Lyapunov-Based Avoidance Controllers With Stabilizing Feedback

For control-affine nonlinear systems, we augment a predefined Lyapunov-based global stabilizer with a hybrid obstacle avoidance design preserving the Lyapunov decrease. While the method can be applied to the general class of control-affine systems, the size of the avoidance neighborhood is not a design parameter. Our design shows that a system can achieve global asymptotic stability with simultaneous unsafe set avoidance via hybrid feedback, which overcomes well-known issues of topological obstructions.