Adaptive Leader-Follower Formation Control of Nonholonomic Mobile Robots with Prescribed Transient and Steady-State Performance

In this article, we study the formation tracking control problem for a group of nonholonomic mobile robots under communication constraints. We use a simple leader-follower formation tracking control strategy, in which only the leading robot of the robotic group obtains the given trajectory's information, and each robot only receives information from its immediate leader. Thus, the communication graph forms a static and simple directed spanning tree. We assume that the information exchange among the robots is limited by some given communication radius. Under the limited communication range, the leader-follower distance and bearing angle constraints are considered in the formation control design. To provide the given specifications on the transient and steady-state performances of formation tracking errors, the boundaries of the predefined constraints are enforced by designer-specified performance requirements, which are functions of time. Consequently, we incorporate the barrier Lyapunov function into formation control design to mathematically prove that the formation tracking errors evolve always within the predefined regions and converge asymptotically to zero. The proposed formation control strategy can also guarantee the connectivity maintenance and collision avoidance between the leader and the follower. Simulation results show the performance of the proposed formation tracking control.