Real-Time Predictive Kinematics Control of Redundancy: a Benchmark of Optimal Control Approaches

Modern collaborative manipulators operate in unknown environments and share the work space with human coworkers. To ensure flexibility, their kinematic design is redundant which increases the solution space of the inverse kinematics (IK). We propose a real-time capable Predictive Kinematics Controller (PKC) that tracks task space trajectories as a first priority and computes optimal joint trajectories w.r.t. secondary objectives based on model predictive control (MPC). Therefor, the PKC solves a MPC problem in the nullspace of the task space trajectory. We benchmark a direct shooting, a direct collocation and an indirect gradient method in simulation and we identify the direct shooting method as the most efficient. We demonstrate the superior performance of the PKC compared to state-of-the-art local redundancy resolution approaches. In experiments, we show the real-time capability of our implementation.