Mirror-Descent Inverse Kinematics for Box-constrained Joint Space

This paper proposes a new Jacobian-based inverse kinematics (IK) explicitly considering box-constrained joint space. To control humanoid robots, the reference pose of end effector(s) is planned in task space, then mapped into the reference joints by IK. Due to the limited analytical solutions for IK, iterative numerical IK solvers based on Jacobian between task and joint spaces have become popular. However, the conventional Jacobian-based IK does not explicitly consider the joint constraints, and therefore, they usually clamp the obtained joints during iteration according to the constraints in practice. The problem in clamping operation has been pointed out that it causes numerical instability due to non-smoothed objective function. To alleviate the clamping problem, this study explicitly considers the joint constraints, especially the box constraints in this paper, inside the new IK solver. Specifically, instead of clamping, a mirror descent (MD) method with box-constrained real joint space and no-constrained mirror space is integrated with the conventional Jacobian-based IK methods, so-called MD-IK. In addition, to escape local optima nearly on the boundaries of constraints, a heuristic technique, called $\epsilon$-clamping, is implemented as margin in software level. As a result, MD-IK achieved more stable and enough fast i) regulation on the random reference poses and ii) tracking to the random trajectories compared to the conventional IK solvers.