Enabling safe and robust control of robots via Hamilton-Jacobi Reachability

As autonomous robots become pervasive in daily life, it is important to ensure they successfully accomplish the task while being safe from collisions. These desired behaviours require both perception of the environment and robust control of the robot. Traditional optimal control method Hamilton-Jacobi (HJ) Reachability can formally verify the safety of the robot, but requires an a priori known map and is computationally intractable for high dimensional systems. Machine learning is widely used in machine perception, and recently, End-to-End method has been proposed to bridge the perception and control for robotics. However, it suffers from data inefficiency and lack of robustness when applied to robotics tasks. To address the above challenges, firstly we propose a theoretical improvement on approximating HJ Reachability. Our novel system decomposition technique largely reduces the computation complexity without introducing much conservatism. Both formal mathematical proof and numerical examples are provided to demonstrate its efficiency and guaranteed-safe property. We also present the first HJ Reachability analysis on 6D bicycle model that is previously considered intractable. Secondly, we apply HJ Reachability to learning-based visual navigation in indoor office environment, where a convolutional neural network (CNN) processes the visual input and predicts waypoint that leads to the goal. We propose a novel cost function for waypoint evaluation and generation based on HJ Reachability analysis, and uses disturbances in dynamics to model CNN’s prediction error. Compared to state-of-the-art, our method shows more robust behaviours when navigating in narrow spaces demonstrated in both the simulation and hardware experiment in SFU buildings.