CN109108963B - Space multi-joint robot path planning method based on differential evolution particle swarm algorithm - Google Patents

Space multi-joint robot path planning method based on differential evolution particle swarm algorithm Download PDF

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CN109108963B
CN109108963B CN201810821999.4A CN201810821999A CN109108963B CN 109108963 B CN109108963 B CN 109108963B CN 201810821999 A CN201810821999 A CN 201810821999A CN 109108963 B CN109108963 B CN 109108963B
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base
matrix
particle swarm
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CN109108963A (en
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袁建平
彭志旺
王明明
王铮
方静
徐杨
魏锦源
李晨熹
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Northwestern Polytechnical 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
    • 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
    • B25J9/00—Programme-controlled manipulators
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    • B25J9/1602—Programme controls characterised by the control system, structure, architecture

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Abstract

The invention discloses a space multi-joint robot path planning method based on a differential evolution particle swarm algorithm, which comprises the steps of establishing a kinematics and dynamics model of the change of joint angles of a mechanical arm of a space multi-joint robot, then establishing a model of disturbance of multi-joint robot collision on a base, representing a change track curve of the joint angles as a polynomial function related to time, establishing a total fitness function, using the particle swarm algorithm in an iterative solution, starting the differential evolution algorithm when a stagnation point occurs in the method, exchanging part of individuals of two algorithm groups to change the phase and enlarge the group scale, and completing the path planning of the space multi-joint robot. The method utilizes the particle swarm algorithm after differential evolution and correction to carry out the capture path planning of the space manipulator. The goal of the planning is to bring the end effector of the robotic arm to a fixed position and attitude and control the end-of-time robotic arm configuration so that the impact of the end effector with the target will cause minimal disturbance to the base and minimal total energy consumption of the trajectory.

Description

Space multi-joint robot path planning method based on differential evolution particle swarm algorithm
Technical Field
The invention belongs to the technical field of path planning of space robots, and particularly relates to a path planning method of a space multi-joint robot based on a differential evolution particle swarm algorithm.
Background
Space robots are a hot spot in the current development of space technology. The in-orbit service technology of the space robot is researched in all countries, because the abandoned satellite not only becomes space rubbish, but also occupies precious orbit resources. In addition, the space robot is used for replacing astronauts to work, so that the astronauts can be prevented from being injured, and the benefit of space exploration can be improved.
And planning a proper joint angle change track, which is a precondition for the space multi-joint robot to execute a capture task. Since space articulated robots perform tasks with a variety of constraints and limitations, for example: the method has the advantages that obstacles are avoided, energy consumption is minimum, time is minimum or base disturbance caused by collision is minimum, so that the change track of the joint angle of the multi-joint robot is necessary and necessary to plan in advance based on various conditions and constraints.
Planning the joint angle track of the space multi-joint robot mainly comprises the steps of firstly representing a change curve of a joint angle into an analytic form, generally a polynomial function or a variant thereof, and converting optimization of the joint angle into optimization of a polynomial coefficient; then, determining the relation of each secondary coefficient according to the conditions of the boundary values (such as initial joint angle, initial joint angular velocity, initial joint angular acceleration, terminal joint angle, terminal joint angular velocity, terminal joint angular acceleration and the like), thereby reducing the number of unknown quantities and simplifying the optimization difficulty; finally, a specific numerical optimization method is used to solve the possible optimal solution that satisfies the constraint. The optimization algorithm may generally employ a path search algorithm, such as: particle Swarm Optimization (PSO), Differential Evolution (DE), Genetic Algorithm (GA), and the like.
Various search algorithms have disadvantages such as search stagnation, premature convergence, unstable results, poor repeatability, susceptibility to initial values and parameters, and the like.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a space multi-joint robot path planning method based on differential evolution particle swarm optimization, aiming at overcoming the defects in the prior art, through combining PSO and DE for cross application, the population scale is improved through phase change on the premise of not increasing the operation time too much, and the accuracy and the stability of the multi-joint robot joint angle path planning result are improved.
