Distributed Hybrid Feedback for Global Pose Synchronization of Multiple Rigid Body Systems on $SE(3)$
This addresses coordination challenges in multi-agent robotics, but appears incremental as it builds on existing geometric control methods.
The paper tackles the problem of pose synchronization for multiple rigid body systems on SE(3) by proposing a distributed hybrid feedback control scheme with global asymptotic stability guarantees, achieving synchronization using relative pose and group velocity measurements.
This paper investigates the problem of pose synchronization for multiple rigid body systems evolving on the matrix Lie group $\SE(3)$. We propose a distributed hybrid feedback control scheme with global asymptotic stability guarantees using relative pose and group velocity measurements. The key idea consists of constructing a new potential function on $\SE(3) \times \mathbb{R}$ with a generalized non-diagonal weighting matrix, and a set of auxiliary scalar variables with continuous-discrete hybrid dynamics. Based on the new potential function and the auxiliary scalar variables, a geometric distributed hybrid feedback designed directly on $\SE(3)$ is proposed to achieve global pose synchronization. Numerical simulation results are presented to illustrate the performance of the proposed distributed hybrid control scheme.