Optimal trajectory planning method for cable parallel spraying robot

Abstract

The invention relates to an optimal trajectory planning method for a cable parallel spraying robot, and aims to improve the smoothness, stability and controllability of the trajectory of the robot and optimize the operation efficiency, energy consumption and residual vibration at the same time. According to the method, on the basis of improved quintic B-spline interpolation, by introducing a jerk boundary constraint condition, residual vibration at the starting moment and the ending moment of a track is effectively restrained. And virtual control points are introduced at the starting position and the ending position of the path, and nodes are redistributed, so that the dynamic response characteristics of the system are further optimized. Besides, a time-energy-vibration optimization model is constructed, and time parameters are globally optimized by adopting a quantum particle swarm optimization algorithm, so that high efficiency, stability and smoothness of the trajectory are realized. Simulation experiments show that compared with a traditional B-spline interpolation method, the method achieves remarkable optimization effects in the aspects of running time, energy consumption, jerk variance and the like, and an effective trajectory planning solution is provided for application of the cable parallel spraying robot in a complex working environment.

Description

Technical Field

[0001] The present application relates to the technical field of cable-parallel spraying robots, and in particular to an optimal trajectory planning method for cable-parallel spraying robots. Background Art

[0002] With the rapid development of industrial automation, cable-parallel spray robots have found widespread application in aerospace, warehousing and logistics, motion simulation, and other fields. These robots, with their large workspace, strong load capacity, excellent power, light weight, and low cost, meet the modern industry's demand for efficient and precise spraying operations.

[0003] Patent CN113524152A, a B-spline trajectory planning method for a cable-coupled parallel robot, does not quantify the shortcomings of traditional methods (such as "residual vibration amplitude > 5mm"). Trajectory planning for cable-coupled parallel spray robots is one of the key technologies for achieving efficient spraying operations. Through precise trajectory planning, the robot can achieve a larger range of motion in a controllable and stable state, thereby expanding its application scenarios and improving the quality and efficiency of spraying operations.

[0004] However, existing trajectory planning methods for cable-parallel spray robots have limitations. For example, while traditional B-spline interpolation methods can ensure trajectory smoothness, they can easily generate residual vibration at the start and end of the trajectory, affecting spray quality. Furthermore, existing methods still have shortcomings in optimizing the system's dynamic response characteristics and improving trajectory stability and controllability, making them difficult to meet the requirements of high-precision spraying operations.

[0005] Therefore, a new optimal trajectory planning method for cable-parallel spraying robots is studied to address the shortcomings of the existing technology, improve the smoothness, stability and controllability of the trajectory, and optimize the dynamic response characteristics of the system, which is of great significance for improving the overall efficiency and quality of spraying operations. Summary of the Invention

[0006] This paper proposes an optimal trajectory planning method for a cable-parallel spraying robot, addressing shortcomings of existing trajectory planning methods, such as insufficient trajectory smoothness, poor system dynamic response characteristics, and poor trajectory stability and controllability. By employing an improved quintic B-spline interpolation and introducing jerk boundary constraints, this method effectively suppresses residual vibration at the start and end of the trajectory, improving the smoothness and stability of the trajectory. Furthermore, a time-energy-vibration optimization model is constructed that comprehensively considers time constraints, energy consumption, and vibration suppression. This model is solved using a quantum particle swarm optimization algorithm to achieve high efficiency, stability, and smoothness of the trajectory, significantly improving the robot's operational efficiency and stability.

[0007] Compared with existing technologies, the present invention improves trajectory smoothness and stability, optimizes system dynamic response characteristics, and enhances trajectory stability and controllability. The effectiveness of the proposed method was verified through simulation experiments, and the results showed that compared with traditional B-spline interpolation methods, the present invention achieved significant optimization effects in terms of runtime, energy consumption, and acceleration variance. The method of the present invention is applicable to various cable-parallel spray robots and can significantly improve their performance in complex operating environments, possessing broad application prospects and market value.

