Constrained-Differential-Kinematics-Decomposition-Based NMPC for Online Manipulator Control with Low Computational Costs

Abstract

Flexibility combined with the ability to consider external constraints comprises the main advantages of nonlinear model predictive control (NMPC). Applied as a motion controller, NMPC enables applications in varying and disturbed environments, but requires time-consuming computations. Hence, given the full nonlinear multi-DOF robot model, a delay-free execution providing short control horizons at appropriate prediction horizons for accurate motions is not applicable in common use. This contribution introduces an approach that analyzes and decomposes the differential kinematics similar to the inverse kinematics method to assign Cartesian boundary conditions to specific systems of equations during the model building, reducing the online computational costs. The resulting fully constrained NMPC realizes the translational obstacle avoidance during trajectory tracking using a reduced model considering both joint and Cartesian constraints coupled with a Jacobian transposed controller performing the end-effector’s orientation correction. Apart from a safe distance from the obstacles, the presented approach does not lead to any limitations of the reachable workspace, and all degrees of freedom (DOFs) of the robot are used. The simulative evaluation in Gazebo using the Stäubli TX2-90 commanded of ROS on a standard computer emphasizes the significantly lower online computational costs, accuracy analysis, and extended adaptability in obstacle avoidance, providing additional flexibility. An interpretation of the new concept is discussed for further use and extensions.