CN111906789A - Robot joint space trajectory planning method - Google Patents

Robot joint space trajectory planning method Download PDF

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CN111906789A
CN111906789A CN202010911403.7A CN202010911403A CN111906789A CN 111906789 A CN111906789 A CN 111906789A CN 202010911403 A CN202010911403 A CN 202010911403A CN 111906789 A CN111906789 A CN 111906789A
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joint
joint space
robot
trajectory
time interval
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谢能斌
辛绍杰
刘韬伦
朱明明
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Shanghai Dianji University
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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
    • 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 robot joint space trajectory planning method, which comprises the following steps: converting the coordinates of the robot joint at the Cartesian space start and stop points into joint angles at the joint space start and stop points, and interpolating between the joint space start and stop points to obtain joint angles at joint space intermediate points; interpolating a trajectory curve in the joint space using a polynomial interpolation function; constructing a time optimal fitness function and setting kinematic constraint; optimizing the time interval of the trajectory curve by using a PSO algorithm and an SA algorithm under the condition of meeting the kinematic constraint and outputting the time interval; and taking the time interval as a time coefficient of the polynomial interpolation function, and calculating the coefficient of the polynomial interpolation function to further obtain an optimized joint track curve.

Description

Robot joint space trajectory planning method
Technical Field
The invention relates to the technical field of robot intelligent control, in particular to a robot joint space trajectory planning method taking time optimization as a target.
Background
With the advent of industry 4.0, smart manufacturing equipment is playing an increasingly important role in industrial production and daily life. The robot is used as an important component in intelligent manufacturing equipment, is widely applied to the fields of medical treatment, automobile manufacturing, welding, curved surface polishing and the like, relieves the pressure of insufficient labor force, and requires that the industrial robot has high working efficiency and running stability. The reasonable planning is carried out on the track of the joint space of the robot, so that the working efficiency of the robot can be improved, the joint shake is reduced, and the running stability of the robot is improved. Many existing robot joint space trajectory planning methods cannot guarantee stability in a joint movement process, meanwhile, time intervals among path points need to be further optimized, and movement efficiency and stability of a mechanical arm need to be improved urgently.
In the prior art, although some trajectory planning methods meet the continuity of the position, the speed and the acceleration of a joint space trajectory curve, the continuity of the acceleration is not ensured, so that the smoothness of the acceleration trajectory curve is not enough, the vibration of the joint motion process is not effectively controlled, the time interval between two path points is not optimized, and the motion efficiency of the mechanical arm is low. In some track planning methods, the time interval between adjacent path points is optimized by using a particle swarm algorithm, so that the motion time of the mechanical arm is greatly reduced, but the time interval of the track needs to be further optimized because the particle swarm algorithm easily falls into a local optimal solution. Therefore, the existing robot joint space trajectory planning method generally has the problem of discontinuous trajectory jerk curve, and the problem of jitter in the joint motion process is not well solved. Meanwhile, when the intelligent control algorithm is used for optimizing the track time interval, the global searching capability of the algorithm is still to be improved, and a new robot joint space track planning scheme is needed.
Based on the problems in the prior art, how to reasonably plan the space trajectory of the joint of the robot, how to improve the working efficiency of the robot, reduce the joint jitter, improve the running stability of the robot, and how to solve the problem that the global search capability of an intelligent control algorithm is insufficient when the trajectory time interval is optimized is currently and yet to be solved.
Disclosure of Invention
The invention aims to solve the technical problems of how to reasonably plan the space track of the joint of the robot, how to improve the working efficiency of the robot, reduce the shaking of the joint, improve the running stability of the robot and how to solve the problem of insufficient global searching capability of an intelligent control algorithm in the process of optimizing the track time interval, and provides a method for planning the space track of the joint of the robot.
The invention solves the technical problems through the following technical scheme:
a robot joint space trajectory planning method includes:
converting the coordinates of the robot joint at the Cartesian space start and stop points into joint angles at the joint space start and stop points, and interpolating between the joint space start and stop points to obtain joint angles at joint space intermediate points;
interpolating a trajectory curve in the joint space using a polynomial interpolation function;
constructing a time optimal fitness function and setting kinematic constraint;
optimizing the time interval of the trajectory curve by using a PSO-SA algorithm under the condition of meeting the kinematic constraint and outputting the time interval;
and taking the time interval as a time coefficient of the polynomial interpolation function, and calculating the coefficient of the polynomial interpolation function to further obtain an optimized joint track curve.
