Metaheuristic techniques comparison to optimize robotic end-effector behavior and its workspace

Many robots are dedicated to replicate trajectories recorded manually; the recorded trajectories may contain singularities, which occur when positions and/or orientations are not achievable by the robot. The optimization of those trajectories is a complex issue and classical optimization methods present a deficient performance when solving them. Metaheuristics are well-known methodologies for solving hard engineering problems. In this case, they are applied to obtain alternative trajectories that pass as closely as possible to the original one, reorienting the end-effector and displacing its position to avoid the singularities caused by limitations of inverse kinematics equations, the task, and the workspace. In this article, alternative solutions for an ill-posed problem concerning the behavior of the robotic end-effector position and orientation are proposed using metaheuristic algorithms such as cuckoo search, differential evolution, and modified artificial bee colony. The case study for this work considers a three-revolute robot (3R), whose trajectories can contain or not singularities, and an optimization problem is defined to minimize the objective function that represents the error of the alternative trajectories. A tournament in combination with a constant of proportionality allows the metaheuristics to modify the gradual orientation and position of the robot when a singularity is present. Consequently, the procedure selects from all the possible elbow-configurations the best that fits the trajectory. A classical numerical technique, Newton’s method, is used to compare the results of the applied metaheuristics, to evaluate their quality. The results of this implementation indicate that metaheuristic algorithms are an efficient tool to solve the problem of optimizing the end-effector behavior, because of the quality of the alternative trajectory produced.