Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance (Extended Version)

Abstract

This paper explores the design of hybrid feedback for a class of affine nonlinear systems with topological constraints that prevent global asymptotic stability. A new hybrid control strategy is introduced, which differs conceptually from the commonly used synergistic hybrid approaches. The key idea involves the construction of a generalized synergistic Lyapunov function whose switching variable can either remain constant or dynamically change between jumps. Based on this new hybrid mechanism, a generalized synergistic hybrid feedback control scheme, endowed with global asymptotic stability guarantees, is proposed. This hybrid control scheme is then improved through a smoothing mechanism that eliminates discontinuities in the feedback term. Moreover, the smooth hybrid feedback is further extended to a larger class of systems through the integrator backstepping approach. The proposed hybrid feedback schemes are applied to solve the global obstacle avoidance problem using a new concept of synergistic navigation functions. Finally, numerical simulation results are presented to illustrate the performance of the proposed hybrid controllers.

arXiv comment14 pages, 5 figures

References in corpus (5)

• Robust Global Exponential Stabilization on the $n$-Dimensional Sphere with Applications to Trajectory Tracking for Quadrotors
• Obstacle Avoidance via Hybrid Feedback
• Hybrid Feedback for Global Tracking on Matrix Lie Groups $SO(3)$ and $SE(3)$
• Synergistic Potential Functions from Single Modified Trace Function on SO(3)
• Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance (Extended Version)

Cited by in corpus (1)

• Hybrid Feedback for Affine Nonlinear Systems with Application to Global Obstacle Avoidance (Extended Version)