Completeness results for a point-to-point inverse kinematics algorithm

We propose a novel and global algorithm to solving the point-to-point inverse kinematics problem for redundant manipulators. Given an initial configuration of the robot, the problem is to find a reachable (path-connected) configuration that corresponds to a desired position and orientation of the end-effector. Our approach was inspired by recent motion planning research and explicitly takes into account constraints due to joint limits, self-collisions and static obstacles in the environment. The problem is posed as an optimization problem. Central to solving this optimization problem is a novel representation, the kinematic roadmap of a manipulator. The kinematic roadmap captures the connectivity of the connected component of the free configuration space of the manipulator in a finite graph like structure. The point-to-point inverse kinematics problem is then solved (with a local planner) using this roadmap. In this paper, we provide completeness results for our algorithm