[0008] In order to achieve the above objectives, the technical solution adopted by this application is:

[0009] In a first aspect, the present application proposes a quintic B-spline curve interpolation method, the method comprising the following steps:

[0010] Since the p-order B-spline is Cp-1 continuous, in order to ensure the smoothness of the acceleration, C(u) is set to C4 continuous, and p≥5 is derived. Considering the instability of high-order curves, p=5, which is called the quintic B-spline curve. Then m=12+f, n=p+f+1. Its mathematical expression is:

[0011]

[0012] Among them, C(u) represents the interpolation curve, Q i represents the i-th control point, there are n+1 control points in total, and p represents the B-spline basis function N i,p (u) times, u is a normalized parameter used to represent time. N i,p (u) satisfies the De Boor formula:

[0013]

[0014] Among them, u i (i=0, 1, 2…m=n+p+1) is a node sequence.

[0015] By repeating the nodes at both ends of the path p+1 times, we ensure that the trajectory can accurately pass through the specified control points at the start and end points. Two virtual control points are inserted after the first time node and before the last node. Let the number of path points be f, then m = 2(p+1) + f and n = p+f+1. Define U as the node vector set, that is:

[0016]

[0017] The velocity, acceleration, and jerk of the trajectory at the starting and ending points are all 0, and the boundary constraints are:

[0018]

[0019] To ensure that the trajectory passes through f waypoints, the constraint equation is:

[0020]

[0021] In a second aspect, the present application constructs a time-energy-vibration model, and the method comprises the following steps:

[0022] Taking into account the three key factors of time constraint, energy consumption and vibration suppression, a time-energy-vibration optimization model is constructed to achieve high efficiency, stability and smoothness of the trajectory.

[0023] The optimization model is solved using quantum particle swarm optimization algorithm.

[0024] QPSO uses the quantum potential field model to evolve the position. The formula for updating the particle position is:

[0025]

[0026] in:

[0027]

[0028] Where i = 1, 2, ..., I represents the number of particles, j = 1, 2, ..., J represents the dimension of the particles; n = 1, 2, ..., N represents the current number of iterations; is the center position of the best historical positions of all particles in the nth iteration; is the optimal position of the particle in the nth iteration and the global optimal position Random positions between and u are random numbers in (0,1); the parameter α is the expansion and contraction coefficient, which is used to control the convergence speed of QPSO and is the only parameter that needs to be controlled in QPSO.

[0029] α=α min +(α max -α min )·(Nn) / N

[0030] Among them, g is the total number of iterations; α max and α min are two positive constants, usually taken as 1.0 and 0.5 respectively.

[0031] and The update method is:

[0032]

[0033] The f+2 time parameters are the decision variables of the interpolation optimization model. In order to obtain the actual end effector running time, the value range of the particles can be set according to the motor specifications. The initial value of the particles is set as follows:

[0034] X i,j =l1+(l2-l1)·β i,j

[0035] Among them, l1 and l2 are the minimum and maximum values ​​of the settings respectively.

[0036] Set the satisfaction function and fitness function:

[0037] The satisfaction function is used to evaluate the degree of achievement of the optimization goal, and its value range is limited to the closed interval [0,1]. 0 represents complete dissatisfaction and 1 represents complete satisfaction. Let z time and z jerk Z time Satisfaction function, let z energy Z energy Satisfaction function:

[0038]

[0039] Among them, time Indicates the maximum reference value of Ztime, Ψ energy Represents Z energy The maximum reference value, Ψ jerk Represents Z jerk The maximum reference value of ,. Correspondingly, it means Z time The minimum reference value of ψ energy Represents Z energy The minimum reference value of ψ jerk Represents Z jerk The minimum reference value.

[0040] The fitness formula is:

[0041] Fitness=-(c1·z time +c2·z energy +c3·z jerk )

[0042] c1+c2+c3=1

[0043] The time nodes represented by the particles are sorted in non-decreasing order to generate f+1 random particles with values ​​(l1, l2). The particles are represented as q0, q2, …, qf, and the cumulative sum of the time parameters is calculated.

[0044]

[0045] Compared with the prior art, the advantages of this application are:

[0046] This application optimizes the B-spline interpolation method and constructs a time-energy-vibration model, providing CDPR with sufficient safety margin during actual operation, thereby effectively improving the stability and reliability of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0048] Figure 1 This is a flowchart of a QPSO algorithm proposed according to an embodiment of the present application, showing an iterative process diagram of the quantum particle swarm optimization algorithm;

[0049] Figure 2 This is a CDPR workspace diagram of an embodiment of the present application, showing the reachable area of ​​the cable-driven parallel robot.

[0050] Figure 3 This is a time parameter diagram of the traditional B-spline interpolation method in an embodiment of the present application, showing the parameters of the traditional B-spline interpolation method when performing aircraft spraying operations.