The invention adopts the following technical scheme:
a space multi-joint robot path planning method based on differential evolution particle swarm algorithm includes the steps of firstly establishing a kinematics and dynamics model of change of joint angles of a mechanical arm of a space multi-joint robot, then establishing a model of disturbance of collision of the multi-joint robot on a base, representing a change track curve of the joint angles as a polynomial function about time t, and establishing a total fitness function.
Specifically, a kinematics and dynamics model of the change of the joint angle of the mechanical arm is established according to parameters of the mechanical arm DH, and the kinematics and dynamics model comprises a position-level positive kinematics transfer matrix T, a speed-level positive kinematics transfer matrix J, a dynamics coefficient matrix H and a base disturbance model.
Further, the transfer matrix T of the position-level positive kinematics is as follows:
Figure GDA0002535177330000021
wherein the content of the first and second substances,
Figure GDA0002535177330000022
rarepresenting a position vector in the a-joint coordinate system, rbRepresents the position vector in the b-system,
Figure GDA0002535177330000023
which represents a rotational transformation matrix from a coordinate system b to a coordinate system a, is a unitary matrix of 3 × 3,
Figure GDA0002535177330000024
and (b) the position of the origin of the b system in the a coordinate system.
Further, the velocity step positive kinematic transfer matrix J is as follows:
Figure GDA0002535177330000025
wherein v ise∈R3×1Representing the translational movement velocity, omega, of the end-effectore∈R3×1The rotational speed of the end effector is indicated,
Figure GDA0002535177330000026
shows the rotational speeds of 6 joint angles, J (q) ∈ R6×6,J(q)＝[J1J2...J6]，
Figure GDA0002535177330000027
ξiIn the ith joint axis direction, pi→nIs the displacement vector of the ith joint to the terminal joint.
Further, the kinetic coefficient matrix H is as follows:
Figure GDA0002535177330000031
Figure GDA0002535177330000032
the six-dimensional matrix represents the inertia tensor of the base as follows:
Figure GDA0002535177330000033
wherein M represents the total mass of the system, E is a three-dimensional unit matrix, HωIs the angular velocity inertia matrix of the base, rogRepresenting the displacement from the center of mass of the base to the center of mass of the system, rog＝[x,y,z]，HbRepresenting the base inertia matrix, HφIs the tensor of inertia of the mechanical arm,
Figure GDA0002535177330000034
to couple the inertia matrix, Fe＝[fe,τe]Representing external forces and moments, τ, acting on the end-effectormRepresenting the torque made by each joint motor,
Figure GDA0002535177330000035
and
Figure GDA0002535177330000036
are respectively provided withJacobian matrix representing the base and arm, cv、cωAnd cmAre respectively nonlinear terms related to the joint angular velocity in the equation,
Figure GDA0002535177330000037
respectively base acceleration, base angular acceleration, joint angular acceleration, fb、τb、τmThe external force acting on the base, the external moment acting on the base and the joint moment of the mechanical arm are respectively.
Further, the generalized force of six-dimensional vector perturbation is as follows:
Figure GDA0002535177330000038
the base disturbance model is as follows:
Figure GDA0002535177330000039
wherein, is a variation symbol, ωbAs the angular velocity of the base, is,
Figure GDA00025351773300000310
is the angular velocity inertia matrix of the generalized base, rogRepresenting the displacement from the center of mass of the base to the center of mass of the system, rog＝[x,y,z]，HbA matrix of the inertias of the base is represented,
Figure GDA00025351773300000311
is the inertia tensor of the generalized mechanical arm,
Figure GDA0002535177330000041
respectively representing the Jacobian matrixes of the generalized base and the generalized mechanical arm, e is a collision recovery coefficient, vrIs the relative velocity of the end effector and the target before impact, N is the normal vector of the impact, DmAn inertia matrix, D, which is a Jacobian matrix of the robot armtIs an inertia matrix of the target jacobian matrix.
