Mechanical arm control method based on time optimization

Abstract

The invention relates to a mechanical arm control method based on time optimization, and the method comprises the steps: building a mechanical arm model for a mechanical arm, and building a spatial transformation relation of all joints of the mechanical arm model through a D-H parameter method; according to the spatial transformation relation of all the joints and the transition path of the mechanical arm, a joint track on the transition path of the mechanical arm is constructed through 3-5-3 piecewise polynomial interpolation; based on the principle that the movement time of each joint is shortest, a chaos particle swarm algorithm is adopted to optimize the joint track of each joint; and according to the mechanical arm model and the optimized joint track, tracking control is conducted on the mechanical arm through a depth deterministic strategy gradient algorithm. Performance indexes of the method are remarkably broken through, the improved PSO algorithm achieves shortening of total time of a track and increasing of convergence speed by dynamically adjusting inertia weight and learning factors, and compared with a local optimal trap of a traditional PSO algorithm and a speed fluctuation problem of cubic polynomial interpolation, the method shows better time optimization capability.

Description

Technical Field

[0001] This invention relates to the field of spraying control technology, and in particular to a time-optimal robotic arm control method. Background Technology

[0002] In the field of industrial automation, trajectory planning for painting robots is a core element determining production efficiency and work quality. Its optimization objective must simultaneously meet the dual requirements of motion smoothness and time economy. Current mainstream technologies still have significant limitations under complex working conditions, specifically manifested in the following three dimensions: Traditional trajectory generation mainly relies on polynomial interpolation techniques, but it faces a dilemma in order selection: while high-order polynomials can satisfy multi-axis synchronization constraints, they suffer from poor convex hull properties, easily leading to unexpected trajectory fluctuations; while low-order polynomials, although simple to calculate, cannot achieve continuous acceleration, causing the robotic arm to experience impact vibrations at inflection points. This contradiction is particularly prominent in high-speed spraying scenarios, directly affecting coating uniformity and equipment lifespan.

[0003] Existing intelligent optimization methods have obvious shortcomings. Traditional particle swarm optimization (PSO) algorithms are prone to getting stuck in local optima in high-dimensional trajectory parameter spaces due to the lack of an effective global search mechanism, and the convergence speed decreases exponentially with the number of iterations. Although genetic algorithms have strong global optimization capabilities, their crossover and mutation operations lead to a surge in computational complexity. In a 6-DOF robot system, the time taken for a single planning often exceeds 200 ms, which is difficult to meet the requirements of real-time control. Summary of the Invention

[0004] This invention provides a time-optimal robotic arm control method to address the problem that the traditional particle swarm optimization (PSO) algorithm exhibits lag in convergence speed, resulting in excessively long trajectory optimization process and difficulty in meeting the needs of high-efficiency production.

[0005] The technical solution of the present invention is as follows: A time-optimal robotic arm control method, comprising: S10: Establish a model of the robotic arm and use the DH parameter method to establish the spatial transformation relationship of each joint of the robotic arm model; S20: Based on the spatial transformation relationship of each joint and the transition path of the robotic arm, the joint trajectory on the transition path of the robotic arm is constructed by 3-5-3 piecewise polynomial interpolation. S30: Based on the principle of minimizing the motion time of each joint, the joint trajectory of each joint is optimized using the chaotic particle swarm optimization algorithm; S40: Based on the robotic arm model and the optimized joint trajectory, the robotic arm is tracked and controlled using a depth-deterministic policy gradient algorithm.

[0006] Furthermore, N position points on the transition path are selected as interpolation points for robot trajectory planning; the angle θ corresponding to the h-th trajectory point of the i-th joint is obtained through inverse kinematics. ih The 3-5-3 piecewise polynomial interpolation method is used to plan the joint space trajectory of the transition path and construct a 3-5-3 piecewise polynomial function.

[0007] Furthermore, the 3-5-3 piecewise polynomial function is as follows: , In the formula: Let a represent the joint trajectories of the i-th joint in segments 1, 2, and 3, respectively. i1m a i2m a i3m These represent the m-th coefficients of the i-th joint in the polynomial function of segments 1, 2, and 3, respectively. The restrictions are as follows: , Among them, t i1 t i2 t i3 These represent the time of the three-segment polynomial interpolation of joint i.

