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Research Papers

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

[+] Author and Article Information
Prem Kumar, B. Bhavya Anoohya

Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore 560012, India

Radhakant Padhi

Professor
Department of Aerospace Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: padhi@iisc.ac.in

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received August 27, 2017; final manuscript received August 28, 2018; published online October 19, 2018. Assoc. Editor: Soo Jeon.

J. Dyn. Sys., Meas., Control 141(2), 021014 (Oct 19, 2018) (12 pages) Paper No: DS-17-1428; doi: 10.1115/1.4041356 History: Received August 27, 2017; Revised August 28, 2018

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.

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References

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Figures

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Fig. 1

Differential wheel drive two wheel mobile robot kinematic model

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Fig. 2

Block diagram representation for a realistic simulation environment

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Fig. 3

Mobile robot trajectory for ∞-shaped reference trajectory

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Fig. 4

Mobile robot position and vehicle orientation for ∞-shaped reference trajectory

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Fig. 5

Mobile robot position tracking errors (Δx,Δy) for ∞-shaped reference trajectory

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Fig. 6

Wheel rotation rate for ∞-shaped reference trajectory

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Fig. 7

Differential drive two wheeled mobile robot

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Fig. 8

Experimental setup

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Fig. 9

Path of the mobile robot corresponding to ∞-shaped reference trajectory during experiment

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Fig. 10

x-position, y-position, and heading angle (ϕ) of the mobile robot corresponding to ∞-shaped reference trajectory during experiment

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Fig. 11

Angular speed of the motors of right and left wheels of the mobile robot during experiment corresponding to ∞-shaped reference trajectory

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Fig. 12

Tracking error in the x and y positions corresponding to ∞-shaped reference trajectory during experiment

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