Multiple Nonholonomic Systems Research Articles

Fast finite-time consensus protocol of multi-agent systems with nonholonomic constraints

In this paper, a fast finite-time consensus protocol for multi-agent systems with nonholonomic constraints is studied. First, the chained form nonholonomic systems are transformed into two subsystems, which are the first-order subsystem and the reduced-order subsystem. Based on graph theory content and fast finite-time control theory, the fast finite-time consensus problems of the two subsystems are taken into consideration separately. Second, a switching control strategy is proposed to ensure that all states of multiple nonholonomic systems converge instantly to the same state in finite time. Finally, a numerical example is given to verify the effectiveness of the proposed control algorithm.

Bounded Observer-Based Consensus Algorithm for Robust Finite-Time Tracking Control of Multiple Nonholonomic Chained-Form Systems

This article is concerned with the leader–follower consensus tracking problem for multiagent systems with nonholonomic high-order chained-form dynamics subject to external disturbances. A novel distributed and bounded observer is first developed for each follower to estimate the leader information in a finite time. Then, a bounded fast terminal sliding-mode control protocol is constructed for each follower to track the estimated leader's states leading to the fast convergence performance as well as strong robustness. Contrary to some existing finite-time consensus tracking schemes, the control input constraint is taken into account by utilizing hyperbolic tangent saturation function to reduce the risk of the actuator saturation. Moreover, an approximation-based technique is introduced to reduce the conservatism of the upper bound of convergence time. Finally, some simulations for a set of wheeled mobile robots are carried out to demonstrate the efficiency of the proposed control algorithm.

Leader-Following Bipartite Formation Control of Multiple Nonholonomic Robot Systems Over Signed Graph

This paper studies the bipartite formation control problem of multiple nonholonomic robot systems over signed graph. To overcome nonholonomic and underactuated control challenges, the hand position output is defined to obtain a linear hand position subsystem. A distributed control law is designed, which uses sliding mode control technology to eliminate the influence of dynamic leader, so that the global index of position formation error converges to an arbitrary small neighborhood of the origin. Then, the zero dynamic equation is computed, and based on it and Lyapunov method, the convergence conditions on controller parameters and on leader’s velocities are derived to guarantee the angle error is bounded and convergent. Finally, a simulation example containing eight robots and one leader is given to demonstrate the effectiveness of the proposed control strategy. In contrast to related results, this paper presents the complete stability analysis and corresponding stability conditions, in addition to the control law and stability of position subsystems.

Neural-Adaptive Finite-Time Formation Tracking Control of Multiple Nonholonomic Agents With a Time-Varying Target

This paper investigates the leader-following formation tracking problem (FTP) for multiple nonholonomic agent systems (MNASs) in the presence of external disturbances and parametric uncertainties, where both the kinematics and dynamics of the agents are taken into consideration. A novel finite-time distributed controller-estimator algorithm (DCEA) is designed to handle such a challenging problem. Based on Lyapunov stability method, the sufficient conditions for finite-time stability of the closed-loop system are derived. Finally, the simulation results are presented to demonstrate the effectiveness and the robustness of the proposed DCEA.

Robust Fixed-Time Consensus Tracking Control of High-Order Multiple Nonholonomic Systems

Convergence rate is an important performance index in consensus control. Yet, most of the existing results can only achieve asymptotic consensus, or finite-time consensus whose settling time is contingent on initial conditions. This paper studies the robust fixed-time consensus tracking control problem for high-order nonholonomic chained-form systems subject to unknown parameters and nonlinear uncertainties. By using the modified power integrator method, we propose a new robust fixed-time consensus tracking algorithm, with which the consensus tracking can be achieved in a fixed time independent of initial conditions even in the presence of uncertainties. An observer-based fixed-time consensus tracking algorithm is also developed as an alternative method to overcome the communication loop problem. Lyapunov analysis shows the fixed-time stability of the closed-loop system. An application to multiple wheeled mobile robots is presented.

