  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.
