Computing an Inner and an Outer Approximation of the Viability Kernel

International audienceThe viability kernel corresponds to the set of all state vectors of a controlled dynamic system that are viable, i.e., such that there exists an input such that the system will not enter inside a forbidden zone. In this paper, we propose a method which computes an inner and an outer approximation of the viability kernel in a guaranteed way. Our method is based on interval analysis and uses the notions of V-viability and capture basin. We illustrate our approach on the car on the hill problem. A software package has been developed to solve any 2D-problem

Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019