Approximate continuous-time optimal control in obstacle avoidance by time/space discretization of non-convex state constraints

H.L. Hagenaars, J. Imura, H. Nijmeijer

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

21 Citations (Scopus)

Abstract

This paper addresses an approximate version of the optimal control problem with non-convex state constraints via discretization of time and space, where the specific application pursued is the obstacle avoidance problem. First, it is pointed out that the standard continuous-time cost function with the final state fixed is not suitable to the optimal control problem under the non-convex state constraints, and then a new cost function including intermediate target states is proposed. Next, for the optimal control problem with this cost function, where the non-convex state constraints are discretized with respect to time axis and state space, an optimal continuous-time control is given in an explicit form, including the intermediate target states obtained by solving a discrete optimization problem. Efficient algorithms such as the breadth first search algorithm can be applied to this discrete problem. Thus the continuous-time trajectory as well as the discretized state at each discrete time is simultaneously optimized. Finally, we illustrate the effectiveness of the proposed approach with numerical simulations
Original languageEnglish
Title of host publicationProceedings of the 2004 IEEE international conference on control applications : September 2-4, 2004, Taipei, Taiwan
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages878-883
ISBN (Print)0-7803-8633-7
Publication statusPublished - 2004

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