Preferably, the Matlab robot toolbox is used to interpolate between the joint space start and stop points.
Preferably, the constraint condition of the polynomial interpolation function is: the positions of the joint space starting point and the joint space middle point are known, the speed, the acceleration and the jerk of the joint space starting point and the joint space middle point are zero, and the position, the speed, the acceleration and the jerk of the joint space middle point and the fourth derivative of the track curve are all continuous.
Preferably, when the number of the intermediate points is two, the fitness function is
Figure BDA0002663426440000021
Figure BDA0002663426440000022
Said t isi1，ti2，ti3And time intervals corresponding to the three sections of the track curves of the robot joint are respectively set.
More preferably, the kinematic constraints comprise joint velocity constraints and joint acceleration constraints, respectively:
Figure BDA0002663426440000031
wherein the content of the first and second substances,
Figure BDA0002663426440000032
the maximum rotating speed of the joint is set,
Figure BDA0002663426440000033
the maximum acceleration of the joint.
Preferably, the optimizing the time interval of the trajectory graph using the PSO-SA algorithm and outputting the time interval includes:
initializing basic parameters of a PSO algorithm and an SA algorithm;
initializing the speed and the position of m particles in a random mode;
judging whether the positions of the particles meet the kinematic constraint or not, and calculating the fitness value of each particle;
comparing the fitness value of each particle, and solving the individual optimal position P of the particleibAnd the historical best position g of the populationb；
Updating the inertia weight value W and the dynamic learning factors C1 and C2;
updating the speed and the position of the m particles, and judging whether the kinematic constraint is met;
judging whether the particles accept new solutions according to an improved Metropolis criterion;
determining the individual optimal position P of the particleibAnd the historical best position g of said populationb；
Updating the temperature of the simulated annealing algorithm to reduce the temperature;
judging whether the maximum iteration is reached, and if the maximum iteration is less than the maximum iteration, returning the updated inertia weight value W and the dynamic learning factors C1 and C2; otherwise, exiting the iteration and outputting the time interval.
Preferably, when the number of the intermediate points is two, the polynomial interpolation function has the highest degree of 5, 7, and 5, respectively.
On the basis of the common knowledge in the field, the above preferred conditions can be combined randomly to obtain the preferred embodiments of the invention.
The positive progress effects of the invention are as follows: the continuity of the position, the speed, the acceleration and the jerk of the joint track curve is ensured, and the shake of the joint is reduced; the time interval of the track is optimized, the track time is shortened on the premise of meeting the kinematic constraint, and the motion efficiency of the mechanical arm is improved on the premise of reducing the joint shake.
Drawings
Fig. 1 is a trajectory planning flowchart in an embodiment of a robot joint space trajectory planning method of the present invention;
fig. 2 is a flowchart of optimizing joint trajectory curve time interval by using a PSO algorithm and an SA algorithm in an embodiment of a robot joint space trajectory planning method according to the present invention.
Detailed Description
To facilitate an understanding of the present application, the present application will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present application are shown in the drawings. This application may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
It will be understood that when an element is referred to as being "connected" to another element, it can be directly connected to the other element and be integral therewith, or intervening elements may also be present. The terms "mounted," "one end," "the other end," and the like are used herein for illustrative purposes only.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the description of the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
Fig. 1 shows a trajectory planning flowchart of the present invention:
step S01: converting the coordinates of the robot joint at the Cartesian space start and stop points into joint angles at the joint space start and stop points, and interpolating between the joint space start and stop points to obtain joint angles at joint space intermediate points;
in one example, a Matlab robot Toolbox Robotic _ Toolbox is used for interpolating a starting point and an end point of the joint space to obtain joint angles of two middle points of each joint. The specific programming statements are as follows:
the mdl _ PUMA560 statement is used in Matlab to open a model that PUMA _560 robot has built in robot toolkit Robotic _ Toolbox, said PUMA _560 robot being a six degree of freedom robot. Using q1The sentence p560.ikine6s (T1) relates the starting point position coordinate T in the cartesian space to1Conversion to joint angles q of joints in joint space by inverse kinematics1Said q is1Is a matrix of 1 row and 6 columns. Using q4The sentence p560.ikine6s (T4) coordinates the position of the termination point in the cartesian space by T4Conversion to joint angles q of joints in joint space by inverse kinematics4Said q is4Is a matrix of 1 row and 6 columns. Using q ═ jtraj (q)1,q4And 4) interpolating the start point and the stop point in a joint space to generate joint angles of 6 joints corresponding to 4 path points including the start point and the two intermediate points in the joint space, wherein q is a matrix with 4 rows and 6 columns.
