A high-energy-efficiency trajectory optimization method for a robot arm

Abstract

The application discloses a kind of high-energy efficiency trajectory optimization methods of mechanical arm.S1.Set mechanical arm has N Discrete trajectory type value point Q i , the limit minimum value of time interval between each adjacent type value point is calculated h i,0 ;S2.The degree of repetition at the end of node vector is set to q +1, based on N-1 time interval, construct normalized non-uniform node u r ;S3.Get trajectory curve with mechanical arm joint jerk motion constraint;S4.Judge whether the motion state of each joint of mechanical arm on the trajectory segment between every two adjacent type value points Q i And Q i+1 Always meet motion constraint;S5.If meeting motion constraint, then calculate the boundary value of multidimensional decision space of mechanical arm trajectory and execute step S6;S6.In the boundary limited range of decision space, initialize a group of particles;The initial position of all particle individuals is set as linear uniform distribution, and the initial speed of all particle individuals is set as random distribution.The application solves the problems of low constraint boundary exploration efficiency and long time consumption caused by insufficient use of infeasible solution information.

Description

Technical Field

[0001] This invention relates to the field of robotic arm trajectory optimization technology, and in particular to a high-efficiency trajectory optimization method for robotic arms. Background Technology

[0002] The purpose of robotic arm trajectory optimization is to generate a smooth motion state trajectory connecting discrete path nodes for the robotic arm joint tracking controller, and to iteratively optimize the trajectory parameters so that the robotic arm can efficiently reach the target pose and perform the task by following the reference trajectory. To improve the efficiency of the robotic arm, the state trajectory should minimize the trajectory time from the initial configuration to the target configuration in each operation. Furthermore, considering the limited power supply, the robotic arm should maximize energy efficiency and minimize energy consumption. However, minimizing trajectory time and minimizing energy consumption are conflicting performance objectives; there is no solution that simultaneously optimizes both. A trade-off must be made between these objectives to achieve a comprehensive optimum, minimizing both trajectory time and energy consumption. Traditional multi-objective trajectory optimization methods typically transform the multi-objective optimization problem into a single-objective optimization problem through non-negative weighted summation, and then solve the single-objective optimization problem. This requires pre-setting the relative importance weights between the performance indicators of each objective. However, in practical optimization problems, this weight information is difficult to obtain accurately in advance and can only be adjusted through trial and error based on experience. Moreover, single-objective optimization problems can only yield one optimal solution and cannot reflect the correlation between multiple objectives, resulting in poor interpretability of the results.

[0003] In recent years, scholars both domestically and internationally have successively proposed bio-inspired multi-objective optimization algorithms, such as multi-objective particle swarm optimization (PSO). These algorithms simulate complex foraging behaviors in natural biological groups, such as flocks of birds, based on cooperation among multiple simple individuals. By solving these problems through multi-objective collaborative optimization, non-dominated feasible solution sets and Pareto fronts are obtained, significantly enhancing interpretability. PSO adaptively iterates to find better solutions through a particle swarm information-sharing mechanism and a parallel exploration mechanism among multiple particles. It is unaffected by the shape of the objective space and the characteristics of the cost function, and is widely used in multi-objective optimization problems. However, existing PSO algorithms set the search range of the decision space very broadly, resulting in low optimization efficiency. Furthermore, existing PSO algorithms directly discard infeasible solutions during the exploration process, using only feasible solution information to guide the particle swarm's optimization. This leads to strong blindness in the optimization process, low efficiency in boundary exploration, and long search time, indicating significant room for improvement in optimization efficiency. Summary of the Invention

[0004] The purpose of this invention is to provide a high-efficiency trajectory optimization method for robotic arms. This invention solves the problems of low efficiency in particle swarm optimization due to the very broad search range of the decision space in existing multi-objective trajectory optimization algorithms, as well as low efficiency and long time consumption in constraint boundary exploration caused by the incomplete utilization of infeasible solution information.

