interpolation points, a Cartesian space parameter, a joint space parameter and a kinetic equation coefficient, wherein the Cartesian space parameter comprises: position, gesture, linear velocity, euler angular velocity, linear acceleration and euler angular acceleration, joint space parameter includes: joint angle, joint velocity, and joint acceleration;
2.1 number of interpolation points: the value formula is n-mxl, wherein m is an empirical coefficient;
2.2 if the path is a circular arc track, the circle center, the radius and the circle center angle need to be calculated, and if the path is a straight line or a spline curve, the step is skipped;
2.3 Cartesian spatial parameters: specifically analyzing different paths, expressing positions and postures by adopting an expression related to a path parameter s, expressing the postures by adopting quaternion, calculating the middle posture by adopting spherical linear interpolation, wherein linear velocity and Euler angular velocity are differential values related to the positions and postures, and linear acceleration and Euler angular acceleration are second-order differential values related to the positions and postures;
2.4 joint space parameters: the known position and posture obtains a joint angle through an inverse solution, and then the relation between the linear velocity ps and the joint velocity qs is utilized:
qs＝J-1·ps
determining the joint velocity, wherein J represents the Jacobian matrix,
then, performing two-side derivation on the formula to obtain the joint acceleration;
2.5 calculation of kinetic equation coefficients: the derivative of the joint angle q with respect to the time t of path completion has the following relationship with the path parameter s:
Figure BDA0003049769050000021
Figure BDA0003049769050000022
the nonlinear dynamical model of the robot derived by the lagrange equation method is known as follows:
Figure BDA0003049769050000031
wherein M (q) represents an inertia matrix,
Figure BDA0003049769050000032
representing a matrix of Coriolis force and centrifugal force, g (q) representing a moment vector caused by gravity, substituting the two formulas into a kinetic model, and finishing to obtain:
Figure BDA0003049769050000033
directly solving the coefficient of the dynamic equation by a formula method;
step 3, calculating a speed range: analyzing each interpolation point, wherein the constraints comprise Cartesian space constraints and joint space constraints, the Cartesian space constraints comprise linear velocity constraints, Euler angular velocity constraints, linear acceleration constraints and Euler angular acceleration constraints, the joint space constraints comprise joint torque constraints, joint speed constraints and joint acceleration constraints, corresponding parameter values are smaller than constraint values, the joint acceleration constraints are not considered when the joint torque constraints are considered, the constraints are converted into a formula containing parameter velocity squares and parameter accelerations, the Cartesian space constraints and the joint space constraints are comprehensively considered, the maximum value of the parameter velocity squares of each interpolation point is calculated point by point, the minimum value is 0, and the surrounded area is the velocity range which can be reached by the robot;
step 4, calculating an optimal speed value: each section of track is regarded as an acceleration section, a middle section and a deceleration section, and in order to obtain a track with optimal time, the acceleration section needs to be accelerated at the maximum acceleration, the middle section needs to run close to the upper limit of the speed, the deceleration section needs to be decelerated at the minimum acceleration, the dynamics and the kinematics constraint are comprehensively considered, the limit acceleration which can be reached by each interpolation point is given, and the kinematics formula is utilized to carry out the optimal solution calculation;
step 5, track smoothing: carrying out smoothing treatment on the track obtained in the step 4;
step 6, outputting joint parameters: and (5) rearranging the interpolation points in the step 5 according to the interpolation period to obtain new interpolation points, and then calculating the joint parameters related to time.