Specifically, the method for establishing the disturbance model of the multi-joint robot collision on the base specifically comprises the following steps:
representing the final disturbance quantity as a function of the joint angle configuration, the collision relative speed and the collision direction; representing the energy consumption of the joint angle change process as a function of the joint angular velocity;
the disturbance model is as follows:
ωb＝f(θ,N,vr)
the energy consumption model is as follows:
Figure GDA0002535177330000042
wherein N is a normal vector of a collision position; omegabIs the angular velocity of the base, t0Is an initial time tfIn order to terminate the time of day,
Figure GDA0002535177330000043
is the joint angular velocity.
Specifically, the joint angle change fitting function is as follows:
θi(t)＝ai5t5+ai4t4+ai3t3+ai2t2+ai1t+ai0
wherein i ═ 1,2,3, ·, n, ai0、ai1、ai2、ai3、ai4、ai5Is the coefficient to be found, the initial and end conditions are as follows:
Θ(t0)＝Θ0,T0e(tf)＝TMinDisturbe
Figure GDA0002535177330000044
Figure GDA0002535177330000045
wherein, theta (t)0)、
Figure GDA0002535177330000046
And
Figure GDA0002535177330000047
are respectively the starting time (t)0) The joint angle, the joint angular velocity and the joint angular acceleration of the mechanical arm; theta0、
Figure GDA0002535177330000048
And
Figure GDA0002535177330000049
are all given constant vectors; t is0e(tf)＝TMinDisturbeIndicates the termination time (t)f) Is configured to minimize collision disturbances;
Figure GDA00025351773300000410
and
Figure GDA00025351773300000411
respectively, indicates the termination time (t)f) Joint angular velocity and joint angular acceleration of;
Figure GDA00025351773300000412
and
Figure GDA00025351773300000413
are given constant vectors.
Specifically, after a stagnation point appears for the first time, a population of the particle swarm optimization is used for initializing a differential evolution algorithm and starting variation, intersection and selection operations of the population, two populations are operated in parallel, when the stagnation point appears again after a certain step number operation, part of individuals of the two populations are exchanged, and the like.
Specifically, the overall fitness function is characterized as follows:
fpath＝kdwb|f(θ,N,vr)|+kene|Energy|
the constraints are:
kIKR|qR-qR0|+kIKr|r-r0|＜
therein, get 10-4The initial population size of the particle swarm algorithm is 800, the iteration step number is 450, the inertia coefficient w is 0.8, the self-learning factor c1 is 0.5, the population learning factor c2 is 0.5, and the stagnation point is characterized by fpath(tk)-fpath(tk-m) When m is 0, m is 5.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention discloses a space multi-joint robot path planning method based on a differential evolution particle swarm algorithm, which is characterized in that a robot joint angle is expressed in a polynomial form, coefficients of the polynomial are taken as individual characteristic variables, an objective function depends on performance coordinates and can be minimum in energy consumption, shortest in time and the like, obstacles can be set, and an optimal path is searched by utilizing a combined random search algorithm; the combined algorithm means that firstly, the particle swarm algorithm is used for searching the optimal solution, when the stagnation point of the population occurs, the differential evolution algorithm is used for randomly reinitializing partial individuals of the population so as to avoid possible suboptimal solutions and improve the solving reliability.
Furthermore, a position-level positive kinematics transmission matrix T, a speed-level positive kinematics transmission matrix J and a dynamics coefficient matrix H are time-varying and are determined by DH parameters and joint rotation angles, the time-varying position-level positive kinematics transmission matrix T, the speed-level positive kinematics transmission matrix J and the dynamics coefficient matrix H reflect the motion state and the dynamic characteristics of the mechanical arm, and have great effects in coordinate conversion and motion planning on the mechanical arm, and the establishment of a base disturbance model equation is used for establishing the relation between the relative speed of the end effector and a target at the base disturbance and collision time and the configuration of the mechanical arm, and the optimal configuration of the end of the mechanical arm is obtained according to the relation.
Furthermore, the conversion relation of the same position vector in the space in the coordinate systems of the two adjacent joints is established through an equation, and the conversion matrixes T of all the adjacent joints are multiplied to obtain the conversion relation from the position vector in the coordinate system of the end effector to the coordinate system of the base and even to the inertial reference system.