[0005] The technical solution of this invention. A high-efficiency trajectory optimization method for a robotic arm, comprising the following steps: S1. Assume the robotic arm has N A discrete trajectory-type value point Q i Calculate the minimum limit of the time interval between each adjacent type value point. h i,0 ; S2. Set the repetition at both ends of the node vector to 1. q +1, based on N-1 time intervals Construct normalized non-uniform nodes u r This leads to the normalization of non-uniform node vectors. U ={ u r}; S3. Based on vector U Solving B-spline basis functions B i,q ( u The value of ) and then combined N indivual Q i Construct constraint equations and perform inverse calculations. q Control points of the second-order B-spline curve P i , to conduct based q The trajectory planning of the robot arm using a B-spline curve yields a trajectory curve with motion constraints of joint angular displacement, joint angular velocity, joint angular acceleration, and joint angular jerk. S4. Determine the value points of each pair of adjacent type points. Q i and Q i+1 On the trajectory segment, does the motion state of each joint of the robotic arm always satisfy the aforementioned motion constraints? S5. If the motion constraints are satisfied, calculate the boundary value of the multidimensional decision space of the robotic arm trajectory and execute step S6; S6. Initialize a group of particles within the boundary of the decision space. The position of each particle represents a potential solution to the robot arm trajectory optimization problem. Set the initial position of all individual particles to a linear uniform distribution and the initial velocity of all individual particles to a random distribution. S7. Perform constraint violation checks on all solutions obtained from particle swarm optimization and store feasible solutions in the main memory pool. In the middle, infeasible solutions are stored in the secondary memory pool. In the middle; through non-dominated sorting The relative merits of all feasible solutions are quantitatively compared to obtain non-dominated feasible solutions. Then, by sorting by sparseness, the non-dominated feasible solution with the largest current sparseness is selected as the optimal exploration position of the swarm, guiding the particle swarm to accelerate the exploration of the region where the current non-dominated feasible solution is sparsely distributed. S8. All particles in the particle swarm are at their current optimal positions. and the optimal position of the group Adjust your exploration speed under guidance Then, the particle positions are iteratively updated in the decision space. And share the currently found optimal position information of an individual with other particles; S9. Targeting Each infeasible solution ,choose The feasible solution that is closest to its decision space Connect them and grow a new solution among them. ;like Constraint violation degree If it is not zero, then use replace In . In the aforementioned high-efficiency trajectory optimization method for robotic arms, in S4, if there is a violation of constraints, the time interval between the two model points corresponding to this trajectory is increased accordingly.

[0006] In the aforementioned high-efficiency trajectory optimization method for robotic arms, if the motion constraints are not met in step S5, steps S2 to S4 are executed again based on the updated time interval to reconstruct the normalized non-uniform node vector. U And plan the motion state trajectory curve of the robotic arm.

[0007] In the aforementioned high-efficiency trajectory optimization method for robotic arms, in S9, if Constraint violation degree If it is zero, then... Add to middle.

[0008] The aforementioned high-efficiency trajectory optimization method for robotic arms also includes S10, which determines whether the particle swarm iteration count has reached the maximum iteration count. If the maximum number of iterations has not been reached, continue executing steps S6 to S9.

[0009] In the aforementioned high-efficiency trajectory optimization method for robotic arms, if the following conditions are met... End the iteration and output. The Pareto front is composed of all nondominated feasible solutions and their objective function values.

[0010] In the aforementioned high-efficiency trajectory optimization method for robotic arms, in S1,

[0011] in, Indicates the joints of the robotic arm Maximum permissible angular velocity, .

[0012] In the aforementioned high-efficiency trajectory optimization method for robotic arms, in S2,

[0013] in, The total duration of the robotic arm's motion trajectory, i.e. .

[0014] In the aforementioned high-efficiency trajectory optimization method for robotic arms, in S2, .

[0015] In the aforementioned high-efficiency trajectory optimization method for robotic arms, in S3, Robotic arm joint angular displacement trajectory curve

[0016] Robotic arm joint angular velocity trajectory curve

[0017] Robotic arm joint angular acceleration trajectory curve

[0018] Robotic arm joint angle acceleration trajectory curve .

[0019] The beneficial effects of this invention are as follows: ① To address the problem that existing multi-objective particle swarm optimization algorithms have low efficiency in particle swarm exploration and optimization due to setting the decision space search range too broadly, this invention proposes a constraint-guided adaptive boundary adjustment strategy. By selectively adjusting the time interval between the value points that violate the constraints in small increments, it achieves precise adaptive adjustment of the boundary of the multi-dimensional decision space, reduces the dependence on the decision-maker's experience in setting parameters, improves the efficiency of particle swarm optimization, and thus greatly shortens the convergence time of iterative optimization.

