Model Predictive Static Programming for Optimal Command Tracking: A Fast Model Predictive Control Paradigm

Abstract

Inspired by fast model predictive control (MPC), a new nonlinear optimal command tracking technique is presented in this paper, which is named as “Tracking-oriented Model Predictive Static Programming (T-MPSP).” Like MPC, a model-based prediction-correction approach is adopted. However, the entire problem is converted to a very low-dimensional “static programming” problem from which the control history update is computed in closed-form. Moreover, the necessary sensitivity matrices (which are the backbone of the algorithm) are computed recursively. These two salient features make the computational process highly efficient, thereby making it suitable for implementation in real time. A trajectory tracking problem of a two-wheel differential drive mobile robot is presented to validate and demonstrate the proposed philosophy. The simulation studies are very close to realistic scenario by incorporating disturbance input, parameter uncertainty, feedback sensor noise, time delays, state constraints, and control constraints. The algorithm has been implemented on a real hardware and the experimental validation corroborates the simulation results.