Real-time Inverse Kinematics of (2n + 1) DOF hyper-redundant manipulator arm via a combined numerical and analytical approach

Abstract

The task of solving Inverse Kinematics (IK) for redundant serial chain manipulators has been and still continues to be quite challenging in the field of robotics. Researchers from different fields have succeeded in solving the IK of different robot configurations for various applications. However, the challenge of computational efficiency still remains, in particular for complex robot configurations, to be used for real-time applications. This paper presents a novel, computationally efficient method of performing IK for general 2n+1 (n is the number of joints) DOF manipulators with a spherical joint at the wrist. It uses the simplicity of analytical solutions to enhance the speed of numerical solvers that operate on each joint location individually. The problem of IK is approached as a constrained optimization, where obstacle avoidance and limit avoidance at joints are used as illustrations. The joint limitations are handled implicitly as boundary conditions for the numerical algorithm. The algorithm was executed and implemented on various paths for a 9 DOF arm and also simulated for a 13 DOF arm for generalization purposes.