Distributed adaptive control for multiple nonholonomic systems with nonlinearly parameterized uncertainties

SummaryThis paper investigates the distributed adaptive control problem for multiple nonholonomic systems with nonlinearly parameterized uncertainties. Under the assumption that the graph topology is directed and the leader is globally reachable, distributed adaptive controllers are designed recursively by using backstepping technique and algebra graph theory. It is shown that all the followers' outputs will exponentially converge to the reference output signal while all the signals of the closed‐loop system are bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control scheme.

Distributed adaptive consensus control for high-order multiple non-holonomic systems

ABSTRACT In this paper, we investigate the consensus problem for high-order multiple non-holonomic systems, in which the leader's reference input signals are unknown to all the followers. Under the assumption that the leader is the root of a spanning tree, by using the backstepping design method, distributed adaptive controllers are constructed recursively. To assure the stability of the overall scheme, projection techniques are employed to modify the uncertain parameters of the desired trajectory. By using algebraic graph theory and Lyapunov theory, it is shown that all closed-loop signals are bounded, and the followers' states converge to the desired reference trajectory asymptotically. Finally, simulation examples are given to show the effectiveness of the proposed control scheme.

Event-Triggered Consensus for Multiple Nonholonomic Systems

The paper investigates the consensus problem of multiple nonholonomic systems. Two event-triggered control strategies, one centralized and the other distributed, are developed, which can reduce the frequency of control updating. Under the proposed protocols, the multiple nonholonomic systems can achieve consensus, and the bound of inter-event time intervals is provided to illustrate that no Zeno behavior exists. Finally, numerical simulations are also provided to demonstrate the effectiveness of the proposed control strategies.

Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer

The consensus tracking problem of multiple nonholonomic high-order chained-form systems is considered in this paper. A finite-time observer-based distributed control strategy is proposed. At the first step, a distributed finite-time convergent observer is proposed for each agent to estimate the leader’s state in a finite time. Then, a finite-time tracking controller is designed to track the estimated state and the leader’s attitude in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

Finite-Time Consensus Algorithm for Multiple Nonholonomic Disturbed Systems with Its Application

This paper deals with the problem of finite-time consensus of multiple nonholonomic disturbed systems. To accomplish this problem, the multiple nonholonomic systems are transformed into two multiple subsystems, and these two multiple subsystems are studied, respectively. For these two multiple subsystems, the terminal sliding mode (TSM) algorithms are designed, respectively, which achieve the finite-time reaching of sliding surface. Next, a switching control strategy is proposed to guarantee the finite-time consensus of all the states for multiple nonholonomic systems with disturbances. Finally, we demonstrate the effectiveness of the proposed consensus algorithms with application to multiple nonholonomic mobile robots.

Leader-following control of multiple nonholonomic systems over directed communication graphs

This paper considers the leader-following control problem of multiple nonlinear systems with directed communication topology and a leader. If the state of each system is measurable, distributed state feedback controllers are proposed using neighbours’ state information with the aid of Lyapunov techniques and properties of Laplacian matrix for time-invariant communication graph and time-varying communication graph. It is shown that the state of each system exponentially converges to the state of a leader. If the state of each system is not measurable, distributed observer-based output feedback control laws are proposed. As an application of the proposed results, formation control of wheeled mobile robots is studied. The simulation results show the effectiveness of the proposed results.

Consensus of multiple nonholonomic chained form systems

Consensus problems of multiple nonholonomic systems are considered in this paper. This problem is simplified into consensus problems of two subsystems based on the cascaded structure of nonholonomic chained form systems. Continuous and hybrid distributed controllers have been constructed for these two subsystems respectively based on the theory of cascaded systems. Consensus of multiple nonholonomic chained form systems can be realized using the methodology proposed in this paper no matter whether the group reference signal is persistently exciting or not. Different to previous assumptions on group reference such as persistent excitation or converging to nonzero constant, the condition on the group reference signal have been further relaxed in this paper. Simulation results using Matlab have illustrated the effectiveness of the results presented in this paper.

