Inter-sample avoidance in trajectory optimizers using mixed-integer linear programming

Arthur Richards*, Oliver Turnbull

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

28 Citations (Scopus)


This paper proposes an extension to trajectory optimization using mixed-integer linear programming. The purpose of the extension is to ensure that avoidance constraints are respected at all times between discrete samples, not just at the sampling times themselves. The method is very simple and involves applying the same switched constraints at adjacent time steps. This requires fewer additional constraints than the existing approach and is shown to reduce computation time. A key benefit of efficient inter-sample avoidance is the facility to reduce the number of time steps without having to compensate by enlarging the obstacles. A further extension to the principle is presented to account for curved paths between samples, proving useful in cases where narrow passageways are traversed.

Original languageEnglish
Pages (from-to)521-526
Number of pages6
JournalInternational Journal of Robust and Nonlinear Control
Issue number4
Early online date12 Nov 2013
Publication statusPublished - 10 Mar 2015


  • Collision avoidance
  • Mixed integer linear programming
  • Trajectory optimization


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