Trajectory planning in parallel kinematic manipulators using a constrained multi-objective evolutionary algorithm

Abstract

Generating manipulator trajectories considering multiple objectives with kinematics and dynamics constraints is a non-trivial optimization. In this paper, a constrained multi-objective genetic algorithm (MOGA) based technique is proposed to address this problem for a general motor-driven parallel kinematic manipulator. The planning process is composed of searching for a motion ensuring the accomplishment of the assigned task, minimizing the traverse time, and expended energy subject to various constraints imposed by the associated kinematics and dynamics of the manipulator. This problem is treated via an adequate parametric path representation in the task space of the moving platform, and then the use of the constrained MOGA for solving the resulted nonlinear multi-objective optimization problem. Simulation results are presented for the trajectories of the parallel kinematic manipulator, and a subsequent comparison with the weighted sum method is also carried out.

Reconfiguration for the Maximum Dynamic Wrench Capability of a Parallel Robot

“…On the basis of the developed structured Boltzmann-Hamel-d'Alembert formulism for a parallel mechanism [23][24][25], the dynamics of the PR can be given as…”

“…The allowable dynamic wrench capability is defined as the following: firstly, by discretizing the task trajectory under a presumed configuration a i , the dynamic wrench force f w and wrench moment n w at each spaced point are obtained by minimizing the fitness function given in Equation (26) subject to the equality constraint Equation (22) and the inequality constraints formulated in Equations (27) and (28). Then, the minimal dynamic wrench force and wrench moment are searched along the trajectory and then substituted into the Equation (25) so that the cost function value is defined as the allowable dynamic wrench capability for the task-dependent trajectory.…”

“…Thus, the generated optimization process can be realized as a typical linear programming such that the Simplex-type linear programming method can be directly applied to determine the maximal dynamic wrench capability at each discrete point of the given trajectory. Next, from the obtained values, the minimum dynamic wrench force and moment are chosen as the allowable wrenches, and then the allowable dynamic wrench capability for this task trajectory is evaluated by substituting the minimum dynamic wrenches into the cost function, Equation (25).…”

Kinematics Analysis and Numerical Simulation of Hybrid Serial-Parallel Manipulator Based on Neural Network

“…Kizir et al [15] used Kane transition function to generate several trajectories for controlling a high precision hybrid platform by a PID and sliding mode controller. Chen et al [5] proposed a multi-objective genetic algorithm trajectory planner for a PKM, based on the dynamics approach. Parikh et al [18] presented iteration neural network strategy for solution of forward kinematic of parallel mechanisms.…”

Design for Optimal Performance of 3-RPS Parallel Manipulator Using Evolutionary Algorithms

“…Lara-Molina et al [30] performed the optimal design of a spatial Stewart-Gough platform based on multi-objective optimization; the objective functions are Global Condition Index (GCI), Global Payload Index (GPI) and Global Gradient Index (GGI) using multi-objective Evolutionary Algorithm (MOEA). Chun-Ta Chen et al [31] presented a constrained multi-objective genetic algorithm for a general motor-driven parallel kinematic manipulator 3UPS for the optimal trajectory of a PKM with linear actuators, in which travelling time and energy expended in driving the platform from one pose to another are minimized. Antonio M. Lopes and E.J.…”