Design of a fast model predictive controller based on the fully actuated system approach

Nonlinear Model Predictive Control (NMPC) demonstrates strong capability in handling complex constrained systems; however, its non-convex optimization nature results in high computational complexity that limits practical implementation in real-time control scenarios. To address this computational bottleneck, this paper proposes an efficient Fully Actuated Fast Model Predictive Control (FA-FMPC) method. This method leverages the fully actuated (FA) system approach to modify the open-loop characteristics of nonlinear systems exhibiting complex nonlinearity, strong coupling, or time-delay effects, thereby constructing a linear time-invariant closed-loop system with a freely configurable characteristic structure. Based on this linear time-invariant system, a Fast Model Predictive Control (Fast MPC) method is designed. When the system constraints are convex, the NMPC problem can be transformed into a convex MPC problem. To improve computational efficiency, the Alternating Direction Method of Multipliers (ADMM) is employed to decompose the global optimization problem into multiple subproblems and solve them through alternating iterations. Meanwhile, the Riccati solution of the Linear Quadratic Regulator (LQR) is utilized to optimize the primal variable update process in ADMM, and by precomputing matrix operation components, online matrix decomposition is avoided, significantly enhancing computational efficiency. To validate the effectiveness of the proposed method, simulation verification is conducted on an under-actuated robotic system and a Universal Robots UR5 manipulator simulated in ROS Noetic with Gazebo.