Robust Optimal Inverse Kinematics with Self-Collision Avoidance for a Humanoid Robot

A singularity-robust inverse kinematics framework with self-collision avoidance is proposed for a 7 degree-of-freedom (DOF) robot arm, based on minimization of energy consumption. We consider a fully revolute and redundant robot arm, consisting of two spherical joints located at the shoulder and the wrist, connected by a hinge joint at the elbow. This kinematic configuration allows the elbow to swivel freely about an axis joining the wrist and shoulder, thus allowing the redundancy to be parameterized by a single variable, namely the swivel angle. Closed form solutions for the inverse kinematics (IK) problem exist if the elbow position is known. Generally, a set of valid IK solutions, which comply with structural constraints, can be obtained from the entire range of solutions that are generated by swiveling the elbow through 360°. An objective function is proposed to determine the optimal joint trajectory based on a minimum energy criterion. To complete the framework, the issue of kinematic singularity is handled by using the concept of energy minimization.