Abstract
Viability theory provides a set of concepts and algorithms to study uncertain continuous dynamic systems under viability (or state) constraints. Interval computation is about guaranteed numerical methods for approximating sets. The main tool to be used is based on the idea of enclosing real numbers in intervals and real vectors in boxes. Refined interval techniques as contractor programming and guaranteed integration allow to implement the viability kernel and the capture basin algorithms. Results are provided considering the kinematics of the game of two cars. Viability kernel and capture basin algorithms are used to compute backward reachable sets which are differential game capture zones assuming predefined maximum time horizons. Then, collision avoidance between two noncooperative ground mobile robots is performed based on the backward reachable sets mentioned above.
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Acknowledgements
This work was supported by “Agence Nationale de la Recherche” through the ANR ASTRID Maturation funding scheme, VIATIC2 project. The author would like also to thanks the viability theoreticians who suggested remarks and advices to improve this work.
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Le Ménec, S. (2017). Interval Computing of the Viability Kernel with Application to Robotic Collision Avoidance. In: Apaloo, J., Viscolani, B. (eds) Advances in Dynamic and Mean Field Games. ISDG 2016. Annals of the International Society of Dynamic Games, vol 15. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-70619-1_13
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