Game-Based Social Learning Particle Swarm Optimizer for Inverse Kinematics of Robotic Arms

Robot inverse kinematics is the foundation of robotics and an indispensable part of robot development and applications. The inverse kinematics of a robotic arm involves its specific configuration, the non-convex coupling relationships between joints, and the presence of multiple solutions, among other factors. Existing works usually focus on the robotic arm as a whole, emphasizing the pose accuracy of the robot's end-effector, without considering the individuality of each joint. In this paper, the inverse kinematics problem of robotic arms is formulated as a non-convex optimization problem, with the goal of optimizing the contribution of each joint. Game theory is rigorously introduced to convert the optimization problem into a joint game Nash equilibrium (NE) problem. A generalized Lagrange method is used to handle coupling constraints by introducing additional penalty terms into the objective function. We propose a game-based social learning particle swarm optimization (GSLPSO) algorithm that combines NE strategy and social learning mechanism to enhance the problem-solving process. The proposed GSLPSO is compared with existing relevant algorithms and verified on a real-world robotic arm AUBO i16, which proves the superiority and practicality of the proposed algorithm.