[0008] Further, step S30 includes: The optimization objective is to minimize the movement time of each joint, and constraints are established accordingly. The particle population of the PSO algorithm is initialized using a chaotic sequence; The inertia weights of the PSO algorithm are dynamically adjusted nonlinearly. Genetic algorithm selection, crossover, and mutation operators are introduced to perform evolutionary operations on the PSO population.

[0009] Furthermore, an initial particle population is generated using a Logistic mapping μ=4, and the population diversity is improved through the ergodicity and randomness of the chaotic sequence. Logistic chaotic sequence, the formula is: , Where μ is the control coefficient, and μ=4 in order to make the particle swarm completely chaotic.

[0010] Furthermore, the inertia weight for nonlinear dynamics is: , , Let represent the minimum and maximum values ​​of the inertia weight, respectively, and T be the maximum number of iterations. =0.9、 =0.4.

[0011] Furthermore, single-point crossover is performed on the top 30% of particles by fitness value, and Gaussian mutation is performed on the best particle.

[0012] Furthermore, the crossover probability P of a single-point crossover c The mutation probability P of Gaussian mutation is set to 0.7. m Set to 0.1.

[0013] Furthermore, the constraints include: joint angular displacement constraints, joint velocity constraints, and joint acceleration constraints; The joint angular displacement constraint is θ i ∈ [θ imin θ imax ], where θ i Let be the angular displacement of the i-th joint; The joint velocity constraint is as follows: The maximum speed limit is determined by converting the rated speed of the motor to the reduction ratio; The joint acceleration constraint is The maximum acceleration limit is determined based on the output torque of the driver and the stiffness of the mechanical structure.

[0014] The beneficial effects of this invention are as follows: The invention achieves a significant breakthrough in performance indicators. The improved PSO algorithm, through dynamic adjustment of inertia weights and learning factors, reduces the total trajectory time by 20%-25% and increases the convergence speed by 25%. Compared to the local optimum traps and speed fluctuations caused by third-order polynomial interpolation in the traditional PSO algorithm, it demonstrates superior time optimization capabilities. This invention is deeply adapted to six-degree-of-freedom robotic arms. Through the adaptability of the trajectory planning algorithm, it can meet the painting requirements of complex curved surface workpieces such as aero-engine blades and wind turbine towers. However, in the path transition phase, the trajectory generated using the equal-time method requires a transition time of up to 9 seconds, reducing overall work efficiency and affecting the stability of painting quality due to the excessively long movement time. Attached Figure Description

[0015] Figure 1 This is a flowchart of a time-optimal robotic arm control method according to the present invention. Detailed Implementation

[0016] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments. The described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0017] This method aims for time optimization and proposes a time-optimal trajectory planning method for workpiece painting robots. It employs a fusion framework of "3-5-3 interpolation + genetic chaotic PSO," achieving high-precision and high-efficiency painting operation control through the collaborative design of trajectory generation and intelligent optimization. This framework combines the smoothness of polynomial interpolation with the global optimization capability of the improved particle swarm optimization algorithm, forming a complete technical chain from trajectory parameterization to time parameter optimization.

[0018] The following describes a six-degree-of-freedom robotic arm as the execution carrier, with a repeatability of ±0.1mm, a joint rotation range of ±170°, and an end effector speed of 30-50cm / s, which can meet the automated spraying needs of complex curved workpieces.

[0019] In the technical solution of the present invention, Figure 1 This is a flowchart of a time-optimal robotic arm control method according to the present invention, as shown below. Figure 1 As shown, it includes: S10: Establish a model of the robotic arm and use the DH parameter method to establish the spatial transformation relationship of each joint of the robotic arm model.

[0020] Physical modeling and kinematic analysis of the robotic arm using the Denavit-Hartenberg method: A coordinate system for the robotic arm links is established, and the spatial transformation relationship between each joint is described by the Denavit-Hartenberg parametric method. The pose of the end effector is obtained by solving the forward kinematic equations.

[0021] S20: Based on the spatial transformation relationship of each joint and the transition path of the robotic arm, the joint trajectory on the transition path of the robotic arm is constructed by 3-5-3 piecewise polynomial interpolation.

[0022] The trajectory generation uses a three-segment polynomial structure (cubic-quintic-cubic) to construct the joint space trajectory, and ensures motion stability through continuity constraints at the connection points.