Further, the relationship between the joint angular velocity and the velocity and angular velocity of the end effector can be obtained by the jacobian matrix j (q). The constraint of joint angular velocity can be inferred inversely, taking into account the tip velocity and angular velocity constraints.
Further, kinetic coefficients are the dominant and decisive terms, and nonlinear terms are generally small and often ignored. The motion state changes of all parts of the system, including all joints and the base, under the action of external force and external moment of the system can be obtained through equations.
Further, the base disturbance model equation is established for establishing the relationship between the relative speed between the end effector and the target at the base disturbance and collision time and the configuration of the mechanical arm, and the optimal configuration of the end of the mechanical arm is obtained based on the relationship.
Further, after a disturbance model and an energy consumption model are established, a fitness function of the particle swarm algorithm can be obtained.
Further, the joint angle change fitting function is used for quantifying the change of the joint angle of the mechanical arm to form a continuous smooth function with time correlation, so that the change of the angular velocity of the joint can be represented by a derivative of the joint angle change fitting function, and the change of the angular acceleration of the joint can be represented by a second derivative.
Furthermore, the particle swarm algorithm is known as fast convergence speed, but the algorithm is easy to fall into a local optimal solution, so that the final result is poor. A Differential Evolution Algorithm (DE) is an efficient global optimization Algorithm, including mutation, hybridization, and selection operations, which is relatively difficult to fall into local optimality, and the final result is better, but the convergence rate at the early stage is not as good as that of the particle swarm Algorithm. Therefore, the differential evolution process is introduced after the particle swarm optimization is stopped, the final result of the particle swarm optimization can be optimized, and meanwhile, the early-stage faster convergence speed is kept.
Furthermore, the fitness function or the index function and the objective function are indexes and necessary factors for solving by the particle swarm algorithm and are basis for comparing the advantages and disadvantages of the probe points by the particle swarm algorithm. The fitness function is set to be necessary for solving the particle swarm optimization. The fitness function is established based on minimum collision disturbance and minimum energy consumption of the mechanical arm, and the minimum disturbance, namely the optimal configuration at the termination moment, and the minimum energy consumption, namely the minimum total rotation quantity of the joint angle, are ensured in the solving process. The constraint is to ensure that the end effector reaches the target at the termination time with a specific pose, which is a prerequisite for capture and collision.
In conclusion, the invention utilizes the particle swarm algorithm after differential evolution correction to carry out the capture path planning of the space manipulator, the planning aims at enabling the manipulator end effector to reach a fixed position and a posture, and the manipulator configuration at the termination time is controlled, so that the disturbance of the collision of the end effector and the target on the base is minimum, and the total energy consumption of the running track is minimum.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
Fig. 1 is a graph of the variation of the fitness function of the combinatorial algorithm with the number of iterations.
Detailed Description
The invention provides a space multi-joint robot path planning method based on differential evolution particle swarm algorithm, which comprises the steps of firstly establishing a kinematics and dynamics model of mechanical arm joint angle change, then establishing a model of disturbance of multi-joint robot collision on a base, expressing a change track curve of a joint angle as a polynomial function about time t, establishing a total fitness function, firstly using the particle swarm algorithm in an iterative solution method, starting the differential evolution algorithm when a stagnation point occurs in the method, and exchanging part of individuals of two algorithm populations to change the phase, enlarge the population scale and improve the solution precision.
