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This paper addresses forward motion control for trajectory tracking andmobile formation coordination for a group of non-holonomic vehicles on SE(2).Firstly, by constructing an intermediate attitude variable which involvesvehicles' position information and desired attitude, the translational androtational control inputs are designed in two stages to solve the trajectorytracking problem. Secondly, the coordination relationships of relativepositions and headings are explored thoroughly for a group of non-holonomicvehicles to maintain a mobile formation with rigid body motion constraints. Weprove that, except for the cases of parallel formation and translationalstraight line formation, a mobile formation with strict rigid-body motion canbe achieved if and only if the ratios of linear speed to angular speed for eachindividual vehicle are constants. Motion properties for mobile formation withweak rigid-body motion are also demonstrated. Thereafter, based on the proposedtrajectory tracking approach, a distributed mobile formation control law isdesigned under a directed tree graph. The performance of the proposedcontrollers is validated by both numerical simulations and experiments.

Mobile Formation Coordination and Tracking Control for Multiple Non-holonomic Vehicles