[0020] ② To address the problems of low efficiency and long time consumption in constraint boundary exploration caused by the failure of existing multi-objective particle swarm optimization algorithms to fully utilize infeasible solution information, this invention proposes a complementary dual-memory pool heuristic edge expansion strategy. By simultaneously constructing two external memory pools (the main memory pool is used to store the set of non-dominated feasible solutions, and the secondary memory pool is used to store the set of non-dominated infeasible solutions) to connect the feasible and infeasible regions, this invention fully utilizes the information of infeasible solutions near the constraint boundary and heuristically guides the particle swarm to efficiently explore the region approaching the constraint boundary, greatly enhancing the constraint boundary exploration efficiency of the particle swarm and thus quickly obtaining more high-quality non-dominated solutions.

[0021] In summary, this invention, using robotic arms as the application target and addressing the need for high-energy-efficiency trajectory optimization under multiple constraints, proposes a constraint-guided adaptive boundary adjustment strategy and a complementary dual-memory pool heuristic edge expansion strategy. It designs a high-energy-efficiency trajectory optimization method for robotic arms based on these two strategies, improving the efficiency of particle swarm optimization iterative search, shortening the iteration convergence time, and enhancing the constraint boundary exploration efficiency of the particle swarm. This allows for the rapid acquisition of more high-quality non-dominated solutions, effectively meeting the requirements for high-energy-efficiency trajectory optimization of robotic arms and demonstrating significant engineering application value. Attached Figure Description

[0022] Figure 1 This is a flowchart of a high-energy-efficiency trajectory optimization method for robotic arms based on constraint-guided boundary adjustment and dual-memory-pool heuristic edge extension strategies in an embodiment of the present invention; Figure 2 A schematic diagram illustrating the efficient approximation of the region near the constraint boundary by particle swarm optimization inspired by dual memory pools. Figure 3 A schematic diagram of the evolution curve of the area of ​​the dominated region during the algorithm iteration process. Detailed Implementation

[0023] Example 1. A high-energy-efficiency trajectory optimization method for robotic arms based on constraint-guided boundary adjustment and dual-memory-pool heuristic edge extension strategies, such as... Figures 1-3 As shown, the steps are as follows: S1, for a given robotic arm A discrete trajectory-type value point First, the minimum time interval between adjacent model points is calculated by setting all joints of the robotic arm to always maintain their maximum movement speed. h i,0 for

[0024] in, Indicates the joints of the robotic arm Maximum permissible angular velocity, .

[0025] S2, in order to make The starting and ending points of the second-order B-spline trajectory curve coincide with the first and last data points, respectively. The repetition degree at both ends of the node vector is set to... ,based on time interval Construct normalized non-uniform nodes for

[0026] in, The total duration of the robotic arm's motion trajectory, i.e. .

[0027] Thus, we obtain from Nodes Normalized non-uniform node vector U for

[0028] S3. Solve for the B-spline basis function based on the normalized non-uniform node vector. value u , u These are the normalized interpolation parameters of the B-spline curve, satisfying... u ∈[0,1]. Then, combined with Individual value points Construct constraint equations and perform inverse calculations. Control points of the second-order B-spline curve , to conduct based Robotic arm trajectory planning using B-spline curves to obtain the joint angular displacement of the robotic arm. Joint angular velocity Joint angular acceleration Joint angular acceleration trajectory curve; Robotic arm joint angular displacement trajectory curve

[0029] Robotic arm joint angular velocity trajectory curve

[0030] Robotic arm joint angular acceleration trajectory curve

[0031] Robotic arm joint angle acceleration trajectory curve

[0032] S4. For every two adjacent shape points on the entire trajectory and For each trajectory segment, determine whether the motion state of each joint of the robotic arm on this segment consistently satisfies the given constraints such as joint angular displacement, joint angular velocity, joint angular acceleration, and joint angular jerk. If any constraint violation occurs, add two adjacent type value points corresponding to this trajectory segment. and The time interval between

[0033] in, △h For single-step increments of time intervals, To constrain violations of the standard, when the joint angular displacement... Joint angular velocity Joint angular acceleration Joint angular acceleration When all given constraints are met, The value is 0; otherwise, if any one of the states does not satisfy the constraints... The value is 1.

