Infeasibility-free inverse kinematics method

The problem of inverse kinematics is revisited in the present paper. The paper is focusing on the problem of solving the inverse kinematics problem while respecting velocity limits on both the robot's joints and the end-effector. Even-though the conventional inverse kinematics algorithms have been proven to be efficient in many applications, defining an admissible trajectory for the end-effector is still a burdensome task for the user, and the problem can easily become unsolvable. The main idea behind the proposed algorithms is to consider the sampling time as a free variable, hence adding more flexibility to the optimization problem associated with the inverse kinematics. We prove that the reformulated problem has always a solution if the end-effector path is in the reachable space of the robot, thus solving the problem of infeasibility of conventional inverse kinematics methods. To validate the proposed approach, we have conducted three simulations scenarios. The simulation results point that while the conventional inverse kinematics methods fail to track precisely a desired end-effector trajectory, the proposed algorithms always succeed.