Algorithm for inverse kinematics of a multi-link manipulator

Invers kinematics methods are fundamental for many kinds of robotics control systems. This paper presents a heuristic inverse kinematic algorithm MAR (Mixed Angle Reaching), which combines two approaches: analytical calculations and geometric transformations. This algorithm uses methods for determining intersections of spheres in a 3D space and methods for correcting the length of virtual arms. It was assumed that the multi-link manipulators can be described using Extended Denavit-Hartenberg (EDH) notation for multi-DOF joints. As a result, a compact modular notation was obtained that can be further reproduced. The MAR algorithm is applicable to redundant robots with 7 or more DOF. The proposed method has been compared with two other methods for IK: Damped Least Squares(DLS), which belongs to the analytical solutions family, and Backward Reaching Inverse Kinematics (FABRIK), which is a representative of the family of IK heuristic methods. Our results show that the MAR method can be very attractive for redundant manipu-lators, consisting of several links and multi-DOF joints. It can give performance advantages and higher accuracy compared to DLS and FABRIK algorithms. The proposed algorithm MAR has been successfully tested in a Matlab/Simulink environment and the simulation results has been discussed.