Step S02: interpolating a trajectory curve in the joint space using a polynomial interpolation function;
in one example, a three-segment trajectory curve for each joint is interpolated using a 5-7-5 polynomial interpolation function. Three-segment trajectory polynomial h of joint ii1(t)、hi2(t)、hi3(t) is:
hi1(t)＝ai15t5+ai14t4+ai13t3+ai12t2+ai11t+ai10
hi2(t)＝ai27(t-ti1)7+ai26(t-ti1)6+ai25(t-ti1)5+ai24(t-ti1)4+ai23(t-ti1)3+ai22(t-ti1)2+ai21(t-ti1)+ai20
hi3(t)＝ai35(t-ti1-ti2)5+ai34(t-ti1-ti2)4+ai33(t-ti1-ti2)3+ai32(t-ti1-ti2)2+ai31(t-ti1-ti2)+ai30
the trajectory polynomial has the following constraints: the positions of the joint space starting point and the joint space stopping point and the positions of the two intermediate points are known, the speed, the acceleration and the jerk of the joint space starting point and the joint space stopping point are 0, and the four-order derivatives of the positions, the speed, the acceleration, the jerk and the track curve of the two intermediate points are continuous. And solving the coefficients of the 5-7-5 track polynomial through the constraint conditions so as to determine the 5-7-5 track polynomial.
The trajectory polynomial coefficient solving method is as follows:
the starting point position is thetai1：ai10＝θi1
The starting point speed is 0:
Figure BDA0002663426440000051
the starting point acceleration is0：
Figure BDA0002663426440000061
The starting point jerk is 0:
Figure BDA0002663426440000062
the position of the termination point is thetai4：
Figure BDA0002663426440000063
The end point speed is 0:
Figure BDA0002663426440000064
the end point acceleration is 0:
Figure BDA0002663426440000065
the end point jerk is 0:
Figure BDA0002663426440000066
the first intermediate point is at a position thetai2：
Figure BDA0002663426440000067
ai20＝θi2
The second intermediate point is at a position of θi3：
Figure BDA0002663426440000068
ai30＝θi3
The speed at the first intermediate point continues:
Figure BDA0002663426440000069
at the first intermediate pointAcceleration is continuous:
Figure BDA00026634264400000610
the jerk at the first intermediate point continues:
Figure BDA00026634264400000611
the fourth derivative of the trajectory at the first intermediate point is continuous: 120a ofi15ti1+24ai14＝24ai24
The speed at the second intermediate point continues:
Figure BDA00026634264400000612
the acceleration at the second intermediate point continues:
Figure BDA00026634264400000613
the jerk at the second intermediate point is continuous:
Figure BDA0002663426440000071
the fourth derivative of the trajectory at the second intermediate point is continuous:
Figure BDA0002663426440000072
theta is describedi1、θi2、θi3、θi4Respectively representing the joint angles of the joint i at four path points. Obtaining a polynomial coefficient matrix a according to the constraint condition:
Figure BDA0002663426440000073
the A matrix is a time coefficient matrix.
The position parameter matrix b of the joint i is as follows:
b＝[θ1,0,0,0,θ4,0,0,0,θ2,θ2,θ3,θ3,0,0,0,0,0,0,0,0]T
by the formula a ═ A-1B, solving a coefficient a matrix of the joint track polynomial, and solving the 5-7-5 track polynomial according to the coefficient a matrix of the joint track polynomial.
Step S03: constructing a time optimal fitness function and setting kinematic constraint;
in one example, the fitness function is
Figure BDA0002663426440000081
T in the fitness functioni1、ti2、ti3And respectively representing time intervals corresponding to three sections of trajectories of the joint i. The joint velocity and acceleration constraints in the third step are as follows:
Figure BDA0002663426440000082
Figure BDA0002663426440000083
the above-mentioned
Figure BDA0002663426440000084
Representing the maximum rotational speed and maximum acceleration constraints of the joint, respectively.
