In this paper we present a receding-horizon leader—follower (RH-LF) control framework to solve the formation problem of multiple non-holonomic mobile robots with a rapid error convergence rate. To maintain the desired leader—follower relationship, we propose a separation—bearing—orientation scheme (SBOS) for two-robot formations and separation—separation—orientation scheme (SSOS) for three-robot formations in deriving the desired postures of the followers. Unlike the other leader—follower approaches in the existing literature, the orientation deviations between the leaders and followers are explicitly controlled in our framework, which enables us to successfully solve formation controls when robots move backwards, which is termed as a formation backwards problem in this paper. Further, we propose to incorporate the receding-horizon scheme into our leader—follower controller to yield a fast convergence rate of the formation tracking errors. Experiments are finally performed on a group of mobile robots to demonstrate the effectiveness of the proposed formation control framework.
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