Formation Control Of Multi-mobile Robots Based On Cross-Coupling Approach

The essential question of formation control lies on the ways to coordinate the system of multi-mobile robots to accomplish the specified formation tasks.The problem of formation can be generalized as formation planning and formation keeping. For the reason that the position errors and formation errors are hard to avoid when it attempts to the goal of formation, the quality of formation can be evaluated by the position errors of the composed mobile robots and the formation errors of the whole multi-mobile robots system. Reducing both the position errors and formation errors by an appropriate strategy is one of the significant problems of formation control.The cross-coupling approach enhances the coupling property of the composed systems, it not only makes formation control more precise also makes components of system under a balance situation, and increases the robust of formation keeping meanwhile. The development of nonlinear robot control makes it possible to integrate the cross-coupling approach and the theory of nonlinear control. With the distributed structure, we can accomplish the high-precision position tracking of the composed robots and formation control of the whole system.In this paper, based on the cross-coupling approach, we proposed several strategies for the different tasks of formation control of multi-mobile robots. By using the hyperbolic tangent function and the defined coupled position error, A nonlinear proportion-differential (PD) strategy is first proposed. With the excellent robustness of sliding mode control, a linear sliding mode control strategy for uncertain multi-mobile robots system is then proposed. For the systems with unknown inertia, an adaptive formation control law is developed. The closed loops of system under the proposed strategies are proved to be asymptotic stable by the Lyapunov stability theory. Extensive simulations are carried out to show the effectiveness of the proposed strategies.