Formal Policy Learning from Demonstrations for Reachability Properties

Abstract

We consider the problem of learning structured, closed-loop policies (feedback laws) from demonstrations in order to control under-actuated robotic systems, so that formal behavioral specifications such as reaching a target set of states are satisfied. Our approach uses a "counterexample-guided" iterative loop that involves the interaction between a policy learner, a demonstrator and a verifier. The learner is responsible for querying the demonstrator in order to obtain the training data to guide the construction of a policy candidate. This candidate is analyzed by the verifier and either accepted as correct, or rejected with a counterexample. In the latter case, the counterexample is used to update the training data and further refine the policy.The approach is instantiated using receding horizon modelpredictive controllers (MPCs) as demonstrators. Rather than using regression to fit a policy to the demonstrator actions, we extend the MPC formulation with the gradient of the cost-to-go function evaluated at sample states in order to constrain the set of policies compatible with the behavior of the demonstrator. We demonstrate the successful application of the resulting policy learning schemes on two case studies and we show how simple, formally-verified policies can be inferred starting from a complex and unverified nonlinear MPC implementations. As a further benefit, the policies are many orders of magnitude faster to implement when compared to the original MPCs.

Funnel-based Reachability Control of Unknown Nonlinear Systems using Gaussian Processes

“…This work will consider the controller synthesis problem for reachability specification for unknown dynamical systems. In the past few decades, there have been several works in the literature addressing reachability problem (see [10], [11], [12], [13], [14]) for known dynamical systems. To solve this problem, we leverage the funnel-based control approaches [15] that have been extensively used for controlling systems with prescribed performance constraints (see [16] and references therein for examples).…”