Parametrized hyperplane arrangements for control design with collision avoidance constraints

Daniel Ioan (1) , Sorin Olaru (1) , Ionela Prodan (2) , Florin Stoican (3) , Silviu-Iulian Niculescu (1)

1 L2S - Laboratoire des signaux et systèmes
2 LCIS - Laboratoire de Conception et d'Intégration des Systèmes
3 UPB - University Politehnica of Bucharest [Romania]

This paper concerns the problem of collision avoidance in a dynamical multi-obstacle environment. The design problem is commonly stated in the literature in terms of a receding-horizon constrained optimization problem over a non-convex domain. Preliminary results based on hyper-plane arrangements lead to a mixed-integer formulation of the problem. This formalism is adequate for a static multi-obstacle environment, but may be impractical in a dynamical context. Nevertheless, this shortcoming can be alleviated by considering an additional analysis step and by an appropriate proper choice of the representation of the environment in a time-varying framework. The present paper tackles this issue by using zonotopes and discussing their parametrization in a collision avoidance type of application.

Domaines: Automatique

Daniel Ioan, Sorin Olaru, Ionela Prodan, Florin Stoican, Silviu-Iulian Niculescu. Parametrized hyperplane arrangements for control design with collision avoidance constraints. 15th IEEE International Conference on Control and Automation (ICCA), Jul 2019, edinburgh, United Kingdom. ⟨10.1109/ICCA.2019.8899977⟩. ⟨hal-02329329⟩