Containment Control based Formation Tracking for Multi-vehicles on Lie Group

This paper considers formation tracking for full-actuated multi-vehicles based on containment control. Inspired by the concept of convex combination on Euclidean space, we get the expression of convex combination (geodesic) of two points on Lie group and then extend the result to give the definition of convex combination of multiple points on Lie group. Then, the virtual leaders are constructed by the dynamics of convex polytope which is generated from neighboring vehicles as its vertexes. Based on containment control, we propose a formation tracking control law for multi-vehicles evolving on SE(n) under a class of directed acyclic graph. Finally, the theoretical results are verified through a numerical simulation.