The invention discloses a space multi-joint robot path planning method based on a differential evolution particle swarm algorithm, which comprises the following steps of:
s1, establishing a kinematics and dynamics model of the change of the joint angle of the mechanical arm according to the parameters of the mechanical arm DH, wherein the kinematics and dynamics model comprises a position-level positive kinematics transfer matrix T, a speed-level positive kinematics transfer matrix J, a dynamics coefficient matrix H and a base disturbance model equation;
taking a six-joint robot as an example, the multi-joint robot position-level positive kinematics model is as follows:
Figure GDA0002535177330000071
Figure GDA0002535177330000072
wherein the content of the first and second substances,
Figure GDA0002535177330000073
rarepresenting a position vector in the a-joint coordinate system, rbRepresents the position vector in the b-system,
Figure GDA0002535177330000081
which represents a rotational transformation matrix from a coordinate system b to a coordinate system a, is a unitary matrix of 3 × 3,
Figure GDA0002535177330000082
and (b) the position of the origin of the b system in the a coordinate system.
The velocity level positive kinematics model is as follows:
Figure GDA0002535177330000083
Figure GDA0002535177330000084
wherein v ise∈R3×1Representing the translational movement velocity, omega, of the end-effectore∈R3×1The rotational speed of the end effector is indicated,
Figure GDA0002535177330000085
representing the rotational speeds of 6 joint angles, the Jacobian matrix J (q) ∈ R6×6,J(q)＝[J1J2...J6]，
Figure GDA0002535177330000086
Wherein, ξiIn the ith joint axis direction, pi→nIs the displacement vector of the ith joint to the terminal joint.
The kinetic model is as follows:
Figure GDA0002535177330000087
Figure GDA0002535177330000088
the six-dimensional matrix represents the inertia tensor of the base as follows:
Figure GDA0002535177330000089
wherein HbRepresenting the base inertia matrix, M the total mass of the system, E the three-dimensional identity matrix, HωIs the angular velocity inertia matrix of the base, rogRepresents the displacement from the center of mass of the base to the center of mass of the system, and if rog＝[x,y,z]Then r isogThe following were used:
Figure GDA00025351773300000810
wherein the content of the first and second substances,
Figure GDA0002535177330000091
is the tensor of inertia of the mechanical arm,
Figure GDA0002535177330000092
to couple the inertia matrix, Fb＝[fb,τb]Is a six-dimensional vector representation of external forces and moments acting on the base, for the same reason Fe＝[fe,τe]Representing external forces and moments, τ, acting on the end-effectormRepresenting the torque made by each joint motor,
Figure GDA0002535177330000093
and
Figure GDA0002535177330000094
jacobian matrix representing the base and arm, respectively, cv、cωAnd cmAre respectively nonlinear terms related to the joint angular velocity in the equation,
Figure GDA0002535177330000095
respectively base acceleration, base angular acceleration, joint angular acceleration, fb、τb、τmThe external force acting on the base, the external moment acting on the base and the joint moment of the mechanical arm are respectively.
The first column of the second and third rows is eliminated using the first row of equation set (5), resulting in the following equation set:
Figure GDA0002535177330000096
wherein the content of the first and second substances,
Figure GDA0002535177330000097
Figure GDA0002535177330000098
and (3) instantaneously taking a variation of the system collision, neglecting a smaller nonlinear term c, and obtaining a base disturbance model as follows:
Figure GDA0002535177330000099
wherein, is a variation symbol, ωbAs the angular velocity of the base, is,
Figure GDA00025351773300000910
is the angular velocity inertia matrix of the generalized base, rogRepresenting from base centroid to system centroidA displacement of rog＝[x,y,z]，HbA matrix of the inertias of the base is represented,
Figure GDA00025351773300000911
is the inertia tensor of the generalized mechanical arm,
Figure GDA00025351773300000912
respectively representing the Jacobian matrixes of the generalized base and the generalized mechanical arm, e is a collision recovery coefficient, vrIs the relative velocity of the end effector and the target before impact, N is the normal vector of the impact, DmAn inertia matrix, D, which is a Jacobian matrix of the robot armtIs an inertia matrix of the target jacobian matrix.
The six-dimensional vector disturbance generalized force is as follows:
Figure GDA00025351773300000913
s2, establishing a model of base disturbance caused by multi-joint robot collision, and expressing the final disturbance quantity as a function of joint angle configuration, collision relative speed and collision direction; representing the energy consumption of the joint angle change process as a function of the joint angular velocity;
the disturbance model is as follows:
ωb＝f(θ,N,vr)
the energy consumption model is as follows:
Figure GDA0002535177330000101
wherein N is a normal vector of a collision position; omegabIs the angular velocity of the base, t0Is an initial time tfIn order to terminate the time of day,
Figure GDA0002535177330000102
is the joint angular velocity.
