Learning Stabilizable Dynamical Systems via Control Contraction Metrics
This work addresses the need for more reliable model-based reinforcement learning in robotics by integrating nonlinear control theory, though it is incremental as it builds on existing methods.
The authors tackled the problem of learning stabilizable nonlinear dynamical systems for robotics by introducing a control-theoretic regularizer based on stabilizability, which improved trajectory generation and tracking performance, especially with few demonstrations, as validated on a simulated planar quadrotor system.
We propose a novel framework for learning stabilizable nonlinear dynamical systems for continuous control tasks in robotics. The key idea is to develop a new control-theoretic regularizer for dynamics fitting rooted in the notion of stabilizability, which guarantees that the learned system can be accompanied by a robust controller capable of stabilizing any open-loop trajectory that the system may generate. By leveraging tools from contraction theory, statistical learning, and convex optimization, we provide a general and tractable semi-supervised algorithm to learn stabilizable dynamics, which can be applied to complex underactuated systems. We validated the proposed algorithm on a simulated planar quadrotor system and observed notably improved trajectory generation and tracking performance with the control-theoretic regularized model over models learned using traditional regression techniques, especially when using a small number of demonstration examples. The results presented illustrate the need to infuse standard model-based reinforcement learning algorithms with concepts drawn from nonlinear control theory for improved reliability.