Online Predictive Motion Control of Redundant Robots via Model Predictive Control and Full Null Space Parameterization

This paper presents an online control method for redundant robots, designed to predictively prevent future violations of additional objectives while maintaining precise end-effector tracking. In this paper, we propose to use full null space parametrization (FNSP) to determine the optimal linear combination of null space basis vectors and use model predictive control (MPC) to optimize future control sequences for generating joint commands with foresight. Another critical aspect of this work is the online implementation. Analytical gradients of the formulated nonlinear programming (NLP) problem are derived to improve computational speed, and a retained rolling scheme is introduced within the MPC framework to reduce optimization dimensions. The proposed method is validated through tests on a 4-DOF planar manipulator and a 7-DOF Franka Panda robot, with numerical results demonstrating its efficiency.