[0051] Figure 4 This is a time parameter diagram of the optimized B-spline interpolation method in an embodiment of the present application, showing the parameters of the optimized B-spline interpolation method when performing aircraft spraying operations.

[0052] Figure 5 This is a diagram of the change of cable paths and cable forces in an embodiment of the present application, showing the change of the cable forces of each cable over time under two methods.

[0053] Figure 6 This is a motion profile diagram of the four cable paths of an embodiment of the present application, showing the motion process of the end effectors of each cable. DETAILED DESCRIPTION

[0054] To make the purpose, technical solutions, and advantages of the embodiments of this application more clear, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. Obviously, the described embodiments are part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0055] The embodiments of the present application are further described in detail below with reference to the accompanying drawings.

[0056] The embodiment of this application simulates the movement of the end effector under different trajectory paths during aircraft spraying operations, and conducts a comparative study and analysis of the traditional B-spline interpolation method and the optimized interpolation method proposed in this article. In the traditional B-spline interpolation method, the time parameter is calculated using the chord length accumulation method; while the method proposed in this article uses an optimization model that comprehensively considers time, energy consumption, and vibration characteristics, uses the time parameter as the optimization variable, and finally obtains a set of optimal time allocation parameters through multiple rounds of iterative optimization using a quantum particle swarm algorithm. In order to achieve the above technical effects, the overall idea of ​​this application is as follows:

[0057] An optimal trajectory planning method for a cable-connected parallel spraying robot, the method comprising the following steps:

[0058] S1. Use the traditional B-spline interpolation method to calculate the time parameter table for the aircraft spraying operation;

[0059] S2. Using the quantum particle swarm optimization algorithm and the optimized B-spline interpolation method for solving the time-energy-vibration multi-objective optimization model to calculate the time parameter table for the aircraft spraying operation;

[0060] S3, compare and analyze the execution time, energy consumption and acceleration variance calculated by the two methods;

[0061] S4. Comparative analysis of cable forces simulated by the two methods;

[0062] S5. Compare and analyze the motion process of each cable end effector simulated by the two methods;

[0063] The embodiments of the present application are further described in detail below with reference to the accompanying drawings.

[0064] See also Figure 1 As shown, QPSO expands the search range through quantum behavior and avoids premature convergence; the embodiment of the present application provides an optimal trajectory planning method for a parallel spraying robot, which includes the following steps:

[0065] S1. Use the traditional B-spline interpolation method to calculate the time parameter table for aircraft spraying operation, see Figure 3 ;

[0066] S2. Use the quantum particle swarm optimization algorithm combined with the optimized B-spline interpolation method to solve the time-energy-vibration multi-objective optimization model for aircraft spraying operations to calculate the time parameter table, see Figure 4 ;

[0067] S3, compare and analyze the execution time, energy consumption and acceleration variance calculated by the two methods;

[0068] S4. Comparative analysis of cable forces simulated by the two methods, see Figure 5 ;

[0069] S5. Comparative analysis of the simulation trajectories of the two methods, see Figure 6 ;

[0070] The simulation experiment simulates the movement of the end effector under different trajectory paths during aircraft spraying operations, and conducts a comparative study and analysis between the traditional B-spline interpolation method and the optimized B-spline interpolation method proposed in this paper.

[0071] The optimal execution time obtained by the traditional B-spline interpolation method is 26.4985 seconds, the energy consumption is 33210J, and the acceleration variance is 2.4286cm 4 / s 6 The optimal execution time obtained by optimizing the B-spline interpolation method is 24.2338 seconds, the energy consumption is 28594J, and the acceleration variance is 0.4331cm 4 / s 6 .

[0072] By comparison, the optimized B-spline interpolation method can reduce execution time and energy consumption, and is more stable.

[0073] See also Figure 5 The cable force variations obtained using the two methods were compared. It can be observed that the trajectory obtained using this optimization method results in significantly smaller cable force fluctuations in the four cables compared to the traditional method. This optimization effect not only helps improve the operational stability of the robotic system but also reduces structural fatigue caused by significant cable force fluctuations, thereby extending the system's service life.

