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.

Approach and landing guidance using constrained model predictive static programming

“…To deal with the constrained problem, the input command vector U comprising of angle of attack α and pitch rate ω constrained for every step k and bounded by the constraints (10) and ( 11) is expressed as (29).…”

“…MPSP helps in obtaining the solution in a faster sense by the formulation of a static costate vector and offers the viability of computation of sensitivity matrices recursively [26]. The technique is applied to various aerospace guidance applications with faster computational requirements [27][28][29]. Closed-loop guidance based on MPSP is proposed to increase the accuracy of satellite-carrier boosters' landing point [30].…”

Fuzzy predictive controller for trajectory tracking of a wheeled mobile root

“…Simultaneously, [10] unveiled an integrated control strategy. These latter combined kinematic with dynamic models, incorporating adaptive fuzzy integral Studies in Engineering and Exact Sciences, Curitiba, v.5, n.1, p.449-472, 2024 terminal sliding mode control and robust compensation.…”

A Multi-Switching Tracking Control Scheme for Autonomous Mobile Robot in Unknown Obstacle Environments

“…Robots follow a desired trajectory generated by a virtual mobile robot based on its kinematic model and initial posture, which can navigate the mobile robot to the desired position. This tracking problem has been studied by many researchers, and there are a lot of control strategies are proposed for mobile robots, such as model predict control (MPC) [20][21][22], sliding mode control (SMC) [23][24][25][26], fuzzy control [27][28][29], adaptive control [30][31][32], and intelligent control [33,34], etc. However, most of them studied the trajectory tracking problem under the assumption that the movement of the robot is in an obstacle-free environment.…”