Guaranteeing safe, i.e. collision-free, motion for robotic systems is usually tackled in the Inevitable Collision State (ICS) framework. This paper explores the use of the more general Viability theory as an alternative when safe motion involves multiple motion constraints and not just collision avoidance. Central to Viability is the so-called viability kernel, i.e. the set of states of the robotic system for which there is at least one trajectory that satisfies the motion constraints forever. The paper presents an algorithm that computes off-line an approximation of the viability kernel that is both conservative and able to handle time-varying constraints such as moving obstacles. Then it demonstrates, for different robotic scenarios involving multiple motion constraints (collision avoidance, visibility, velocity), how to use the viability kernel computed off-line within an on-line reactive navigation scheme that can drive the robotic system without ever violating the motion constraints at hand.

A prerequisite to safe robot motion is to avoid Inevitable Collision States (ICS). However, the characterization of the ICS set is a challenge. Several approximation methods have been proposed, most of which either are overly conservative or fail to provide proper motion safety guarantees. In order to to improve safety guarantees, we build upon Viability Theory and adapt an algorithm designed to approximate the Viability Kernel, a concept similar to ICS. Our algorithm is applied first to a challenging static environment scenario. It is then extended to handle dynamic environments. Although it is not possible in general to ensure safety forever, we manage nonetheless to achieve infinite motion safety in two special cases.