مدل سازی مسیر تکاملی چندمعیاره روبات های صنعتی در حضور موانع

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.

The design of engineering systems involves simultaneous consideration of multiple criteria or objectives. Some of these objectives will be in conflict often. Thus, a trade-off exists, which can be investigated by using multi-objective optimization methods. In such a problem, no single optimal solution exists; rather there is a set of equally valid optimal solutions known as the Pareto optimal set. The solutions in this set show the designer what is possible and allow him to make a fully informed choice. The goal of robot systems is to do tasks at a cost as low as possible. Thus, the minimum-cost trajectory planning in the two-stage realization of manipulators control (i.e., planning first and tracking next) is an important effort to accomplish the goal. A large number of robotic applications involve repetitive processes. This technological characteristic justifies offline trajectory planning. In order to maximize the speed of operation that affects the productivity in industrial situations, it is necessary to minimize the total traveling time of the robot. More research works have been carried out to get minimum time trajectories (Shiller and Dubowsky, 1991).

Two new general strategies using NSGA-II and MODE for the off-line tridimensional optimal trajectory planning of the industrial robot manipulator (STANFORD robot) in the presence of fixed obstacles are presented. When dealing with fixed obstacles, both the objective functions and the constraint functions have to be up-dated simultaneously at each time instant. Two methods (normalized weighting objective functions method and average fitness factor method) are combinedly used to select best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely SSM and ratio of non-dominated individuals are used to evaluate the strength of 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. Two numerical examples demonstrated the efficiency of the proposed techniques. Both NSGA-II and MODE techniques are better than SUMT (Saramago and Steffen, 2001). It is observed that MODE technique converges quickly than NSGA-II. Also the computational time to find Pareto optimal front in MODE is one-third of that of the NSGA-II (Table 13). So MODE is faster than NSGA-II. From Fig. 11 and Fig. 12, it is observed that NSGA-II gives more number of non-dominated solutions than MODE. Also Pareto optimal front from NSGA-II is better than that of MODE according to distance metric. So NSGA-II technique is best for this multi-criterion optimization problem, if the user wants more number of solutions for his choice. To get more accurate and high flexible trajectory, NURBS function with more number of control points will be used to represent the trajectory in future work. This work opens the door for further investigations on how the evolutionary optimization techniques can be used to solve complex problems.