No abstract

Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical success, these controllers still lack theoretical guarantees on their performance, such as Lyapunov stability (i.e., all trajectories of the closed-loop system are guaranteed to converge to a goal state under the control policy). This is in stark contrast to traditional model-based controller design, where principled approaches (like LQR) can synthesize stable controllers with provable guarantees. To address this gap, we propose a generic method to synthesize a Lyapunov-stable neural-network controller, together with a neural-network Lyapunov function to simultaneously certify its stability. Our approach formulates the Lyapunov condition verification as a mixed-integer linear program (MIP). Our MIP verifier either certifies the Lyapunov condition, or generates counter examples that can help improve the candidate controller and the Lyapunov function. We also present an optimization program to compute an inner approximation of the region of attraction for the closed-loop system. We apply our approach to robots including an inverted pendulum, a 2D and a 3D quadrotor, and showcase that our neural-network controller outperforms a baseline LQR controller. The code is open sourced at https://github.com/StanfordASL/neural-network-lyapunov.

To work in unknown outdoor environments, autonomous sampling machines need the ability to target samples despite limited visibility and robotic arm reach distance. We design a heuristic guided search method to speed up the search process and more efficiently localize the approximate center of soil regions. Through simulation experiments, we assess the effectiveness of the proposed algorithm and discover superior performance in terms of speed, distance traveled, and success rate compared to naive baselines.