[0023] The specific process is as follows: N points on the transition path are selected as interpolation points for robot trajectory planning; The angle θ corresponding to the h-th trajectory point of the i-th joint is obtained by inverse kinematics. ih ; The 3-5-3 piecewise polynomial interpolation method is used to plan the joint space trajectory of the transition path, and a 3-5-3 piecewise polynomial function is constructed.

[0024] Four position points P1, P2, P3, and P4 on the transition path are selected as interpolation points for robot trajectory planning. The angle θ corresponding to the h-th trajectory point of the i-th joint is obtained through inverse kinematics. ih The joint space trajectory is planned using the 3-5-3 piecewise polynomial interpolation method for the transition path.

[0025] The 3-5-3 piecewise polynomial function is as follows: , In the formula: Let a represent the joint trajectories of the i-th joint in segments 1, 2, and 3, respectively. i1m a i2m a i3m These represent the m-th coefficients of the i-th joint in the polynomial function of segments 1, 2, and 3, respectively. By solving for the 16 undetermined coefficients to satisfy the continuity conditions of position, velocity, and acceleration, the following constraints are imposed: , Among them, t i1 t i2 t i3 These represent the time of the three-segment polynomial interpolation of joint i.

[0026] Compared with traditional high-order polynomial interpolation or spline interpolation, this method has significant advantages: on the one hand, by using piecewise low-order polynomial design, the computational complexity is controlled at the O(n³) level, reducing the computational load in real-time control; on the other hand, it avoids the Runge phenomenon common in high-order interpolation, ensuring the monotonicity and overshoot-free characteristics of joint motion, and is particularly suitable for the stringent requirements of trajectory smoothness in spraying operations.

[0027] S30: Based on the principle of minimizing the motion time of each joint, the joint trajectory of each joint is optimized using the chaotic particle swarm optimization algorithm.

[0028] Based on the standard particle swarm optimization (PSO) algorithm, the following key improvements are made to construct a genetic chaotic PSO algorithm to improve the time parameter optimization performance: The optimization objective is to minimize the movement time of each joint, and constraints are established accordingly.

[0029] The constraints include: joint angular displacement constraints, joint velocity constraints, and joint acceleration constraints.

[0030] The joint angular displacement constraint is θ i ∈ [θ imin θ imax ], where θ i Let be the angular displacement of the i-th joint.

[0031] The joint velocity constraint is as follows: The maximum speed limit is determined by converting the rated speed of the motor to the reduction ratio.

[0032] The joint acceleration constraint is The maximum acceleration limit is determined based on the output torque of the driver and the stiffness of the mechanical structure.

[0033] By transforming the above constraints into penalty function terms embedded in the objective function, the improved PSO algorithm can automatically eliminate infeasible solutions during the optimization process, ensuring that the optimization results meet the physical performance boundaries of the robot and avoiding safety risks such as mechanical impact or motor overload.

[0034] The particle population of the PSO algorithm is initialized using a chaotic sequence.

[0035] An initial particle population is generated using a Logistic mapping with μ=4, and population diversity is improved by leveraging the ergodicity and randomness of the chaotic sequence. Logistic chaotic sequence, the formula is: , Where μ is the control coefficient, and μ=4 in order to make the particle swarm completely chaotic.

[0036] An initial particle population is generated using a Logistic mapping (μ=4). The ergodicity and randomness of the chaotic sequence enhance population diversity and prevent the algorithm from getting trapped in local optima. When the control parameter μ=4, the Logistic mapping enters a completely chaotic state, and the particle position distribution satisfies the ergodicity theorem, ensuring uniform coverage of the initial solution space.

[0037] The inertia weights of the PSO algorithm are dynamically adjusted nonlinearly.

[0038] The inertia weight for nonlinear dynamics is: , , Let represent the minimum and maximum values ​​of the inertia weight, respectively, and T be the maximum number of iterations. =0.9、 =0.4. This nonlinear strategy enables the algorithm to maintain a strong global search capability (high w value) in the early stages of iteration, and gradually enhance the local exploitation capability (low w value) in the later stages, achieving an adaptive balance between exploration and exploitation.

[0039] Genetic algorithm selection, crossover, and mutation operators are introduced to perform evolutionary operations on the PSO population.

[0040] Single-point crossover is performed on the top 30% of particles by fitness value, and Gaussian mutation is applied to the best particle. The crossover probability P of the single-point crossover is... c The mutation probability P of Gaussian mutation is set to 0.7. m Set to 0.1.

