Efficient algorithms for collision avoidance at intersections

Authors:
Alessandro Colombo;Domitilla Del Vecchio
Affiliations:
MIT, Cambridge, USA;MIT, Cambridge, USA
Venue:
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Year:
2012

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Abstract

We consider the problem of synthesising the least restrictive controller for collision avoidance of multiple vehicles at an intersection. The largest set of states for which there exists a control that avoids collisions is known as the maximal controlled invariant set. Exploiting results from the scheduling literature we prove that, for a general model of vehicle dynamics at an intersection, the problem of checking membership in the maximal controlled invariant set is NP-hard. We then describe an algorithm that solves this problem approximately and with provable error bounds. The approximate solution is used to design a supervisor for collision avoidance whose complexity scales polynomially with the number of vehicles. The supervisor is based on a hybrid algorithm that employs a dynamic model of the vehicles and periodically solves a scheduling problem.