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Robust Obstacle Avoidance for Constrained Linear Discrete Time Systems: A Set-theoretic Approach


Sasa V. Rakovic, F. Blanchini, E.Cruck, M. Morari

IEEE Conference on Decision and Control

This paper considers the robust obstacle avoidance problem for constrained linear discrete time systems from the set–theoretic point of view. We first consider the simple problem of avoiding a single convex obstacle and we show that even in the presence of linear dynamics and convex constraints on the controls and uncertainty the convexity of the capture region is lost, so the exact computational procedure becomes very hard. Then we provide inner and outer approximation methods based on sequences of convex sets. We then face the problem of multiple convex obstacles. We introduce the distinction between interacting or non–interacting obstacles depending whether the avoidance region for the set of obstacles can be computed as the intersection of the individual avoidance regions. We provide a set of illustrative and telling examples, in particular, we report an example having a robust avoidance region which is strongly disconnected.

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% Autogenerated BibTeX entry
@InProceedings { RakEtal:2007:IFA_2839,
    author={Sasa V. Rakovic and F. Blanchini and E.Cruck and M. Morari},
    title={{Robust Obstacle Avoidance for Constrained Linear Discrete
	  Time Systems: A Set-theoretic Approach}},
    booktitle={IEEE Conference on Decision and Control},
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