A Study on Sparse Hierarchical Inverse Kinematics Algorithms for Humanoid Robots

In humanoid robotic platforms, classical inverse kinematics algorithms, based on L2-regularization of joint velocities or accelerations, tends to engage the motion of all the available degrees of freedom, resulting in movements of the whole robot structure, which are inherently not sparse. The role of sparsity in motion control has recently gained interest in the robotics community for various reasons, e.g., human-like motions, and human-robot interaction, actuation parsimony, yet an exhaustive mathematical analysis is still missing. In order to address this topic, we here propose and compare possible sparse optimization approaches applied to hierarchical inverse kinematics for humanoid robots. This is achieved through LASSO regression and MILP optimization to resolve the IK problem. A first order formulation of the sparse regression problem is further introduced to reduce chattering on the joint velocity profiles. This article presents the theory behind the proposed approaches and performs a comparison analysis based on simulated and real experiments on different humanoid platforms.