Time-energy-jerk optimal trajectory planning for high-speed parallel manipulator based on quantum-behaved particle swarm optimization algorithm and quintic B-spline

Abstract

This paper presents a technique for multi-node trajectory planning for high-speed parallel manipulators that optimizes the execution time, energy consumption and jerk (the time derivative of the acceleration of the manipulator joints) to improve working efficiency, decrease energy consumption, dampen vibration and ensure mechanism protection. Initially, an improved quintic B-spline interpolation model is proposed, incorporating additional jerk boundary constraints to dampen residual vibrations at the start and end of the trajectory. Subsequently, the time-energy-jerk optimization model is formulated, with the maximum angular velocity, acceleration, and jerk serving as constraints. The normalized parameter of the B-spline curve is considered to divide the whole model into two submodels. In the first submodel, the satisfaction function is proposed to convert energy and jerk indices into one comprehensive objective for optimization with the quantum-behaved particle swarm optimization (QPSO) algorithm. Time parameters are to be decided as decision variables, regardless of kinematic constraints and execution time. In the second submodel, the optimal time parameters obtained in the first submodel are used as input arguments, and the optimal execution time is determined with respect to the kinematic constraints. The simulation results on a planar parallel manipulator show that the proposed method achieves an efficient trajectory, which is energy-saving and possesses reduced vibration. Application of the comprehensive trajectory generated by the proposed method, rather than the classical method, enhances the maximum productivity of the fast pick-and-place operation to 155 picks per minute from 97 picks/min. This improvement is accomplished by using less energy and reducing vibration.