[0041] Selection, crossover, and mutation operators are introduced to perform evolutionary operations on the PSO population. Single-point crossover is performed on the top 30% of particles with fitness values ​​(crossover probability Pc=0.7), and Gaussian mutation is performed on the best particle (mutation probability Pm=0.1). Through the genetic mechanism, the transmission and mutation of high-quality genes are promoted, further improving the algorithm's ability to escape local optima.

[0042] S40: Based on the robotic arm model and the optimized joint trajectory, the robotic arm is tracked and controlled using a depth-deterministic policy gradient algorithm.

[0043] This invention proposes a three-level technical path: "joint space interpolation - polynomial smoothing - improved PSO optimization". Joint space interpolation ensures trajectory accuracy, polynomial smoothing improves dynamic stability, and the improved PSO algorithm achieves optimal time planning. Ultimately, while meeting the ±0.1mm repeatability accuracy requirement, the spraying cycle of aerospace workpieces is significantly shortened.

[0044] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A time-optimal based robot control method, characterized by, Comprise: S10: a mechanical arm model is established for the mechanical arm, and a spatial transformation relationship of each joint of the mechanical arm model is established by using a D-H parameter method; S20: according to the spatial transformation relationship of each joint and the transition path of the mechanical arm, a 3-5-3 segmented polynomial interpolation is used to construct the joint trajectory on the transition path of the mechanical arm; S30: based on the principle of the shortest time of each joint movement, a chaotic particle swarm optimization algorithm is used to optimize the joint trajectory of each joint; S40: according to the mechanical arm model and the optimized joint trajectory, a deep deterministic policy gradient algorithm is used to track and control the mechanical arm.

2. The time-optimal mechanical arm control method according to claim 1, wherein, N position points on the transition path are selected as interpolation points for robot trajectory planning; Solve the angle θ corresponding to the i th joint and h th trajectory point by inverse kinematics ih ; A 3-5-3 segmented polynomial interpolation method is used for joint space trajectory planning of the transition path to construct a 3-5-3 segmented polynomial function.

3. The time-optimal mechanical arm control method according to claim 2, wherein, The 3-5-3 segmented polynomial function is as follows: , In the formula: Let a represent the joint trajectories of the i-th joint in segments 1, 2, and 3, respectively. i1m a i2m a i3m These represent the m-th coefficients of the i-th joint in the polynomial function of segments 1, 2, and 3, respectively. The constraints are as follows: , where t i1 , t i2 , t i3 represent the time of three-segment polynomial interpolation of joint i respectively.

4. The time-optimal based robot control method of claim 1, wherein, The step S30 comprises: Taking the shortest time of each joint movement as the core optimization target and establishing constraint conditions; A chaotic sequence is used to initialize the particle population of the PSO algorithm; The inertia weight of the PSO algorithm is nonlinearly and dynamically adjusted; Selection, crossover and mutation operators of the genetic algorithm are introduced to perform evolutionary operations on the PSO population.

5. The time-optimal based robot control method of claim 4, wherein, Logistic mapping μ=4 is used to generate the initial particle population, and the ergodicity and randomness of the chaotic sequence are used to improve the population diversity; The Logistic chaotic sequence is as follows: , Wherein, μ is the control coefficient, in order to make the particle population completely in chaotic state, μ=4.

6. The time-optimal mechanical arm control method according to claim 4, wherein, The inertia weight of the nonlinear dynamics is: , , respectively represent the minimum and maximum values of the inertia weight, T is the maximum number of iterations, wherein, = 0.9, = 0.

4.

7. The time-optimal based robot control method of claim 4, wherein, Single-point crossover is performed on the particles with the top 30% fitness values, and Gaussian mutation is performed on the optimal particle.

8. The time-optimal based robot control method of claim 7, wherein, The intersection probability P of the single-point intersection c The mutation probability P of the Gaussian mutation is set to 0.7 m is set to 0.

1.

9. The time-optimal based robot control method of claim 1, wherein, The constraint conditions include joint angle displacement constraint, joint velocity constraint and joint acceleration constraint; The joint angle displacement constraint is θ i ∈ [θ imin , θ imax ], wherein θ i is the angle displacement of the i-th joint. The joint velocity constraint is The maximum velocity limit is determined according to the rated motor speed and the reduction ratio conversion; The joint acceleration constraint is The maximum acceleration limit is determined according to the driver output torque and the mechanical structure stiffness.

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