Multi-objective optimal trajectory planning of manipulators based on quintic NURBS

In this paper an interpolation method based on quintic non-uniform rational B-spline(NURBS) is proposed to construct curves when to plan the trajectory of manipulators with respect to three objectives, time optimal, energy optimal and smoothness optimal. The mathematical model of quintic NURBS curve is set up to gain high-order continuous trajectories with endpoint configuration parameters can be specified, and a fast and elitist multi-objective genetic algorithm (NSGA-II) is adopted to optimize the trajectory of manipulators aims to get a series of Pareto optimal solutions under the three objectives. Through the simulation with six-degree of freedom robot shows that quintic NURBS curve can get high-order continuous trajectories and NSGA-II algorithm can provide an effective approach to get the perfect Pareto solutions for quintic NURBS curve. By constructing a average fuzzy membership function, a potential optimal solution can be selected from Pareto optimal set, then the high-order continuous optimal trajectory can be obtained.