Evolutionary multi-criteria trajectory modeling of industrial robots in the presence of obstacles

Optimal trajectory planning for robot manipulators is always a hot spot in research fields of robotics. This paper presents two new novel general methods for computing optimal motions of an industrial robot manipulator (STANFORD robot) in presence of obstacles. The problem has a multi-criterion character in which three objective functions, a maximum of 72 variables and 103 constraints are considered. The objective functions for optimal trajectory planning are minimum traveling time, minimum mechanical energy of the actuators and minimum penalty for obstacle avoidance. By far, there has been no planning algorithm designed to treat the objective functions simultaneously. When existing optimization algorithms of trajectory planning tackle the complex instances (obstacles environment), they have some notable drawbacks viz.: (1) they may fail to find the optimal path (or spend much time and memory storage to find one) and (2) they have limited capabilities when handling constraints. In order to overcome the above drawbacks, two evolutionary algorithms (Elitist non-dominated sorting genetic algorithm (NSGA-II) and multi-objective differential evolution (MODE) algorithm) are used for the optimization. Two methods (normalized weighting objective functions method and average fitness factor method) are combinedly used to select best optimal solution from Pareto optimal front. Two multi-objective performance measures (solution spread measure and ratio of non-dominated individuals) are used to evaluate strength of the Pareto optimal fronts. Two more multi-objective performance measures namely optimizer overhead and algorithm effort are used to find computational effort of NSGA-II and MODE algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analyzed.