Real-time Nonlinear Model Predictive Control of a Robotic Arm Using Spatial Operator Algebra Theory

Abstract

Nonlinear model predictive control (NMPC) has inherent challenges, such as high computational burden, nonconvex optimization, and the necessity of powerful and fast processors with large memory for real-time robotics. In this study, a new NMPC strategy is proposed using Spatial Operator Algebra (SOA) theory to address these challenges, and experimental results are presented for the five degrees of freedom robot manipulator. The proposed scheme is based on an NMPC controller using the SOA-based dynamic model to provide good tracking performance and ensure the satisfaction of constraints. Two novel control schemes, SOA–NMPC and SOA–NMPC proportional-derivative (PD), are introduced for a comprehensive analysis of the proposed innovative approach. The validity of the proposed scheme is experimentally tested through robustness analysis conducted across various tasks, including the addition of weight and exposure to internal/external disturbances. The effectiveness of the proposed approach is demonstrated through benchmarking against NE-NMPC using the Newton–Euler (NE) algorithm, classical MPC, MPC-PD, and PID techniques. The comparative results show that the SOA–NMPC controller provides effective performance and ensures constraints for the entire trajectory of the manipulator, even under varying conditions. © 2025 The Author(s). Journal of Field Robotics published by Wiley Periodicals LLC.