Formation Tracking of Nonholonomic Systems on the Special Euclidean Group under Fixed and Switching Topologies: An Affine Formation Strategy
Junyi Yang, Feng Xiao, Tongwen Chen · SIAM Journal on Control and Optimization · 2021
An affine formation tracking problem of multiple mobile agents is studied in this work. Each agent in the system is modeled as an underactuated kinematic rigid body with nonholonomic constraints, maneuvering on the special Euclidean group $(SE(3))$. A controller is designed for each agent directly on the corresponding Lie algebra of $SE(3)$. Moreover, only local information accessible to each agent in its body-fixed frame is involved. The proposed control protocol can be implemented under both directed and undirected topologies. In addition, for directed graphs, an algorithm is proposed to realize the formation under switching topologies. Finally, numerical simulations are given to illustrate the efficiency and feasibility of the proposed results.