Smooth time-invariant control for leaderless consensus of networked nonholonomic systems

Abstract

This article studies the leaderless consensus control problem of multiple nonholonomic chained systems. Two smooth time-invariant static distributed controllers are derived based on Lyapunov method, graph theory, and LaSalle invariance principle. Both of the proposed controllers guarantee that the states of the multiple nonholonomic systems globally asymptotically converge to a common vector, provided that the interconnection topology is undirected and connected. In particular, the second control scheme can reduce the size of the control inputs via saturated control and is more applicable in real engineering. Several numerical simulations are implemented for kinematic models of four nonholonomic unicycle mobile robots, demonstrating the effectiveness of the proposed control schemes.

Global formation control of nonholonomic unicycle vehicles with guaranteed rate of convergence

“…• Compared with the works [5,18,21] with local results, this paper presents a global control law. • The results in Jafarian, [19] Maghenem et al [20], Du et al [22], Zhai et al [23], Xie and Ma [24], and Xie et al [25] depend on undirected connected information topology, while our approach relaxes this condition to a more relaxed one that only requires directed communication graph with a spanning tree. • The existing works [5,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] do not take into account the guarantee of convergence rate; nevertheless, this paper can ensure a prescribed convergence speed.…”

“…• The results in Jafarian, [19] Maghenem et al [20], Du et al [22], Zhai et al [23], Xie and Ma [24], and Xie et al [25] depend on undirected connected information topology, while our approach relaxes this condition to a more relaxed one that only requires directed communication graph with a spanning tree. • The existing works [5,[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] do not take into account the guarantee of convergence rate; nevertheless, this paper can ensure a prescribed convergence speed. In the literature, similar results on guaranteed convergence rate control are provided for consensus control of linear systems; see, for example, Fruhnert and Corless [26] and Amini et al [27] and reference therein, and distinct from them, this work provides a new controller that reaches a prescribed rate of convergence for formation control of unicycle vehicles with nonlinear models.…”

“…Since the decay rates are determined by controller coefficients, the proposed control strategy is modified to additionally guarantee the prescribed rate of convergence by resetting appropriate controller gains. Compared with the existing results, main contributions and advantages of this paper consist of the following: Different from previous studies [8–17] which only consider position formation/rendezvous, this paper is concerned with solving the full‐state formation control of unicycle vehicles in terms of both position and orientation. Compared with the works [5,18,21] with local results, this paper presents a global control law. The results in Jafarian, [19] Maghenem et al [20], Du et al [22], Zhai et al [23], Xie and Ma [24], and Xie et al [25] depend on undirected connected information topology, while our approach relaxes this condition to a more relaxed one that only requires directed communication graph with a spanning tree. The existing works [5,8–25] do not take into account the guarantee of convergence rate; nevertheless, this paper can ensure a prescribed convergence speed. In the literature, similar results on guaranteed convergence rate control are provided for consensus control of linear systems; see, for example, Fruhnert and Corless [26] and Amini et al [27] and reference therein, and distinct from them, this work provides a new controller that reaches a prescribed rate of convergence for formation control of unicycle vehicles with nonlinear models. …”

“…In Du et al [22], a discontinuous control law was derived based on recursive design method and the first‐order consensus theory, reaching global finite‐time consensus of nonholonomic systems with high‐order chained structure. Based on Laplacian based Lyapunov function, smooth time‐invariant static distributed controllers were developed in Zhai et al [23], Xie and Ma [24], and Xie et al [25] to globally asymptotically steer the consensus error of chained systems to zero with time‐varying common configuration.…”

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

“…To stabilized the augmented system and deal with parametric uncertainties, we then propose a new adaptive control law in dynamic level. Theoretical analysis in Lyapunov sense proves that the formation errors, including both position and orientation, 33 are globally uniformly ultimately convergent to arbitrarily small balls near the origin.…”