Compared with the prior art, the invention has the beneficial effects that: the invention considers kinematic constraint and introduces a dynamic model to consider dynamic constraint, compared with the traditional track planning method, the robot finishes the same path by spraying, and has obvious advantages in time.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram comparing a conventional trajectory with the time-optimal trajectory of the present invention;
FIG. 3 is a schematic diagram of a time-optimal trajectory of an embodiment;
FIG. 4 is a graphical representation of the joint angle ratio values of the embodiments;
FIG. 5 is a graphical representation of joint velocity ratio values of an embodiment;
FIG. 6 is a graphical representation of the joint moment ratio values of the embodiments.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
As shown in fig. 1, a method for planning a time-optimal trajectory of a spray robot based on dynamics includes the following steps:
step 1, giving a Cartesian space path: giving a teaching point by using a teaching device of the spraying robot, and determining a path through the teaching point;
step 2, calculating relevant parameters of the interpolation points: introducing a path parameter s, wherein s represents the path length from a starting point to an interpolation point, setting the path length as l, s belongs to [0, l ], changing s to change the speed and the acceleration so as to finish planning, and calculating the number of the interpolation points, the Cartesian space parameters, the joint space parameters and the kinetic equation coefficients, wherein the Cartesian space parameters comprise: position, gesture, linear velocity, euler angular velocity, linear acceleration and euler angular acceleration, joint space parameter includes: joint angle, joint velocity, and joint acceleration;
2.1 number of interpolation points: the interpolation point number is increased when the path length is increased, and the value formula is that n is mxl, wherein m is an empirical coefficient;
2.2 if the path is a circular arc track, the circle center, the radius and the circle center angle need to be calculated, and if the path is a straight line or a spline curve, the step is skipped;
2.3 Cartesian spatial parameters: specifically analyzing different paths, expressing positions and postures by adopting an expression related to a path parameter s, expressing the postures by adopting quaternion, calculating the middle posture by adopting spherical linear interpolation, wherein linear velocity and Euler angular velocity are differential values related to the positions and postures, and linear acceleration and Euler angular acceleration are second-order differential values related to the positions and postures;
2.4 joint space parameters: the known position and posture obtains a joint angle through an inverse solution, and then the relation between the linear velocity ps and the joint velocity qs is utilized:
qs＝J-1·ps
determining the joint velocity, wherein J represents the Jacobian matrix,
then, performing two-side derivation on the formula to obtain the joint acceleration;
2.5 calculation of kinetic equation coefficients: the derivative of the joint angle q with respect to the time t of path completion has the following relationship with the path parameter s:
Figure BDA0003049769050000051
Figure BDA0003049769050000052
the nonlinear dynamical model of the robot derived by the lagrange equation method is known as follows:
Figure BDA0003049769050000053
wherein M (q) represents an inertia matrix,
Figure BDA0003049769050000054
representing a matrix of Coriolis force and centrifugal force, g (q) representing a moment vector caused by gravity, substituting the two formulas into a kinetic model, and finishing to obtain:
Figure BDA0003049769050000061
directly solving the coefficient of the dynamic equation by a formula method;
step 3, calculating a speed range: because the corresponding constraint conditions of each interpolation point are different, each interpolation point needs to be analyzed, the constraints comprise Cartesian space constraints and joint space constraints, wherein the Cartesian space constraints comprise linear velocity constraints, Euler angular velocity constraints, linear acceleration constraints and Euler angular acceleration constraints, the joint space constraints comprise joint moment constraints, joint velocity constraints and joint acceleration constraints, and the corresponding parameter values are smaller than the constraint values,
in addition, the joint acceleration constraint is not considered when the joint moment constraint is considered,
converting constraints into square including parametric velocity
Figure BDA0003049769050000062
And parametric acceleration
Figure BDA0003049769050000063
Formula (2) and (2)The Cartesian space constraint and the joint space constraint are considered together, and the speed square of each interpolation point parameter is calculated point by point
Figure BDA0003049769050000064
The minimum value is 0, and the enclosed area is the speed range which can be reached by the robot;
step 4, calculating an optimal speed value: each section of track is regarded as an acceleration section, a middle section and a deceleration section, and in order to obtain a track with optimal time, the acceleration section needs to be accelerated at the maximum acceleration, the middle section needs to run close to the upper limit of the speed, the deceleration section needs to be decelerated at the minimum acceleration, the dynamics and the kinematics constraint are comprehensively considered, the limit acceleration which can be reached by each interpolation point is given, and the kinematics formula is utilized to carry out the optimal solution calculation;
step 5, track smoothing: carrying out smoothing treatment on the track obtained in the step 4;
step 6, outputting joint parameters: and (5) rearranging the interpolation points in the step 5 according to the interpolation period to obtain new interpolation points, and then calculating the joint parameters related to time.
