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Neighboring extremal nonlinear model predictive control of a rigid body on SO(3)

Published online by Cambridge University Press:  06 January 2023

Shiva Bagherzadeh ,
Hossein Karimpour Open the ORCID record for Hossein Karimpour [Opens in a new window]  and
Mehdi Keshmiri
Shiva Bagherzadeh
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
Hossein Karimpour*
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran
Mehdi Keshmiri
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
*
*Corresponding author. E-mail: h.karimpour@eng.ui.ac.ir
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Abstract

The issue of implementing nonlinear model predictive control (NMPC) on mechanical systems evolving on special orthogonal group (SO(3)) is taken into consideration in the first place. Necessary conditions of optimality are extracted based on Lie group variational integrators, leading to a two-point boundary value problem (TPBVP) which is solved using sensitivity derivatives and indirect shooting methods. Fast Newton-like methods referred to as fast solvers which are commonly used to solve the TPBVP are established based on the repetition of a nonlinear process. The numerical schemes employed to alleviate the computation burden consist of eliminating some constraint-related but non-essential terms in the trend of sensitivity derivatives calculation and for solving the TPBVP equations. As another claim, assuming that a first attempt to resolve the NMPC problem is accessible, the problem subjected to some changes in its initial conditions (due to some re-planning schemes) can be resolved cost-effectively based on it. Instead of solving the whole optimization process from the scratch, the optimal control inputs and states of the system are updated based on the neighboring extremal (NE) method. For this purpose, two approaches are considered: applying NE method on the first solution that leads to a neighboring optimal solution, or assisting this latter by updating the NMPC-related optimization using exact TPBVP equations at some predefined intermediate steps. It is shown through an example that the first method is not accurate enough due to error accumulations. In contrast, the second method preserves the accuracy while reducing the computation time significantly.

Keywords

nonlinear model predictive controlneighboring extremalLie group variational integratorssensitivity derivativescomputation time
Type
Research Article
Information
Robotica , Volume 41 , Issue 4 , April 2023 , pp. 1313 - 1334
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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