[0074] See also Figure 6 The kinematic curves reveal that the end-effector's linear velocity, acceleration, and their higher-order derivatives strictly satisfy zero-value constraints at the start and end phases of the trajectory. This characteristic not only helps improve the end-effector's positioning accuracy but also effectively reduces shock and residual vibration, enabling the CDPR to achieve low-vibration trajectory tracking at higher operating speeds, improving the system's dynamic performance and operational stability.

[0075] In the description of this application, it should be noted that the terms "upper" and "lower" and the like indicate positions or locations based on the positions or locations shown in the accompanying drawings. These terms are used solely to facilitate the description of this application and simplify the description. They are not intended to indicate or imply that the devices or components referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on this application. Those skilled in the art will understand the specific meanings of the above terms in this application based on specific circumstances.

[0076] It should be noted that, in this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0077] The foregoing is merely a list of specific embodiments of the present application, intended to enable those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not limited to the embodiments shown herein, but is intended to conform to the broadest scope consistent with the principles and novel features of the present application.

Claims

1. An optimal trajectory planning method for a cable-parallel spraying robot, characterized by: The following steps are involved: The improved quintic B-spline curve is used to interpolate the path points. Two virtual control points are inserted before the first path point and two virtual control points are inserted after the last path point, so that the displacement, velocity, acceleration and jerk at the start and end points of the trajectory are all zero; Constructing a time-energy-vibration multi-objective function: Where T is the movement time, F u,l is the cable tension, j i,k is the three-axis acceleration of the end effector; The quantum particle swarm optimization algorithm (QPSO) is used to solve the problem of v max , a max ,j max The optimal time parameter of the constraint. The first and last virtual control points are introduced to realize the zero-jerk boundary constraint, and the quantum particle swarm optimization algorithm is combined to solve the time-energy-vibration multi-objective optimization.

2. The improved quintic B-spline interpolation method according to claim 1, wherein: By repeating the nodes at both ends of the path p+1 times, we ensure that the trajectory can accurately pass through the specified control points at the start and end points. Two virtual control points are inserted after the first time node and before the last node. Let the number of path points be f, then m = 2(p+1) + f and n = p+f+1. Define U as the node vector set, that is:

3. The improved quintic B-spline interpolation method according to claim 1, wherein: To ensure that the trajectory passes through f waypoints, the constraint equation is:

4. The method of constructing a time-energy-vibration multi-objective function according to claim 1, wherein: The mathematical description of the optimization problem is as follows: Among them, T represents the motion time of the end effector in seconds, Z energy represents the integral of the tension of the four cables during the entire motion process, Z jerk is the acceleration variance of the end effector in the x, y, and z directions, which is used to measure the smoothness of the trajectory. u,l represents the tension of the lth cable at time u, j i,k Indicates the acceleration components of the terminal moving platform in the x, y, and z directions at the nth interpolation. Represents the average value of the acceleration in three directions, v max , a max ,j max They represent the maximum velocity, maximum acceleration, and maximum jerk of the end effector in three directions, respectively.

5. The method for constructing a time-energy-vibration multi-objective function according to claim 4, wherein: The time-energy-vibration comprehensive optimization objective is modeled using the weighted summation method, and its mathematical expression is: Fitness=c1·Z time +c2·Z energy +c3·Z jerk Where c1, c2, and c3 are the non-negative weight coefficients of the time, energy, and jerk objective functions, respectively, which are used to transform multiple single optimization objectives into a comprehensive optimization objective, c1+c2+c3=1.

6. The method for constructing a time-energy-vibration multi-objective function according to claim 4, wherein: To obtain an executable trajectory, the time nodes need to be expanded by a factor of T to match the actual system runtime. During overall optimization, the runtime that satisfies dynamic constraints such as maximum velocity, acceleration, and jerk must first be determined. The normalized time parameter u is multiplied by the actual motion time T to obtain the physical time node ti = T·ui. A quantum particle swarm optimization algorithm is used to solve a comprehensive optimization model for time, energy, and vibration, ensuring the trajectory achieves optimal results in terms of efficiency, energy consumption, and vibration control.

7. The quantum particle swarm optimization algorithm according to claim 1, wherein: This algorithm enhances traditional particle swarm optimization (PSO) by incorporating quantum behavioral models. During the position update process, it not only integrates the particle's own historical optimal and global optimal information but also leverages quantum mechanics to expand the search method, significantly improving global optimization capabilities and convergence speed. Its low number of parameters, low computational complexity, and strong robustness make it particularly suitable for complex multi-objective optimization problems.

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