  In this paper, we present a task space-based local motion planner that
incorporates collision avoidance and constraints on end-effector motion during
the execution of a task. Our key technical contribution is the development of a
novel kinematic state evolution model of the robot where the collision
avoidance is encoded as a complementarity constraint. We show that the
kinematic state evolution with collision avoidance can be represented as a
Linear Complementarity Problem (LCP). Using the LCP model along with Screw
Linear Interpolation (ScLERP) in SE(3), we show that it may be possible to
compute a path between two given task space poses by directly moving from the
start to the goal pose, even if there are potential collisions with obstacles.
The scalability of the planner is demonstrated with experiments using a
physical robot. We present simulation and experimental results with both
collision avoidance and task constraints to show the efficacy of our approach.