Step S04: optimizing the time interval of the trajectory curve by using a PSO (Particle Swarm Optimization) algorithm and an SA (Annealing simulation) algorithm under the condition of meeting the kinematic constraint and outputting the time interval;
in one example, as shown in fig. 2, the step of optimizing the time interval of the trajectory curve using the PSO algorithm and the SA algorithm and outputting the time interval according to the present invention is:
initializing basic parameters of a PSO algorithm and an SA algorithm;
in one example, parameters such as the maximum iteration number of the particle swarm optimization, the number m of particles in the swarm, the position and speed boundaries of the particles, the maximum value and the minimum value of the inertia weight and the like are initialized, and the initial temperature and the temperature attenuation coefficient of the simulated annealing algorithm are initialized.
Initializing the speed and the position of m particles in a random mode;
in one example, the velocity and position of m particles are initialized. An initial position and velocity of the particle is randomly generated within the position and velocity boundary of the particle. Three-segment trajectory polynomial h for the joint i respectivelyi1(t)、hi2(t)、hi3(t) solving a first derivative and a second derivative to obtain joint velocity and acceleration polynomials. And if the real-time speed or the acceleration of any section of the joint does not meet the kinematic constraint, solving that the constraint is not met.
Judging whether the positions of the particles meet the kinematic constraint or not, and calculating the fitness value of each particle;
in one example, if the position of the particle satisfies a kinematic constraint, a fitness value for the particle is calculated using the fitness function. If the position of the particle does not satisfy the kinematic constraint, the fitness value of the particle is equal to a fixed larger value.
Comparing the fitness value of each particle, and solving the individual optimal position P of the particleibAnd the historical best position g of the populationb；
In one example, the position of each particle of the initial population is set as the individual optimal position p of the particleibComparing the fitness function value of each particle, wherein the particle position with the optimal fitness value is the historical optimal position g of the particle populationb。
Updating the inertia weight value W and the dynamic learning factors C1 and C2;
in one example, the sex weight value w updates the formula as follows:
Figure BDA0002663426440000091
the dynamic learning factor c1And c2The update formula is as follows:
Figure BDA0002663426440000092
Figure BDA0002663426440000093
said wmaxAnd wminRespectively, the maximum and minimum values of the weight are respectively taken as 0.9 and 0.4. The iter and itermaxRespectively representing the current iteration number and the maximum iteration number of the algorithm.
Updating the speed and the position of the m particles, and judging whether the kinematic constraint is met;
in one example, the particle update speed and position are formulated as follows:
Figure BDA0002663426440000094
Figure BDA0002663426440000095
the above-mentioned
Figure BDA0002663426440000096
Is the flight velocity of the particle i at the k +1 th iteration, said
Figure BDA0002663426440000097
Is the position in the search space of the particle i at the kth iteration. Said r1And r2Is a random number between 0 and 1. The velocity update formula of the particles shows that the particles can change the flying velocity according to the individual optimal particle positions and the historical optimal positions of the particle swarm, and the flying velocity is changed according to the historical optimal positionsThe location update formula flies to a more optimal location.
Judging whether the particles accept new solutions according to an improved Metropolis criterion;
in one example, the particle swarm algorithm is optimized using a simulated annealing algorithm, in which a simulated annealing mechanism is introduced. Determining whether each particle accepts the new solution generated during the iterative process of the algorithm using an improved Metropolis criterion as follows:
Figure BDA0002663426440000101
Figure BDA0002663426440000102
const-1 in the modified Metropolis criterion represents the solution x of the previous generation of particle iiDoes not satisfy the joint kinematic constraint, then accepts the new solution x generatedi_new. If the previous generation solution meets the kinematic constraint condition, the new solution is accepted when the delta f is less than 0, and the new solution is accepted with a certain probability when the delta f is more than or equal to 0.
Determining the individual optimal position P of the particleibAnd the historical best position g of said populationb；
In one example, the objective function value of each particle of the current iteration population is compared with the individual optimal position p of the particleibIf the objective function value of the current position of the particle is more optimal, p is addedibUpdated to the current position of the particle. The fitness function value of each particle of the current iteration population and the historical optimal position g of the particle swarm are calculatedbComparing the fitness function of the particle swarm, and if the objective function value of the particle is more optimal, comparing the historical optimal position g of the particle swarmbThe position of the particle is updated.
Updating the temperature of the simulated annealing algorithm to reduce the temperature;
in one example, the temperature is updated according to the formula T ═ α × T during the iteration of the algorithm, causing the temperature to drop. And T is the simulated annealing temperature, and alpha is the temperature attenuation coefficient of the simulated annealing algorithm.
