Learning Controllers (and Proofs of Correctness) from Demonstrations

ABSTRACT: We present approaches for learning control algorithms for autonomous vehicles from demonstrations. Given a dynamical model of a vehicle, and a desired specification such as the trajectory to be driven and speed limits to maintain, we wish to learn control laws, along with "certificates" of correctness, expressed in a suitable formal proof system.  Our learning approach is based on a user-provided demonstrator that can be queried at specific system configurations and results in a control input to be used for that configuration.  For instance, nonlinear model predictive controllers (NMPCs) built using optimization solvers and carefully designed cost functions can serve the role of a demonstrator. Given such a demonstrator, we show how to effectively learn a control law and a proof of its correctness for desired properties such as safety, reachability and path following. We prove rapid convergence of our learning scheme in polynomial time using ideas from convex analysis. If successful, the resulting controller comes with a proof of correctness over the given dynamical model.  Finally, we demonstrate some of the advantages of our approach using laboratory experiments that evaluate our controllers on a 1/8th scale model car.

Joint Work with Sina Aghli, Christoffer Heckman  and Hadi Ravanbakhsh.

BIO: Sriram Sankaranarayanan is an associate professor of computer science at CU Boulder. His research interests focus primarily on the formal verification and synthesis of cyber-physical systems with applications to autonomous medical devices and vehicles. He obtained a PhD in Computer Science from Stanford University (2005) and worked as a researcher at NEC Laboratories America in Princeton, NJ, before joining CU Boulder in 2009.