S3, representing a change trajectory curve of the joint angle as a polynomial function related to time t, wherein partial coefficients can be obtained by using a undetermined coefficient method and initial and terminal conditions;
for a six degree-of-freedom robotic arm (n ═ 6), the joint angle change fitting function can be expressed as follows:
θi(t)＝ai5t5+ai4t4+ai3t3+ai2t2+ai1t+ai0
wherein i ═ 1,2,3, ·, n, ai0、ai1、ai2、ai3、ai4、ai5Is the coefficient to be found, the initial and end conditions are as follows:
Figure GDA0002535177330000103
wherein, theta (t)0)、
Figure GDA0002535177330000104
And
Figure GDA0002535177330000105
are respectively the starting time (t)0) The joint angle, the joint angular velocity and the joint angular acceleration of the mechanical arm; theta0、
Figure GDA0002535177330000106
And
Figure GDA0002535177330000107
are all given constant vectors; t is0e(tf)＝TMinDisturbeIndicates the termination time (t)f) Is configured to minimize collision disturbances;
Figure GDA0002535177330000108
and
Figure GDA0002535177330000109
respectively, indicates the termination time (t)f) Joint angular velocity and joint angular acceleration of;
Figure GDA00025351773300001010
and
Figure GDA00025351773300001011
are given constant vectors.
S4, taking independent coefficients of the polynomial function as independent variables of population individuals, carrying out weighted average on the disturbance quantity, the energy consumption and the difference value between the terminal position matrix Trf and the target position Tf to obtain a fitness function, and solving by using a particle swarm algorithm; when a stagnation point occurs in the particle swarm algorithm operation, a differential evolution algorithm is started to reinitialize the population so as to improve the calculation efficiency and avoid the local optimal solution.
The overall fitness function is as follows:
fpath＝kdwb|f(θ,N,vr)|+kene|Energy| (9)
the constraints are:
kIKR|qR-qR0|+kIKr|r-r0|＜ (10)
get 10-4The initial population size of the particle swarm algorithm is 800, the iteration step number is 450, the inertia coefficient w is 0.8, the self-learning factor c1 is 0.5, the population learning factor c2 is 0.5, and the stagnation point is characterized by fpath(tk)-fpath(tk-m) When m is 0, m is 5.
After the stagnation point appears for the first time, the population of the particle swarm algorithm is used for initializing the differential evolution algorithm and starting the variation, crossing and selection operations of the population, the two populations are operated in parallel, when the stagnation point appears again after a certain step number of operation, part of individuals of the two populations are exchanged, and the like.
The disturbance of collision to the base is considered to be minimum, so that the safety of the space manipulator in the actual task execution process is higher, the disturbance to the base is small, the control pressure and the difficulty of the spacecraft body attitude stabilization control system are reduced, the feasibility and the safety of the task are improved, and the fuel of the spacecraft body attitude control system is saved.
The rotation energy consumption of the mechanical arm is minimum, so that the energy consumption of the joint angle rotation in the actual execution task of the space mechanical arm is less, and the energy of the mechanical arm and the service life of a joint motor are saved.
By using the combined algorithm (namely restarting the particle swarm algorithm after stagnation by using the differential evolution idea), the advantage of high convergence speed of the particle swarm algorithm is reserved, and the quality of the final global solution of the particle swarm algorithm is improved. The convergence speed in the planning process is high, the quality of the global solution is good, and the local optimal solution is not easy to fall into.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, one of the results is the simple particle swarm algorithm, and the other is the particle swarm algorithm modified by the differential evolution method. It can be seen that the modified algorithm can achieve a lower fitness function value than the original algorithm, which indicates that the modified algorithm can jump out of the local optimal solution of the original algorithm to obtain a better result.
