Adaptive Dynamic Formation Control of Robotic Vehicle Systems Based on Rigid Graph Theory

In this paper, dynamic formation problem of three-dimensional (3D) robotic vehicle systems with nonholonomic constraint and dynamics model is investigated. The control objectives are to achieve formation acquisition (i.e., vehicles form a predefined geometric shape) and formation maneuvering (vehicles move as a whole following predefined velocity). For the first objective, the nonlinear model is transformed into a dynamic model similar as the Euler-Lagrangian system with uncertain parameters. Then, we propose a rigid graph based adaptive dynamic formation control law, which enables the robotic vehicle system to converge to the target formation. Meanwhile, collision avoidance between vehicles can be achieved because the rigid graph theory naturally ensures the distance constraint. Then, formation maneuvering problem is investigated, on the basis of formation acquisition, a predefined velocity signal is added to the proposed adaptive formation control law such that robotic vehicles move as a whole following the predefined velocity. Compared with the existing results, the proposed rigid graph based formation control method can effectively reduce the appearance of non-desired equilibrium points of traditional distance based methods, moreover, the distance between robot vehicles can be time-varying, and the formation shape or size can be time-varying. Simulation results confirm the effectiveness of the dynamic formation control law.