[0034] S5. If the motion state of the robotic arm at each point along the entire trajectory satisfies all constraints, then calculate the multidimensional decision space boundary value of the robotic arm trajectory according to the following formula and execute step S6; otherwise, based on the updated... time interval Repeat steps S2 to S4 to reconstruct the normalized non-uniform node vector. And plan the motion trajectory curve of the robotic arm.

[0035]

[0036] Wherein, the boundary scaling factor , .

[0037] S6. Initialize a group of particles within the decision space boundary. The position of each particle represents a potential solution to the robotic arm trajectory optimization problem. Set the initial positions of all individual particles to a linear uniform distribution.

[0038] in, M p For the number of particles, X j,0 For the first j The initial position of each particle.

[0039] Set the initial velocity of all individual particles to a random distribution.

[0040] in,V j,0 For the first j The initial velocity of each particle The function is used to generate OK Columns located Random numbers within a range that follow a uniform distribution. The maximum allowable value of particle velocity, i.e., the maximum distance a particle is allowed to move in a single iteration, is expressed as follows:

[0041] No. Maximum permissible speed in each dimension v i_max Set as

[0042] in, This is the velocity coefficient.

[0043] S7. Perform constraint violation checks on all solutions obtained from particle swarm optimization and store feasible solutions in the main memory pool. In the middle, infeasible solutions are stored in the secondary memory pool. In this study, non-dominated feasible solutions are quantitatively compared in terms of relative merit in the main memory pool through non-dominated sorting to obtain non-dominated feasible solutions. Then, through sparse sorting, the non-dominated feasible solution with the largest current sparseness is selected as the optimal exploration position for the swarm, guiding the particle swarm to accelerate the exploration of regions where the current non-dominated feasible solutions are sparsely distributed, thereby improving the uniformity and complete coverage of the Pareto front.

[0044] S8. All particles in the particle swarm are at their current optimal positions. and the optimal position of the group Adjust your exploration speed under guidance Then, the particle positions are iteratively updated in the decision space. And it shares the currently found optimal position information of an individual with other particles. The particle in the first Speed ​​at the next iteration V j,k+1 The iterative update formula is:

[0045] To prevent particles from taking excessively large steps in a single iteration, the maximum velocity of the particles needs to be limited by the following formula.

[0046] No. The particle in the first Particle position at the next iteration Xj,k+1 Iterative update formula X j,k+1 = X j,k + V j,k+1 , =1,2,…, M p (14) To prevent particles from crossing the decision space boundary, the particle position range needs to be limited by the following formula.

[0047] in, M p The number of individual particles in the particle swarm. The maximum number of iterations, The number of cost functions. For inertial weights, For individual learning factors, As a group learning factor, r p , r q A random number within the interval [0,1]. For the first The particle in the first The velocity vector during the next iteration of exploration For the first The particle in the first The position vector during the next iteration of exploration. For the first The individual best position vector of each particle as explored so far in its history. This represents the optimal position vector of the particle swarm discovered so far.

[0048] S9, targeting the secondary memory pool Each infeasible solution Select the main memory pool The feasible solution that is closest to its decision space Connect them and grow a new solution among them. If this new solution Constraint violation degree If it is not zero, then use the new solution. Replace secondary memory pool Infeasible solutions in This guides the infeasible solution set to approach the constraint boundary from the direction of the infeasible region. If the constraint violation degree of this new solution... If it is zero, then the new solution will be... Add to main memory pool This guides the feasible solution set to approach the constraint boundary from the direction of the feasible region.

[0049]

[0050] in, This represents all non-dominated feasible solutions stored in the main memory pool. This represents all non-dominated infeasible solutions stored in the secondary memory pool. This represents the number of non-dominated feasible solutions in the main memory pool. Used to calculate the constraint violation degree function value. For a given number of intermediate interpolation points, express The first in points and All The minimum distance between points, express The first in points and The first in The distance between points is calculated using the following expression:

[0051] By inspiring the particle swarm optimization process through the aforementioned complementary dual memory pools, the constraint boundary is simultaneously approximated from both the feasible and infeasible regions. Figure 2 As shown, this greatly improves the particle swarm optimization efficiency, thereby obtaining more high-quality non-dominated solutions.

