Constrained closed loop inverse kinematics

Abstract

This paper introduces a kinematically constrained closed loop inverse kinematics algorithm for motion control of robots or other articulated rigid body systems. The proposed strategy utilizes gradients of collision and joint limit potential functions to arrive at an appropriate weighting matrix to penalize and dampen motion approaching constraint surfaces. The method is particularly suitable for self collision avoidance of highly articulated systems which may have multiple collision points among several segment pairs. In that respect, the proposed method has a distinct advantage over existing gradient projection based methods which rely on numerically unstable null-space projections when there are multiple intermittent constraints. We also show how this approach can be augmented with a previously reported method based on redirection of constraints along virtual surface manifolds. The hybrid strategy is effective, robust, and does not require parameter tuning. The efficacy of the proposed algorithm is demonstrated for a self collision avoidance problem where the reference motion is obtained from human observations. We show simulation and experimental results on the humanoid robot ASIMO.

Constrained resolved acceleration control for humanoids

“…9 has important characteristics which can be exploited in enforcing kinematic constraints [7], [14]. As will be described in the next section, enforcing constraints at the velocity level can be used in constrained control at the acceleration level.…”

“…In our earlier work, we described an algorithm for solving the first-order constrained closed loop inverse kinematics (CCLIK) problem which proved to be an effective and stable solution for self collision avoidance [7], [14]. The method used a weighted least squares solution to constrain joints from violating their limits and to avoid collisions.…”

“…As described in [7], [14], a singularity robust constrained closed loop inverse kinematics formulation which produces constrained joint velocities,q c , is given bẏ…”

“…This paper examines the problem of task-space control in the presence of joint limit and collision constraints and provides effective solutions to address issues associated with existing algorithms as described above. In particular, the proposed approach uses results from our previously reported constrained inverse kinematics procedure (see [14]), to arrive at a constrained resolved acceleration control formulation which is applicable for redundant as well as non-redundant robotic mechanisms.…”

Self collision avoidance for humanoids using circular and elliptical capsule bounding volumes

“…Dariush et al, in [1] and [2], used a self collision avoidance method in which a virtual surface was placed around one of the colliding body segments. The colliding point was then moved such that it slides along the direction which is tangent to the virtual surface.…”