A geometric algorithm for redundant inverse kinematics with obstacle avoidance in a known environment

Abstract

This paper proposes a geometric method for solving the inverse kinematics (IK) of redundant manipulators while satisfying the collision avoidance criterion. The proposed approach focuses on creating an algorithm for solving the redundant inverse kinematics (RIK) of manipulators in a known environment. Central to the method is the creation of an explicit expression of C-free space of the manipulators by using two new notions, named "inverse Denavit–Hartenberg (D–H) variables" and "interval function". Thus, a single optimized solution far from the obstacles is obtained automatically by exploring in the C-free space, following the principle of selecting the median value of the interval function preferentially. The proposed method is demonstrated using a snake robot, the EAST Articulated Maintenance Arm (EAMA), which is utilized in the EAST (Experimental Advanced Superconducting Tokamak) for maintenance tasks in the vacuum vessel. C-free space of EAMA in EAST is created based on the Obstacle Topology Partition Projection (OTPP) approach and formulated by the interval functions. With the expression of C-free space, a single optimum solution is obtained during the exploration that starts at the end position or pose of the extremity point Pend. Eventually, several tip positions of EAMA are sampled to test the accuracy and correctness of the algorithm.