[0052] Finally, determine whether the particle swarm optimization iteration count has reached the maximum number of iterations. If the maximum number of iterations has not been reached, continue with steps S6 to S9; otherwise, end the iteration and output the Pareto front consisting of all non-dominated feasible solutions in the main memory pool and their objective function values.

[0053] Example 2. A high-energy-efficiency trajectory optimization method for robotic arms based on constraint-guided boundary adjustment and dual-memory-pool heuristic edge extension strategies, such as... Figures 1-3 As shown, it includes: S1, for a given robotic arm A discrete trajectory-type value point The minimum time interval between adjacent model points is calculated by setting all joints of the robotic arm to maintain their maximum movement speed at all times. , .

[0054] S2, in order to make The starting and ending points of the second-order B-spline trajectory curve coincide with the first and last data points, respectively. The repetition degree at both ends of the node vector is set to... ,based on time interval Construct normalized non-uniform nodes And thus obtain from Nodes Normalized non-uniform node vector .

[0055] S3. Solve for the B-spline basis function based on the normalized non-uniform node vector. The value, and then, combined with Individual value points Construct constraint equations and perform inverse calculations. Control points of the second-order B-spline curve , to conduct based The trajectory planning of the robotic arm is performed using B-spline curves, resulting in trajectory curves for the joint angular displacement, joint angular velocity, joint angular acceleration, and joint angular jerk of the robotic arm.

[0056] S4. For every two adjacent shape points on the entire trajectory and The trajectory segment between points is used to determine whether the motion state of each joint of the robotic arm on this trajectory segment always meets the given constraints such as joint angular displacement, joint angular velocity, joint angular acceleration, and joint angular jerk. If the value point... and If a trajectory segment violates constraints, the time interval between the two model points corresponding to that trajectory segment will be increased accordingly.

[0057] S5. If the motion state of the robotic arm at each point along the entire trajectory satisfies all constraints, then calculate the boundary value of the multidimensional decision space of the robotic arm trajectory and execute step S6; otherwise, based on the updated... time interval Repeat steps S2 to S4 to reconstruct the normalized non-uniform node vector. And plan the motion state trajectory curve of the robotic arm.

[0058] S6. Initialize a group of particles within the boundary of the decision space. The position of each particle represents a potential solution to the robot arm trajectory optimization problem. Set the initial positions of all individual particles to a linear uniform distribution and the initial velocities of all individual particles to a random distribution.

[0059] S7. Perform constraint violation checks on all solutions obtained from particle swarm optimization and store feasible solutions in the main memory pool. In the middle, infeasible solutions are stored in the secondary memory pool. In this study, non-dominated feasible solutions are quantitatively compared in terms of relative merit in the main memory pool through non-dominated sorting to obtain non-dominated feasible solutions. Then, through sparse sorting, the non-dominated feasible solution with the largest current sparseness is selected as the optimal exploration position for the swarm, guiding the particle swarm to accelerate the exploration of regions where the current non-dominated feasible solutions are sparsely distributed, thereby improving the uniformity and complete coverage of the Pareto front.

[0060] S8. All particles in the particle swarm are at their current optimal positions. and the optimal position of the group Adjust your exploration speed under guidance Then, the particle positions are iteratively updated in the decision space. It also shares the currently found optimal position information of an individual with other particles.

[0061] S9, targeting the secondary memory pool Each infeasible solution Select the main memory pool The feasible solution that is closest to its decision space Connect them and grow a new solution among them. If this new solution Constraint violation degree If it is not zero, then use the new solution. Replace secondary memory pool Infeasible solutions in This guides the infeasible solution set to approach the constraint boundary from the direction of the infeasible region. If the constraint violation degree of this new solution... If it is zero, then the new solution will be... Add to main memory pool This process guides the feasible solution set to approach the constraint boundary from the feasible region. Through the aforementioned complementary dual-memory pool heuristic edge expansion process, the constraint boundary is simultaneously approached from both the feasible and infeasible regions, greatly improving the particle swarm optimization efficiency and thus obtaining more high-quality non-dominated solutions.

