Safe Autonomous Navigation for Systems with Learned SE(3) Hamiltonian Dynamics

Safe autonomous navigation in unknown environments is an important problem for ground, aerial, and underwater robots. This paper proposes techniques to learn the dynamics models of a mobile robot from trajectory data and synthesize a tracking controller with safety and stability guarantees. The state of a mobile robot usually contains its position, orientation, and generalized velocity and satisfies Hamilton's equations of motion. Instead of a hand-derived dynamics model, we use a dataset of state-control trajectories to train a translation-equivariant nonlinear Hamiltonian model represented as a neural ordinary differential equation (ODE) network. The learned Hamiltonian model is used to synthesize an energy-shaping passivity-based controller and derive conditions which guarantee safe regulation to a desired reference pose. Finally, we enable adaptive tracking of a desired path, subject to safety constraints obtained from obstacle distance measurements. The trade-off between the system's energy level and the distance to safety constraint violation is used to adaptively govern the reference pose along the desired path. Our safe adaptive controller is demonstrated on a simulated hexarotor robot navigating in unknown complex environments.