Inverse Kinematics: An Alternative Solution Approach Applying Metaheuristics

Abstract

The inverse kinematics problem (IKP) is fundamental in robotics, but it gets harder to solve as the complexity of the mechanisms increases. For that reason, several approaches have been applied to solve it, including metaheuristic algorithms. This work presents a proposal for solving the IKP of a doubly articulated kinematic chain by means of a modified differential evolution (DE) algorithm. The novelty of the proposal is both in the modeling of the problem and the modification to the DE for solving it. The modeling is inspired by a technique used in animation software to recreate movements by dividing the complete trajectory in a number of segments. Each segment represents a single optimization problem linked to the IKP as a sequence that is solved by the modified DE where the initial population for each single problem is biased by using the solution of the previous one. The approach produces solutions for positioning the end effector in a specific point within the work space while minimizing the angular displacement between the initial and final poses. The proposal was able to obtain solutions requiring a fewer total execution cycles compared to the usual approach of solving only one optimization problem related to the inverse kinematics. Different trajectories were used to test the solutions generated by the proposed approach, and the set of conditions that must be covered to apply it to solve the IKP of a particular mechanism are presented.