A projected lagrange-d'Alembert principle for forced nonsmooth mechanics and optimal control

David Pekarek, Todd David Murphey

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This paper extends the projected Hamilton's principle (PHP) formulation of nonsmooth mechanics to include systems with nonconservative forcing according to a projected Lagrange-d'Alembert principle (PLdAP). As seen with the conservative PHP, the PLdAP treats mechanical systems on the whole of their configuration space, captures nonsmooth behaviors using a projection mapping onto the system's feasible space, and offers additional smoothness (relative to classical approaches) in the space of solution curves. Examining implications of the PLdAP for fully actuated optimal control problems, we prove that to identify optimal feasible trajectories it is sufficient to find unconstrained trajectories according to an alternate set of optimality conditions. Focusing on the control problem expressed in the unconstrained space, we approximate optimal solutions with a path planning method that dynamically adds and removes impacts during optimization. The method is demonstrated in determining an optimal policy for a forced particle subject to a nonlinear unilateral constraint.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages7777-7784
Number of pages8
ISBN (Print)9781467357173
DOIs
StatePublished - Jan 1 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period12/10/1312/13/13

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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    Pekarek, D., & Murphey, T. D. (2013). A projected lagrange-d'Alembert principle for forced nonsmooth mechanics and optimal control. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 7777-7784). [6761124] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6761124