Cascades-Based Leader–Follower Formation Tracking and Stabilization of Multiple Nonholonomic Vehicles

Abstract

It is known after [1] that nonholonomic systems on the plane cannot be stabilized on arbitrary leader's trajectories with piece-wise continuous velocities via continuous controllers, even time-varying. In this paper we identify a wide class of smooth bounded reference trajectories (that includes set-points) and we propose a smooth time-varying controller that stabilizes such trajectories, not only for one nonholonomic mobile robot, but also for a network of mobile robots in a leader-follower configuration. We provide new constructions of strict Lyapunov functions with which we establish uniform global asymptotic stability and other strong robustness properties in the formation-error-coordinates space. Thus, our stability statements are unique in the literature and our tools of analysis are original.

Adaptive practical leader‐following formation control of multiple nonholonomic wheeled mobile robots

“…Some researchers turn to investigate deriving a single controller that is capable of realizing both formation tracking and formation stabilization. [23][24][25][26][27][28][29][30][31] In Reference 23, the authors construct a particular time-varying function to provide certain persistency of excitation for formation stabilization task, which can adapt to the formation tracking mission without any switching. The cascade-based control law reported in Reference 24 establishes uniform global asymptotic convergence of the formation errors no matter the leader is always moving or converging to some constant values.…”

“…Nonetheless, the literature [23][24][25][26][27][28][29][30][31] only consider the scenario that the leader is feasible and subject to the same nonholonomic constraint with the follower robot. Under a feasible leader, the derivatives of position errors can be partly rewritten as the function of orientation error.…”

“…Allowing formation with a nonfeasible leader promises wilder applications, compared with results only capable of formation with a feasible leader. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][23][24][25][26][27][28][29][30][31] Since both our control design and closed-loop stability do not rely on any PE condition as those of References 2-8, the leader is allowed either moving or just standing still. Apart from those, the distributed nature of our formation scheme makes it direct to add additional followers to enlarge the capacity of network systems, and the control law with real-time parameter updating endows each follower robot with adaptive capacity toward model uncertainties.…”

“…Some researchers turn to investigate deriving a single controller that is capable of realizing both formation tracking and formation stabilization 23‐31 . In Reference 23, the authors construct a particular time‐varying function to provide certain persistency of excitation for formation stabilization task, which can adapt to the formation tracking mission without any switching.…”

“…In Reference 23, the authors construct a particular time‐varying function to provide certain persistency of excitation for formation stabilization task, which can adapt to the formation tracking mission without any switching. The cascade‐based control law reported in Reference 24 establishes uniform global asymptotic convergence of the formation errors no matter the leader is always moving or converging to some constant values. As the implementations control laws in References 23, 24 steer one robot to follow one another via letting the leader be the root node, it is hard to handle the case when the interaction network is more general, for example, one robot can have two connected neighbors.…”