[0062] Finally, determine whether the particle swarm optimization iteration count has reached the maximum number of iterations. If the maximum number of iterations has not been reached, continue with steps S6 to S9; otherwise, end the iteration and output the Pareto front consisting of all non-dominated feasible solutions in the main memory pool and their objective function values.

Claims

1. A high-efficiency trajectory optimization method for a robotic arm, characterized in that, Includes the following steps: S1. Assume the robotic arm has N A discrete trajectory-type value point Q i Calculate the minimum limit of the time interval between each adjacent type value point. h i,0 ; S2. Set the repetition at both ends of the node vector to 1. q +1, based on N-1 time intervals Construct normalized non-uniform nodes u r This leads to the normalization of non-uniform node vectors. U ={ u r }; S3. Based on vector U Solving B-spline basis functions B i,q ( u The value of ) and then combined N indivual Q i Construct constraint equations and perform inverse calculations. q Control points of the second-order B-spline curve P i , to conduct based q The trajectory planning of the robot arm using a B-spline curve yields a trajectory curve with motion constraints of joint angular displacement, joint angular velocity, joint angular acceleration, and joint angular jerk. S4. Determine the value points of each pair of adjacent type points. Q i and Q i+1 On the trajectory segment, does the motion state of each joint of the robotic arm always satisfy the aforementioned motion constraints? S5. If the motion constraints are satisfied, calculate the boundary value of the multidimensional decision space of the robotic arm trajectory and execute step S6; S6. Initialize a group of particles within the boundary of the decision space. The position of each particle represents a potential solution to the robot arm trajectory optimization problem. Set the initial position of all individual particles to a linear uniform distribution and the initial velocity of all individual particles to a random distribution. S7. Perform constraint violation checks on all solutions obtained from particle swarm optimization and store feasible solutions in the main memory pool. In the middle, infeasible solutions are stored in the secondary memory pool. In the middle; through non-dominated sorting The relative merits of all feasible solutions are quantitatively compared to obtain non-dominated feasible solutions. Then, by sorting by sparseness, the non-dominated feasible solution with the largest current sparseness is selected as the optimal exploration position of the swarm, guiding the particle swarm to accelerate the exploration of the region where the current non-dominated feasible solution is sparsely distributed. S8. All particles in the particle swarm are at their current optimal positions. and the optimal position of the group Adjust your exploration speed under guidance Then, the particle positions are iteratively updated in the decision space. And share the currently searched optimal position information of an individual with other particles; S9. Targeting Each infeasible solution ,choose The feasible solution that is closest to its decision space Connect them and grow a new solution among them. ;like Constraint violation degree If it is not zero, then use replace In .

2. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, In S4, if there is a violation of the constraints, the time interval between the two model points corresponding to this trajectory will be increased accordingly.

3. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, In S5, if the motion constraints are not met, steps S2 to S4 are executed again based on the updated time interval to reconstruct the normalized non-uniform node vector. U And plan the motion state trajectory curve of the robotic arm.

4. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, In S9, if Constraint violation degree If it is zero, then... Add to middle.

5. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, It also includes S10, which determines whether the particle swarm iteration count has reached the maximum number of iterations. If the maximum number of iterations has not been reached, continue executing steps S6 to S9.

6. The high-efficiency trajectory optimization method for robotic arms according to claim 5, characterized in that, If it reaches End the iteration and output. The Pareto front is composed of all nondominated feasible solutions and their objective function values.

7. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, In S1, in, Indicates the joints of the robotic arm Maximum permissible angular velocity, .

8. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, In S2, in, The total duration of the robotic arm's motion trajectory, i.e. .

9. The high-efficiency trajectory optimization method for robotic arms according to claim 8, characterized in that, In S2, 。 10. The high-efficiency trajectory optimization method for robotic arms according to claim 1, characterized in that, In S3 Robotic arm joint angular displacement trajectory curve Robotic arm joint angular velocity trajectory curve Robotic arm joint angular acceleration trajectory curve Robotic arm joint angle acceleration trajectory curve .

Images