Multi-objective Trajectory Planning Method based on the Improved Elitist Non-dominated Sorting Genetic Algorithm

Zesheng Wang,Bo Chen,Wentao Zhu,Ke Chen,Yanbiao Li,Kun Shuai

doi:10.1186/s10033-021-00669-x

Abstract

Robot manipulators perform a point-point task under kinematic and dynamic constraints. Due to multi-degree-of-freedom coupling characteristics, it is difficult to find a better desired trajectory. In this paper, a multi-objective trajectory planning approach based on an improved elitist non-dominated sorting genetic algorithm (INSGA-II) is proposed. Trajectory function is planned with a new composite polynomial that by combining of quintic polynomials with cubic Bezier curves. Then, an INSGA-II, by introducing three genetic operators: ranking group selection (RGS), direction-based crossover (DBX) and adaptive precision-controllable mutation (APCM), is developed to optimize travelling time and torque fluctuation. Inverted generational distance, hypervolume and optimizer overhead are selected to evaluate the convergence, diversity and computational effort of algorithms. The optimal solution is determined via fuzzy comprehensive evaluation to obtain the optimal trajectory. Taking a serial-parallel hybrid manipulator as instance, the velocity and acceleration profiles obtained using this composite polynomial are compared with those obtained using a quintic B-spline method. The effectiveness and practicability of the proposed method are verified by simulation results. This research proposes a trajectory optimization method which can offer a better solution with efficiency and stability for a point-to-point task of robot manipulators.

Highlights

With the advancement of the times, robotics technology is developing rapidly, which makes manipulators widely applied in industrial filed
The results showed that the efficiency obtained by the multi-objective differential evolution (MODE) technique was higher, while the richer the diversity of the Pareto solution was got by NSGA-II
All non-dominated solutions of the trajectory optimizations, from the starting point to the eight ending points, offered by INSGA-II over 100 runs, are compared to that of MO-NSGA-II, SHAMODE-WO, IMOPSO, multi-objective evolutionary algorithms (MOEA)/D-URAW and IMODE in terms of inverted generational distance (IGD), HV and OO, and these experiment results are gathered for statistical analysis

Summary

Introduction

With the advancement of the times, robotics technology is developing rapidly, which makes manipulators widely applied in industrial filed. To improve the convergence and diversity of the Pareto optimal front and the computational efficiency of the traditional NSGA-II, an INSGA-II to obtain the time and torque fluctuation optimal trajectories is proposed. The acceleration of the mechanism is not zero at initial and final points by applying the composite polynomial into constructing trajectory, which is unfavorable for the start and stop of the manipulator. The Bezier curve of Eq (4) provides a better convergence to the starting and ending points, while the polynomial of Eq (5) provides a smooth transition in the vicinity of the endpoints The differences between the individuals are larger, so the exploration is selected to ensure the diversity of the population and avoid the algorithm if ξi

Xi Xi

IMOPSO Mean SD

Conclusions

Findings

Composite polynomials