Example (b): the spraying robot completes a section of circular arc track in a Cartesian space
The specific time optimal trajectory planning method comprises the following steps:
step 1, giving a Cartesian space path: the demonstrator gives three teaching points with the positions and postures of P1 (x)1，y1，z1，α1，β1，γ1)、P2(x2，y2，z2，α2，β2，γ2)、P3(x3，y3，z3，α3，β3，γ3). The first three coordinates in the coordinates represent spatial positions, and the last three coordinates represent postures by Euler angles;
step 2, calculating relevant parameters of the interpolation points:
2.1 number of interpolation points: taking a value according to the length l of the arc path, wherein the value taking formula is that n is mxl, and m is an empirical coefficient;
2.2 determining the circle center and the radius, converting the space circular arc into a plane circular arc, determining an external circle by using a method of obtaining the circle center by intersecting three planes, wherein the equation of a plane A1 where the circle is located is as follows:
a1x+b1y+c1z+d1＝0
the equation for the perpendicular bisecting plane A2 of P1P2 is as follows:
a2x+b2y+c2z+d2＝0
the equation for the perpendicular bisecting plane A3 of P2P3 is as follows:
a3x+b3y+c3z+d3＝0
by combining the above three equations, we can obtain:
Figure BDA0003049769050000071
the center P0 (x) can be found by the above formula0，y0，z0) Then, the radius of the arc can be obtained according to the circle center as follows:
Figure BDA0003049769050000072
after the circle center and the radius are obtained, a new coordinate system is established on the basis of the circle center, the X axis of the new coordinate system is the vector direction of P0P1, and the direction cosine of the X axis is as follows:
Figure BDA0003049769050000073
Figure BDA0003049769050000081
Figure BDA0003049769050000082
the Z axis of the new coordinate system is the normal phasor direction of the plane A1, and the direction cosine is as follows:
Figure BDA0003049769050000083
Figure BDA0003049769050000084
Figure BDA0003049769050000085
after the directions of the X axis and the Z axis of the new coordinate system are determined, the direction of the Y axis of the new coordinate system can be obtained according to the right-hand rule, then a homogeneous transformation matrix R can be determined, and the space circular arc in the base standard system is transformed to the plane circular arc in the new coordinate system through the homogeneous transformation matrix R. Finally, judging whether the arc is clockwise or anticlockwise, and solving a central angle;
2.3 calculating the cartesian space parameters:
the positions of the interpolation points are:
Figure BDA0003049769050000086
wherein C represents the coordinate of the circle center, R represents the radius of the circle center,
the linear velocity is:
Figure BDA0003049769050000087
the linear acceleration is:
Figure BDA0003049769050000091
the expression of the robot attitude adopts a quaternion method, three points P1, P2 and P3 are given, attitude matrixes R1, R2 and R3 can be determined, and then quaternions can be obtainedqa、qb、qc. For the multi-attitude problem, unit quaternion spherical linear interpolation is adopted, then two-stage interpolation is adopted, and the expression is as follows:
Figure BDA0003049769050000092
then, the quaternion is converted into Euler angles alpha, beta and gamma, and the required posture is obtained.
Obtaining an axial angle and an axial speed through quaternion, and obtaining the Euler angular speed by using a relational expression of the rotating shaft speed and the Euler angular speed:
Figure BDA0003049769050000093
wherein J represents a matrix of:
Figure BDA0003049769050000094
the above equation is processed, and then euler angular acceleration can be obtained:
Figure BDA0003049769050000095
wherein, the matrix represented by D is:
Figure BDA0003049769050000096
2.4 calculating joint space parameters:
and (3) obtaining a joint angle q corresponding to each interpolation point by an inverse solution by using the position p obtained in the step (2.3), and then obtaining a joint speed and a joint acceleration by using the relation between the linear velocity and the joint speed as follows:
Figure BDA0003049769050000101
2.5 calculation of kinetic equation coefficients:
the derivative of the joint angle q with respect to the time t of path completion has the following relationship with the path parameter s:
Figure BDA0003049769050000102
Figure BDA0003049769050000103
the nonlinear dynamical model of the robot derived by the lagrange equation method is known as follows:
Figure BDA0003049769050000104
wherein M (q) represents an inertia matrix,
Figure BDA0003049769050000105
representing a matrix of Coriolis force and centrifugal force, g (q) representing a moment vector caused by gravity, substituting the two formulas into a kinetic model, and finishing to obtain:
Figure BDA0003049769050000106
directly solving the coefficient of the dynamic equation by a formula method;
step 3, calculating a speed range:
analysis of constraints due to linear velocity vmaxThe following limitations can be obtained:
Figure BDA0003049769050000107
in the same way, due to the angular velocity wmaxThe following limitations can be obtained:
Figure BDA0003049769050000108
due to linear acceleration amaxThe following limitations can be obtained:
Figure BDA0003049769050000109
by the same token, due to angular acceleration amaxThe following limitations can be obtained:
Figure BDA0003049769050000111
by maximum torque τ of the motormaxBy restriction, we can obtain:
Figure BDA0003049769050000112
from joint velocity qtmaxThe constraint, expressed as:
Figure BDA0003049769050000113
wherein,
Figure BDA0003049769050000114
which is representative of the speed of the parameter,
Figure BDA0003049769050000115
representing the parameter acceleration.