Cooperative control design for non-holonomic chained-form systems

Consensus and formation control problems for multiple non-holonomic chained-form systems are solved in this paper. For consensus problem, based on cascaded structure of the chained-form systems, it amounts to solving two consensus subproblems of two linear subsystems transformed from the original system. With the obtained consensus protocols and the method of virtual structure, decentralised formation controllers can then be designed. According to different desired motion patterns of the entire group, both the formation tracking and formation stabilisation problems can be considered. The significance of this paper lies in adapting theories from non-autonomous cascaded systems for cooperative control design for non-holonomic chained-form systems. A unique feature of our proposed solution is that all states can be cooperatively controlled to achieve the desired references for non-holonomic chained-form system. Simulation results are included to illustrate the effectiveness of the proposed methods in solving cooperative control problems of non-holonomic chained-form systems.

Output consensus for multiple non-holonomic systems under directed communication topology

In this paper, the problem of output consensus for multiple non-holonomic systems in chained form has been investigated. First, an output consensus controller under the strongly connected communication topology is devised by two steps, where a time-varying control strategy and the backstepping design technique are employed. Then, the results are extended to the general directed topology case via graph decomposition, in which the input-to-state stability theory plays a critical role. We prove that the proposed controller can achieve the semi-global output consensus among multiple non-holonomic systems, provided that the interaction graph contains a spanning tree. Finally, numerical examples are provided to illustrate the effectiveness of the designed controller.

Passive Decomposition and Control of Nonholonomic Mechanical Systems

We propose nonholonomic passive decomposition, which enables us to decompose the Lagrange-D'Alembert dynamics of multiple (or a single) nonholonomic mechanical systems with a formation-specifying (holonomic) map h into 1) shape system, describing the dynamics of h(q) (i.e., formation aspect), where q ∈ ℜn is the systems' configuration; 2) locked system, describing the systems' motion on the level set of h with the formation aspect h(q) being fixed (i.e., maneuver aspect); 3) quotient system, whose nonzero motion perturbs both the formation and maneuver aspects simultaneously; and 4) energetically conservative inertia-induced coupling among them. All the locked, shape, and quotient systems individually inherit Lagrangian dynamics-like structure and passivity, which facilitate their control design/analysis. Canceling out the coupling, regulating the quotient system, and controlling the locked and shape systems individually, we can drive the formation and maneuver aspects simultaneously and separately. Notions of formation/maneuver decoupled controllability are introduced to address limitations imposed by the nonholonomic constraint, along with passivity-based formation/maneuver control design examples. Numerical simulations are performed to illustrate the theory. Extension to kinematic nonholonomic systems is also presented.

Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty

This paper considers feedback control of a group of nonholonomic dynamic systems with uncertainty. Decentralized cooperative controllers are proposed with the aid of Lyapunov techniques, results of graph theory, and backstepping techniques. Robustness of the control laws with respect to communication delays is analyzed. An application of the proposed results is discussed. Simulation results show the effectiveness of the proposed controllers.

Passive Decomposition of Multiple Nonholonomic Mechanical Systems under Motion Coordination Requirements

We propose a novel framework, which, under a certain geometric condition, enables us to decompose the second-order Lagrangian dynamics of the multiple nonholonomic mechanical systems into two decoupled systems according to the two most fundamental aspects of the group behaviour: shape system describing the formation aspect (i.e. group's internal shape); and locked system abstracting the maneuver aspect (i.e. group's overall motion). By controlling these decoupled locked and shape systems individually, we can then control the formation and maneuver aspects separately without any crosstalk between them. Moreover, the framework enables us to do this while respecting/utilizing the Lagrangian structure/passivity of the system's open-loop dynamics. Due to this property, we call this framework nonholonomic passive decomposition. A control design example with numerical simulation is also given to highlight some properties of the proposed framework.