Interval Computing of the Viability Kernel with Application to Robotic Collision Avoidance

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.