By synthesizing all the above formulas, the velocity square of each interpolation point parameter is calculated point by point
Figure BDA0003049769050000116
A minimum value of 0;
step 4, calculating an optimal speed value:
considering the kinetic and kinematic constraints, the acceleration is:
Figure BDA0003049769050000117
in the formula, u is a smaller value,
Figure BDA0003049769050000118
representing the square of the maximum velocity corresponding to the next interpolation point.
The square of the velocity of the next interpolation point is obtained by a kinematic formula of physics:
Figure BDA0003049769050000119
thus, the speed optimal value of each interpolation point is obtained in sequence;
step 5, track smoothing:
the conventional method can be adopted, and the following improved moving average filtering method can be selected to divide each path into two sections of processing. The deceleration point is found first, and then the front section and the rear section are processed in different modes respectively.
Route anterior segment:
Figure BDA0003049769050000121
a path rear section:
Figure BDA0003049769050000122
step 6, outputting joint parameters:
the velocity and acceleration reached in step 4 are related to the path parameters and not to time. And setting an interpolation period, and adjusting the obtained sequence value according to the interpolation period to obtain a new sequence value. The terminal linear velocity of the robot is calculated by the difference method, and a velocity time image is drawn as shown in fig. 3. As can be seen in FIG. 3, the image is smooth, the acceleration section accelerates at the maximum acceleration, the middle section runs close to the limit, and the end section runs more smoothly, so that the overall running time has greater advantages than the traditional trajectory planning algorithm. Finally, a joint angle is obtained through inverse solution, then a joint speed and a joint acceleration are obtained through a difference method, a dynamic equation is substituted to obtain a shutdown moment, all obtained joint parameters are divided by limit values of corresponding parameters, and a joint parameter ratio image is obtained, as shown in fig. 4-6. The ratio map does not change the image trend, the ratio is kept between ± 1, representing safe operation, so fig. 4-6 remain substantially within safe limits, and the objects of fig. 3 and 4 are relatively flat and therefore ideal.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (4)

1. A spraying robot time optimal trajectory planning method based on dynamics is characterized in that: the method comprises the following steps:
step 1, giving a Cartesian space path: giving a teaching point by using a teaching device of the spraying robot, and determining a path through the teaching point;
step 2, calculating relevant parameters of the interpolation points: introducing a path parameter s, s representing the path length from a starting point to an interpolation point, setting the path length as l, s belonging to [0, l ], calculating the number of the interpolation points, a Cartesian space parameter, a joint space parameter and a kinetic equation coefficient, wherein the Cartesian space parameter comprises: position, gesture, linear velocity, euler angular velocity, linear acceleration and euler angular acceleration, joint space parameter includes: joint angle, joint velocity, and joint acceleration;
2.1 number of interpolation points: the value formula is n-mxl, wherein m is an empirical coefficient;
2.2 if the path is a circular arc track, the circle center, the radius and the circle center angle need to be calculated, and if the path is a straight line or a spline curve, the step is skipped;
2.3 Cartesian spatial parameters: specifically analyzing different paths, expressing positions and postures by adopting an expression related to a path parameter s, expressing the postures by adopting quaternion, calculating the middle posture by adopting spherical linear interpolation, wherein linear velocity and Euler angular velocity are differential values related to the positions and postures, and linear acceleration and Euler angular acceleration are second-order differential values related to the positions and postures;
2.4 joint space parameters: the known position and posture obtains a joint angle through an inverse solution, and then the relation between the linear velocity ps and the joint velocity qs is utilized:
qs＝J-1·ps
determining the joint velocity, wherein J represents the Jacobian matrix,
