Approximate safety enforcement using computed viability envelopes

A numerical method is proposed for the constraint of the state of a dynamical system such that it cannot enter a predefined failure region. The proposed approach to this viability problem involves an explicit numerical approximation of a viability envelope, coupled with a practical strategy for enforcing containment that is based upon a predictive look-ahead strategy. The approach can be applied to achieve automated "intervention when necessary" to enforce system safety at interactive rates. Applications are shown to several low-dimensional systems, including steering control of a vehicle constrained to a given environment geometry.