Reach-avoid problems with time-varying dynamics, targets and constraints

Jaime F. Fisac, Mo Chen, Claire J. Tomlin, S. Shankar Sastry

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

52 Scopus citations

Abstract

We consider a reach-avoid di erential game, in which one of the players aims to steer the system into a target set without violating a set of state constraints, while the other player tries to prevent the first from succeeding; the system dynamics, target set, and state constraints may all be time-varying. The analysis of this problem plays an important role in collision avoidance, motion planning and aircraft control, among other applications. Previous methods for computing the guaranteed winning initial conditions and strategies for each player have either required augmenting the state vector to include time, or have been limited to problems with either no state constraints or entirely static targets, constraints and dynamics. To incorporate time-varying dynamics, targets and constraints without the need for state augmentation, we propose a modified Hamilton-Jacobi-Isaacs equation in the form of a double-obstacle variational inequality, and prove that the zero sublevel set of its viscosity solution characterizes the capture basin for the target under the state constraints. Through this formulation, our method can compute the capture basin and winning strategies for timevarying games at virtually no additional computational cost relative to the time-invariant case. We provide an implementation of this method based on well-known numerical schemes and show its convergence through a simple example; we include a second example in which our method substantially outperforms the state augmentation approach.

Original languageEnglish (US)
Title of host publicationProceedings of the 18th International Conference on Hybrid Systems
Subtitle of host publicationComputation and Control, HSCC 2015
PublisherAssociation for Computing Machinery, Inc
Pages11-20
Number of pages10
ISBN (Electronic)9781450334334
DOIs
StatePublished - Apr 14 2015
Externally publishedYes
Event18th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2015 - Seattle, United States
Duration: Apr 14 2015Apr 16 2015

Publication series

NameProceedings of the 18th International Conference on Hybrid Systems: Computation and Control, HSCC 2015

Conference

Conference18th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2015
CountryUnited States
CitySeattle
Period4/14/154/16/15

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Computer Science Applications
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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  • Cite this

    Fisac, J. F., Chen, M., Tomlin, C. J., & Shankar Sastry, S. (2015). Reach-avoid problems with time-varying dynamics, targets and constraints. In Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, HSCC 2015 (pp. 11-20). (Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, HSCC 2015). Association for Computing Machinery, Inc. https://doi.org/10.1145/2728606.2728612