Learning Certified Control using Contraction Metric
This work provides a method for designing provably safe and robust control policies for robotic systems, which is critical for safety in motion planning.
This paper addresses the challenge of designing certified control policies for robots to ensure convergence to a desired trajectory or bounded tracking error under disturbances. The authors developed a neural network-based learning framework that co-synthesizes a contraction metric and a controller for control-affine systems, demonstrating improved tracking error and faster execution compared to leading methods.
In this paper, we solve the problem of finding a certified control policy that drives a robot from any given initial state and under any bounded disturbance to the desired reference trajectory, with guarantees on the convergence or bounds on the tracking error. Such a controller is crucial in safe motion planning. We leverage the advanced theory in Control Contraction Metric and design a learning framework based on neural networks to co-synthesize the contraction metric and the controller for control-affine systems. We further provide methods to validate the convergence and bounded error guarantees. We demonstrate the performance of our method using a suite of challenging robotic models, including models with learned dynamics as neural networks. We compare our approach with leading methods using sum-of-squares programming, reinforcement learning, and model predictive control. Results show that our methods indeed can handle a broader class of systems with less tracking error and faster execution speed. Code is available at https://github.com/sundw2014/C3M.