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research-article

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

[+] Author and Article Information
Prem Kumar

Ph.D. student, Dept. of Aerospace Engineering, Indian Institute of Science, Bangalore, India
prem.kr.singh@gmail.com

B. Bhavya Anoohya

ME student (Graduated), Dept. of Aerospace Engineering, Indian Institute of Science, Bangalore, India
bhavyaanoohya.b@gmail.com

Radhakant Padhi

Professor, Dept. of Aerospace Engineering, Indian Institute of Science, Bangalore, India
padhi@iisc.ac.in

1Corresponding author.

ASME doi:10.1115/1.4041356 History: Received August 27, 2017; Revised August 28, 2018

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 is 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 experimental validation corroborates the simulation results.

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