then, performing two-side derivation on the formula to obtain the joint acceleration;
2.5 calculation of kinetic equation coefficients: the derivative of the joint angle q with respect to the time t of path completion has the following relationship with the path parameter s:
Figure FDA0003049769040000021
Figure FDA0003049769040000022
the nonlinear dynamical model of the robot derived by the lagrange equation method is known as follows:
Figure FDA0003049769040000023
wherein M (q) represents an inertia matrix,
Figure FDA0003049769040000024
representing a matrix of Coriolis force and centrifugal force, g (q) representing a moment vector caused by gravity, substituting the two formulas into a kinetic model, and finishing to obtain:
Figure FDA0003049769040000025
directly solving the coefficient of the dynamic equation by a formula method;
step 3, calculating a speed range: analyzing each interpolation point, wherein the constraints comprise Cartesian space constraints and joint space constraints, the Cartesian space constraints comprise linear velocity constraints, Euler angular velocity constraints, linear acceleration constraints and Euler angular acceleration constraints, the joint space constraints comprise joint torque constraints, joint speed constraints and joint acceleration constraints, corresponding parameter values are smaller than constraint values, the joint acceleration constraints are not considered when the joint torque constraints are considered, the constraints are converted into a formula containing parameter velocity squares and parameter accelerations, the Cartesian space constraints and the joint space constraints are comprehensively considered, the maximum value of the parameter velocity squares of each interpolation point is calculated point by point, the minimum value is 0, and the surrounded area is the velocity range which can be reached by the robot;
step 4, calculating an optimal speed value: comprehensively considering dynamics and kinematic constraints, giving the ultimate acceleration which can be reached by each interpolation point, and calculating the optimal solution by using a kinematic formula;
step 5, track smoothing: carrying out smoothing treatment on the track obtained in the step 4;
step 6, outputting joint parameters: and (5) rearranging the interpolation points in the step 5 according to the interpolation period to obtain new interpolation points, and then calculating joint parameters related to time.
2. The dynamics-based time-optimal trajectory planning method for a painting robot according to claim 1, characterized in that: and 4, when the optimal speed value is calculated, each section of track is regarded as an acceleration section, a middle section and a deceleration section, and in order to obtain the track with optimal time, the acceleration section needs to be accelerated at the maximum acceleration, the middle section needs to run close to the upper limit of the speed, and the deceleration section needs to be decelerated at the minimum acceleration.
3. The dynamics-based time-optimal trajectory planning method for a painting robot according to claim 1, characterized in that: and 5, when the track is smoothed, firstly finding a deceleration point for each section of the path and dividing the deceleration point into a front section and a rear section for processing.
4. The dynamics-based time-optimal trajectory planning method for a painting robot according to claim 1, characterized in that: and 6, setting an interpolation period, adjusting the obtained sequence value according to the interpolation period to obtain a new interpolation point, obtaining a joint angle through inverse solution, and obtaining a joint speed and a joint acceleration through a difference method.
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CN113814978A (en) * 2021-09-30 2021-12-21 深圳市优必选科技股份有限公司 Robot control method, robot control device, robot, and storage medium
CN114474043A (en) * 2021-12-20 2022-05-13 埃夫特智能装备股份有限公司 Method for realizing visual intelligent spraying of bedside
CN114750153A (en) * 2022-04-13 2022-07-15 上海电气集团股份有限公司 Motion control system for robot arm, cooperative robot, and storage medium
CN115157270A (en) * 2022-08-26 2022-10-11 北京东土科技股份有限公司 Robot tail end track planning method and device
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WO2024041647A1 (en) * 2022-08-26 2024-02-29 北京东土科技股份有限公司 Cartesian space trajectory planning method and apparatus

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