Safe Online Planning in Unknown Nonconvex Environments with Implicit Controlled Invariant Sets

Abstract

Abstract This work extends recent results on lifted controlled invariant sets for discrete-time controllable linear systems to non-convex safe sets, consisting of a union of polytopes. First, we show how to construct a closed-form expression of an invariant set in an extended state and input space using additional binary variables. A more efficient encoding is also provided albeit with additional conservativeness. By avoiding the projection of this set onto the original state space, we use this implicit representation in the lifted space as a supervisor in an online planning context where the safe set grows as new information about the environment is sensed. An example with a double-integrator model with a LiDAR sensor is used to demonstrate the overall approach.