Time-Energy-Jerk Dynamic Optimal Trajectory Planning for Manipulators Based on Quintic NURBS

In this paper, the multi-objective dynamic optimal trajectory planning of an industrial robot manipulator by considering its kinematic and dynamic constraints is presented. Two multi-objective algorithms viz., a fast and elitist multi- objective genetic algorithm (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO) are proposed to settle this matter. Trajectories are defined by quintic NURBS curve, which mathematical model is set up so that it can be applied to define the trajectory easily. Simulations results are presented for industrial robots (PUMA 560 robot) with respect to three objectives, time optimal, energy optimal and smoothness optimal. The results obtained from NSGA-II and MOPSO techniques are compared and analyzed as well as the Pareto optimal fronts obtained from considering friction or not. At last, a normalized weighting objective function is constructed to select a desired optimal solution from the Pareto optimal fronts, the high-order continuous optimal trajectory therefore can be obtained.