Provably Safe Control of Lagrangian Systems in Obstacle-Scattered Environments
This work addresses safety-critical control for robotics in cluttered environments, representing an incremental advance by combining existing CBF and CLF methods with a novel switching mechanism.
The authors tackled the problem of ensuring safety and stability for Lagrangian systems in obstacle-filled environments by proposing a hybrid feedback control law that interprets path following as a sequence of reach-avoid problems, using ellipsoids for safe regions and encoding CBFs and CLFs into QPs without relaxation, with simulations demonstrating effectiveness in complex scenarios.
We propose a hybrid feedback control law that guarantees both safety and asymptotic stability for a class of Lagrangian systems in environments with obstacles. Rather than performing trajectory planning and implementing a trajectory-tracking feedback control law, our approach requires a sequence of locations in the environment (a path plan) and an abstraction of the obstacle-free space. The problem of following a path plan is then interpreted as a sequence of reach-avoid problems: the system is required to consecutively reach each location of the path plan while staying within safe regions. Obstacle-free ellipsoids are used as a way of defining such safe regions, each of which encloses two consecutive locations. Feasible Control Barrier Functions (CBFs) are created directly from geometric constraints, the ellipsoids, ensuring forward-invariance, and therefore safety. Reachability to each location is guaranteed by asymptotically stabilizing Control Lyapunov Functions (CLFs). Both CBFs and CLFs are then encoded into quadratic programs (QPs) without the need of relaxation variables. Furthermore, we also propose a switching mechanism that guarantees the control law is correct and well-defined even when transitioning between QPs. Simulations show the effectiveness of the proposed approach in two complex scenarios.