A Real-Time-Capable Closed-Form Multi-Objective Redundancy Resolution Scheme for Seven-DoF Serial Manipulators

Using a closed-form inverse kinematics solution for motion planning has many advantages compared to traditional numerical approaches, most notably much faster computation times and better suitability for real-time applications. Steady progress has been made to develop an analytic inverse kinematics solution for seven degrees of freedom (DoF) manipulators without joint offsets. Redundancy resolutions have been proposed to push the individual joint angles away from their limits. However, no further objectives are considered in these closed-form solutions. We propose a multi-objective real-time optimization approach that is able to minimize joint velocities and accelerations, while still avoiding joint limits. A closed-form solution to the optimization is derived, which only requires a single intuitive tuning parameter. We provide a free and open-source software implementation of the full kinematics algorithm that covers the complete solution space. The null-space motion resulting from our method is evaluated, achieving faster motion times and smoother arm motions along Cartesian paths in comparison to the state-of-the-art approach. Finally, experimental results with a KUKA iiwa robot are reported.