Optimal trajectory generation method to find a smooth robot joint trajectory based on multiquadric radial basis functions

Nadir, Bendali; Ouali, Mohammed; Nguyen, Minh-Tuan; Said, Abderrezak

doi:10.1007/s00170-022-08696-1

Cited by 16 publications

(4 citation statements)

References 44 publications

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“…When planning a time-optimal trajectory for manipulators, the goal is to generate a path that satisfies the manipulator's kinematic constraints while also minimizing the time required to complete the task. One approach that was proposed in paper [8] is to use multiple quadratic radial basis functions to generate smooth motion trajectories for the manipulator. This method uses two objective functions, one based on the total running time and the other on the square of the jerk, which are minimized in order to achieve a manipulator's optimal trajectory in time.…”

Section: Introductionmentioning

confidence: 99%

Time-Optimal Trajectory Planning for the Manipulator Based on Improved Non-Dominated Sorting Genetic Algorithm II

Hou

Chen

2023

Applied Sciences

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To address the issues of low efficiency and lengthy running time associated with trajectory planning for 6-degree-of-freedom manipulators, this paper introduces a novel solution that generates a time-optimal path for a manipulator while adhering to its kinematic limitations. The proposed method comprises several stages. Firstly, the kinematics of the manipulator are analyzed. Secondly, the manipulator’s joint-space path points are interpolated via the quintic B-spline curve. Subsequently, the non-dominated sorting genetic algorithm II (NSGA-II) is improved by applying reinforcement learning to optimize its crossover and mutation probabilities, and the variable neighborhood search (VNS) algorithm is integrated to enhance its local search capability. Finally, the joint increments and running time of the manipulator are optimized using the improved NSGA-II, and the time-optimal trajectory is then determined by simulation on MATLAB. Furthermore, compared with other conventional optimization methods, the proposed approach has reduced the total running time by 19.26%, effectively improving the working efficiency of the manipulator.

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Section: Introductionmentioning

confidence: 99%

Time-Optimal Trajectory Planning for the Manipulator Based on Improved Non-Dominated Sorting Genetic Algorithm II

Hou

Chen

2023

Applied Sciences

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“…Considering the execution characteristics of joint actuators, most trajectory smoothing planning considers the planning method in joint space. This takes joint velocity, acceleration, and jerk continuity as the trajectory smoothing targets [16,17]. Considering the Gaussian interpolation of the boundary conditions, a radial basis function method was proposed by Chettibi [18] to generate point-to-point smooth trajectories of robot arms.…”

Section: Introductionmentioning

confidence: 99%

Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space

Zhu,

He,

et al. 2023

Mathematics

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Delta parallel robots have been widely used in precision processing, handling, sorting, and the assembly of parts, and their high efficiency and motion stability are important indexes of their performance.Corners created by small line segments in trajectory planning cause abrupt changes in a tangential discontinuous trajectory, and the vibration and shock caused by such changes seriously affect the robot’s high-speed and high-precision performance. In this study, a trajectory-planning method combining Cartesian space and joint space is proposed. Firstly, the vector method and microelement integration method were used to establish the complete kinematic and dynamic equations of a delta parallel robot, and an inverse kinematic/dynamic model-solving program was written based on the MATLAB software R2020a. Secondly, the end-effector trajectory of the delta parallel robot was planned in Cartesian space, and the data points and inverse control points of the end effector’s trajectory were obtained using the normalization method. Finally, the data points and control points were mapped to the joint space through the inverse kinematic equation, and the fifth-order B-spline curve was adopted for quadratic trajectory planning, which allowed the high-order continuous smoothing of the trajectory planning to be realized. The simulated and experimental results showed that the trajectory-smoothing performance in continuous high-order curvature changes could be improved with the proposed method. The peak trajectory tracking error was reduced by 10.53%, 41.18%, and 44.44%, respectively, and the peak torque change of the three joints was reduced by 3.5%, 11.6%, and 1.6%, respectively.

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“…MQ-RBF compelled them to utilize a generalized cross-validation criterion to locate the shape parameter. There are also some methods [10][11][12][13][14][15][16] that have been developed that significantly advance the selection method research for shape parameters for MQ-RBF interpolation. However, many individuals still encounter challenges.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Selection Method for Shape Parameters in MQ-RBF Interpolation for Two-Dimensional Scattered Data and Its Application to Integral Equation Solving

Sun

Gong

2023

Fractal Fract

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The paper proposes an adaptive selection method for the shape parameter in the multi-quadratic radial basis function (MQ-RBF) interpolation of two-dimensional (2D) scattered data and achieves good performance in solving integral equations (O-MQRBF). The effectiveness of MQ-RBF interpolation for 2D scattered data largely depends on the choice of the shape parameter. However, currently, the most appropriate parameter is chosen by empirical techniques or trial and error, and there is no widely accepted method. Fourier transform can linearly represent 2D scattering data as a combination of sine and cosine functions. Therefore, the paper employs an improved stochastic walk optimization algorithm to determine the optimal shape parameters for sine functions and their linear combinations, generating a dataset. Based on this dataset, the paper trains a particle swarm optimization backpropagation neural network (PSO-BP) to construct an optimal shape parameter selection model. The adaptive model accurately predicts the ideal shape parameters of the Fourier expansion of 2D scattering data, significantly reducing computational cost and improving interpolation accuracy. The adaptive method forms the basis of the O-MQRBF algorithm for solving one-dimensional integral equations. Compared with traditional methods, this algorithm significantly improves the precision of the solution. Overall, this study greatly facilitates the development of MQ-RBF interpolation technology and its widespread use in solving integral equations.

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Optimal trajectory generation method to find a smooth robot joint trajectory based on multiquadric radial basis functions

Cited by 16 publications

References 44 publications

Time-Optimal Trajectory Planning for the Manipulator Based on Improved Non-Dominated Sorting Genetic Algorithm II

Time-Optimal Trajectory Planning for the Manipulator Based on Improved Non-Dominated Sorting Genetic Algorithm II

Trajectory Smoothing Planning of Delta Parallel Robot Combining Cartesian and Joint Space

An Adaptive Selection Method for Shape Parameters in MQ-RBF Interpolation for Two-Dimensional Scattered Data and Its Application to Integral Equation Solving

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