And judging whether the maximum iteration is reached or not and outputting the time interval.
In one example, in the iterative process of the algorithm, whether the iteration times iter of the PSO algorithm and the SA algorithm are smaller than the maximum iteration times is continuously judged, and if iter is smaller than the maximum iteration times, iter is judged<itermaxThen the iteration number is updated and the loop iteration is continued. If iter ≧ itermaxThen the loop iteration exits.
Step S05: and taking the time interval as a time coefficient of the polynomial interpolation function, and calculating the coefficient of the polynomial interpolation function to further obtain an optimized joint track curve.
In one example, the time interval of the output is taken as the time coefficient of the 5-7-5 trajectory polynomial, according to which a-a-1B, calculating polynomial coefficients of each joint track to obtain each joint track curve, and finishing space time optimal track planning of the robot joints.
While specific embodiments of the invention have been described above, it will be appreciated by those skilled in the art that this is by way of example only, and that the scope of the invention is defined by the appended claims. Various changes and modifications to these embodiments may be made by those skilled in the art without departing from the spirit and scope of the invention, and these changes and modifications are within the scope of the invention.

Claims (7)

1. A robot joint space trajectory planning method is characterized by comprising the following steps:
converting the coordinates of the robot joint at the Cartesian space start and stop points into joint angles at the joint space start and stop points, and interpolating between the joint space start and stop points to obtain joint angles at joint space intermediate points;
interpolating a trajectory curve in the joint space using a polynomial interpolation function;
constructing a time optimal fitness function and setting kinematic constraint;
optimizing the time interval of the trajectory curve by using a PSO algorithm and an SA algorithm under the condition of meeting the kinematic constraint and outputting the time interval;
and taking the time interval as a time coefficient of the polynomial interpolation function, and calculating the coefficient of the polynomial interpolation function to further obtain an optimized joint track curve.
2. A method for planning the spatial trajectory of a robot joint according to claim 1, wherein the Matlab robot toolbox is used to interpolate between the start and end points of the joint space.
3. The method for planning the spatial trajectory of the joint of the robot according to claim 1, wherein the constraint conditions of the polynomial interpolation function are as follows: the positions of the joint space starting point and the joint space middle point are known, the speed, the acceleration and the jerk of the joint space starting point and the joint space middle point are zero, and the position, the speed, the acceleration and the jerk of the joint space middle point and the fourth derivative of the track curve are all continuous.
4. The method for planning the spatial trajectory of a robot joint according to claim 1, wherein when the number of the intermediate points is two, the fitness function is
Figure FDA0002663426430000011
Figure FDA0002663426430000012
Said t isi1，ti2，ti3And time intervals corresponding to the three sections of the track curves of the robot joint are respectively set.
5. The method for planning the spatial trajectory of the joint of the robot according to claim 4, wherein the kinematic constraints comprise joint velocity constraints and joint acceleration constraints, which are respectively:
Figure FDA0002663426430000013
wherein the content of the first and second substances,
Figure FDA0002663426430000014
the maximum rotating speed of the joint is set,
Figure FDA0002663426430000015
the maximum acceleration of the joint.
6. The method of claim 1, wherein the optimizing the time interval of the trajectory curve using the PSO algorithm and the SA algorithm and outputting the time interval comprises:
initializing basic parameters of a PSO algorithm and an SA algorithm;
initializing the speed and the position of m particles in a random mode;
judging whether the positions of the particles meet the kinematic constraint or not, and calculating the fitness value of each particle;
comparing the fitness value of each particle, and solving the individual optimal position P of the particleibAnd the historical best position g of the populationb；
Updating the inertia weight value W and the dynamic learning factors C1 and C2;
updating the speed and the position of the m particles, and judging whether the kinematic constraint is met;
judging whether the particles accept new solutions according to an improved Metropolis criterion;
determining the individual optimal position P of the particleibAnd the historical best position g of said populationb；
Updating the temperature of the simulated annealing algorithm to reduce the temperature;
judging whether the maximum iteration is reached, and if the maximum iteration is less than the maximum iteration, returning the updated inertia weight value W and the dynamic learning factors C1 and C2; otherwise, exiting the iteration and outputting the time interval.
7. A robot joint space trajectory planning method according to any one of claims 1 to 6, wherein when the number of intermediate points is two, the polynomial interpolation functions have the highest degree of 5, 7 and 5 respectively.
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Application publication date: 20201110