A smooth time-varying controller is proposed to simultaneously address the stabilization and tracking problems of nonholonomic mobile robots for most admissible reference trajectories without switching. The controller is developed with the aid of a delicately designed time-varying signal and Lyapunov method. Computational simplification and asymptotic convergence of regulation or tracking errors are achieved by the proposed controller. Our approach provides an interesting way to unify the existing results on point stabilization and trajectory tracking of mobile robots. The simulation and experimental results on a wheeled mobile robot are presented to demonstrate the effectiveness of the proposed controller.Index Terms-Lyapunov method, mobile robots, nonholonomic systems, stabilization and tracking, time-varying feedback. 1063-6536

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A novel time‐varying adaptive controller at the torque level is proposed to simultaneously solve the stabilization and the tracking problem of unicycle mobile robots with unknown dynamic parameters. The idea underlying the controller is intuitively simple: rather than switching between two different types of controllers according to the a priori knowledge of the reference velocities being persistently exciting or not, a new time‐varying signal is introduced to make the single controller capable of adaptively, smoothly, and gradually converting between stabilizer and tracker depending on the instantaneous and past information of the reference velocities. Our control development is based on Lyapunov's direct method and the backstepping technique. Adaptive control techniques are used to deal with parametric uncertainties. The outstanding feature of our controller is computationally simple due to its full use of the existing results on stabilization and tracking control for unicycle robots. With our approach, robots can globally follow a large class of paths including a straight line, a circle, a path approaching a set‐point, or just a set‐point using a single controller. Simulation results for a unicycle‐type mobile robot are provided to illustrate the effectiveness of the proposed controller.

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Purpose The purpose of this paper is to consider the leader-following formation control problem for nonholonomic vehicles based on a novel biologically inspired neurodynamics approach. Design/methodology/approach The interactions among the networked multi-vehicle system is modeled by an undirected graph. First, a distributed estimation law is proposed for each follower vehicle to estimate the state including the position, orientation and linear velocity of the leader. Then, a distributed formation tracking control law is designed based on the estimated state of the leader, where a bio-inspired neural dynamic is introduced to solve the impractical velocity jumps problem. Explicit stability and convergence analyses are presented using Lyapunov tools. Findings The effectiveness and efficiency of the proposed control law are demonstrated by numerical simulations and physical vehicle experiments. Consequently, the proposed protocol can successfully achieve the desired formation under connected topologies while tracking the trajectory generated by the leader. Originality/value This paper proposes a neurodynamics-based leader–follower formation tracking algorithm for multiple nonholonomic vehicles.

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