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.