The particle swarm algorithm is famous for fast convergence speed, but the algorithm is easy to fall into a local optimal solution, so that the final result is poor. A Differential Evolution Algorithm (DE) is an efficient global optimization Algorithm, including mutation, hybridization, and selection operations, which is relatively difficult to fall into local optimality, and the final result is better, but the convergence rate at the early stage is not as good as that of the particle swarm Algorithm. Therefore, the differential evolution process is introduced after the particle swarm optimization is stopped, the final result of the particle swarm optimization can be optimized, and meanwhile, the early-stage faster convergence speed is kept.
By using the combined algorithm (namely restarting the particle swarm algorithm after stagnation by using the differential evolution idea), the advantage of high convergence speed of the particle swarm algorithm is reserved, and the quality of the final global solution of the particle swarm algorithm is improved. The convergence speed in the planning process is high, the quality of the global solution is good, and the local optimal solution is not easy to fall into.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (10)

1. A space multi-joint robot path planning method based on differential evolution particle swarm algorithm is characterized in that a kinematics and dynamics model of joint angle change of a mechanical arm of a space multi-joint robot is established at first, then a model of disturbance of multi-joint robot collision on a base is established, a change track curve of a joint angle is expressed as a polynomial function about time t, a total fitness function is established, in an iterative solution method, a particle swarm algorithm is used at first, when a stagnation point occurs in the method, a differential evolution algorithm is started, and partial individuals of two algorithm groups are exchanged to change phase and expand the group scale, so that the space multi-joint robot path planning is completed.
2. The method for space multi-joint robot path planning based on differential evolution particle swarm optimization according to claim 1, wherein kinematics and dynamics models of mechanical arm joint angle change are established according to mechanical arm DH parameters, and comprise a position-level positive kinematics transfer matrix T, a speed-level positive kinematics transfer matrix J, a dynamics coefficient matrix H and a base disturbance model.
3. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 2, wherein a transmission matrix T of position-level positive kinematics is as follows:
Figure FDA0002535177320000011
wherein the content of the first and second substances,
Figure FDA0002535177320000012
rarepresenting a position vector in the a-joint coordinate system, rbRepresenting the position vector in the b-joint coordinate system,
Figure FDA0002535177320000013
represents a rotational transformation matrix from the b-joint coordinate system to the a-joint coordinate system, which is a unitary matrix of 3 × 3,
Figure FDA0002535177320000014
and (b) indicating the position of the origin of the b joint coordinate system in the a joint coordinate system.
4. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 3, wherein a velocity level positive kinematics transfer matrix J is as follows:
Figure FDA0002535177320000015
wherein v ise∈R3×1Representing the translational movement velocity, omega, of the end-effectore∈R3×1The rotational speed of the end effector is indicated,
Figure FDA0002535177320000016
shows the rotational speeds of 6 joint angles, J (q) ∈ R6×6,J(q)＝[J1J2...J6]，
Figure FDA0002535177320000017
ξiIn the ith joint axis direction, pi→nIs the displacement vector of the ith joint to the terminal joint.
5. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 2, wherein a kinetic coefficient matrix H is as follows:
Figure FDA0002535177320000021
Figure FDA0002535177320000022
the six-dimensional matrix represents the inertia tensor of the base as follows:
Figure FDA0002535177320000023
wherein M represents the total mass of the system, E is a three-dimensional unit matrix, HωIs the angular velocity inertia matrix of the base, rogRepresenting the displacement from the center of mass of the base to the center of mass of the system, rog＝[x,y,z]，HbRepresenting the base inertia matrix, HφIs the tensor of inertia of the mechanical arm,
Figure FDA0002535177320000024
to couple the inertia matrix, Fe＝[fe,τe]Representing external forces and moments, τ, acting on the end-effectormRepresenting the torque made by each joint motor,
Figure FDA0002535177320000025
and
Figure FDA0002535177320000026
jacobian matrix representing the base and arm, respectively, cv、cωAnd cmAre respectively nonlinear terms related to the joint angular velocity in the equation,
Figure FDA0002535177320000027
respectively base acceleration, base angular acceleration, joint angular acceleration, fb、τb、τmThe external force acting on the base, the external moment acting on the base and the joint moment of the mechanical arm are respectively.
6. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 2, wherein the six-dimensional vector disturbance generalized force is as follows:
Figure FDA0002535177320000028
the base disturbance model is as follows:
Figure FDA0002535177320000029
wherein, is a variation symbol, ωbAs the angular velocity of the base, is,
Figure FDA00025351773200000210
is the angular velocity inertia matrix of the generalized base, rogRepresenting the displacement from the center of mass of the base to the center of mass of the system, rog＝[x,y,z]，HbA matrix of the inertias of the base is represented,
Figure FDA00025351773200000211
is the inertia tensor of the generalized mechanical arm,
Figure FDA0002535177320000031
respectively representing the Jacobian matrixes of the generalized base and the generalized mechanical arm, e is a collision recovery coefficient, vrIs the relative velocity of the end effector and the target before impact, N is the normal vector of the impact, DmAn inertia matrix, D, which is a Jacobian matrix of the robot armtIs an inertia matrix of the target jacobian matrix.
7. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 1, wherein the method for establishing the base disturbance model of the multi-joint robot collision comprises the following specific steps:
representing the final disturbance quantity as a function of the joint angle configuration, the collision relative speed and the collision direction; representing the energy consumption of the joint angle change process as a function of the joint angular velocity;
the disturbance model is as follows:
ωb＝f(θ,N,vr)
the energy consumption model is as follows:
Figure FDA0002535177320000032
wherein N is a normal vector of a collision position; omegabIs the angular velocity of the base, t0Is an initial time tfIn order to terminate the time of day,
Figure FDA0002535177320000033
is the joint angular velocity.
8. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 1, wherein a joint angle change fitting function is as follows:
θi(t)＝ai5t5+ai4t4+ai3t3+ai2t2+ai1t+ai0
wherein i ═ 1,2,3, ·, n, ai0、ai1、ai2、ai3、ai4、ai5Is the coefficient to be found, the initial and end conditions are as follows:
Θ(t0)＝Θ0,T0e(tf)＝TMinDisturbe
Figure FDA0002535177320000034
Figure FDA0002535177320000035
wherein, theta (t)0)、
Figure FDA0002535177320000036
And
Figure FDA0002535177320000037
are respectively the starting time (t)0) The joint angle, the joint angular velocity and the joint angular acceleration of the mechanical arm; theta0、
Figure FDA0002535177320000038
And
Figure FDA0002535177320000039
are all given constant vectors; t is0e(tf)＝TMinDisturbeIndicates the termination time (t)f) Is configured to minimize collision disturbances;
Figure FDA0002535177320000041
and
Figure FDA0002535177320000042
respectively, indicates the termination time (t)f) Joint angular velocity and joint angular acceleration of;
Figure FDA0002535177320000043
and
Figure FDA0002535177320000044
are given constant vectors.
9. The method for planning the path of the space multi-joint robot based on the differential evolution particle swarm algorithm according to claim 1, wherein after a stagnation point appears for the first time, the group of the particle swarm algorithm is used for initializing the differential evolution algorithm and starting the variation, crossing and selection operations thereof, the two groups are operated in parallel, when the stagnation point appears again after a certain number of steps of operation, part of individuals of the two groups are exchanged, and so on.
10. The space multi-joint robot path planning method based on the differential evolution particle swarm algorithm according to claim 7, wherein the total fitness function is as follows:
fpath＝kdwb|f(θ,N,vr)|+kene|Energy|
the constraints are:
kIKR|qR-qR0|+kIKr|r-r0|＜
therein, get 10-4The initial population size of the particle swarm algorithm is 800, the iteration step number is 450, the inertia coefficient w is 0.8, the self-learning factor c1 is 0.5, the population learning factor c2 is 0.5, and the stagnation point is characterized by fpath(tk)-fpath(tk-m) When m is 0, m is 5.
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