Chaoli Wang

Distributed Cooperative Control of Multiple Nonholonomic Mobile Robots

In this paper, the distributed cooperative control problem is considered for multiple type (1,2) nonholonomic mobile robots. Firstly, a local change of coordinates and feedback is proposed to transform the original nonholonomic system to a new transformed system. Secondly, a distributed controller for the transformed system is designed by using information of the intrinsic system and its neighbors to make the state converge to the same value asymptotically. Furthermore, it shows that the same value can be confined to the origin, which means that the problem of cooperatively converging to a stationary point of a group of nonholonomic systems can be practically solved. Finally, due to the communication delays are inevitable in practice, new distributed controllers for the transformed system are also proposed making the state converge to the same value or zero asymptotically with considering communication delays. The proposed methods are then extended to the case where the nonholonomic mobile robot needs to form a prescribed formation other than agreeing on a same value. The stability of the proposed methods is proved rigorously. Simulation results confirm the effectiveness of the proposed methods.

Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

ABSTRACT In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.

Designing distributed consensus protocols for second-order nonlinear multi-agents with unknown control directions under directed graphs

Abstract This paper focuses on the leaderless and leader-following consensus problems of second-order nonlinear multi-agents under directed graphs. Both leaderless and leader-following consensus protocols are proposed for multi-agents with unknown control directions based on the Nussbaum-type gains. For the leaderless case, the proposed protocol can guarantee that the consensus errors asymptotically converge to zero. Moreover, for the leader-following case, the Lyapunov stability analysis shows that the consensus tracking errors can be made arbitrarily small by tuning the control parameters. It should also be noted that these proposed protocols do not require any information about the global communication topology and work with only the relative information of neighboring agents. Illustrative examples are given to show the effectiveness of the proposed control protocols.

Distributed adaptive output consensus tracking of higher-order systems with unknown control directions

This paper investigates the distributed adaptive output consensus tracking problem of higher-order subsystems with unknown control directions and unknown dynamic parameters. Only a subset of the subsystems is given access to the desired trajectory information directly, and the subsystems are connected through an undirected and connected graph with a time-invariant topology. A distributed adaptive controller is deduced using the backstepping technique and a Nussbaum-type function to drive all the subsystems to track the desired trajectory asymptotically. Moreover, these controllers are distributed in the sense that the controller design for each subsystem only requires relative state information between itself and its neighbors. It is proven that the output tracking error converges to zero asymptotically and that all the closed-loop system signals are bounded. A simulation is carried out to demonstrate the effectiveness of the proposed control scheme.

Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

ABSTRACT This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.

Fully Distributed Low-Complexity Control for Nonlinear Strict-Feedback Multiagent Systems With Unknown Dead-Zone Inputs

In this paper, the distributed control problem of nonlinear strict-feedback multiagent systems is addressed under directed and time-invariant communication graphs. With the utilization of the prescribed performance control methodology, a control algorithm is proposed to ensure predefined bounds of overshoot, convergence rates, and steady-state values of the neighborhood synchronization errors in the presence of unknown dead-zone inputs. The algorithm is fully distributed in the sense that the control input for each agent is independent of any global information of the communication graph and is solely based on local relative output information from its neighborhood set. The approximating structures, e.g., neural networks or fuzzy systems, and the command filters that are typically incorporated to avoid the need for analytical derivatives in the backstepping design are not employed here, resulting in a low-complexity design. Simulation results are included to verify the algorithm.

Distributed Leaderless and Leader-Following Consensus Control of Multiple Euler-Lagrange Systems with Unknown Control Directions

This paper investigates leaderless and leader-following consensus control problems for a group of Euler-Lagrange systems with unknown identical control directions under an undirected connected and time-invariant graph in the presence of parametric uncertainties. For both leaderless and leader-following consensus cases, distributed adaptive controllers are presented using the backstepping technique and a Nussbaum-type function. Moreover, these controllers are distributed in the sense that the controller design for each system only requires relative information between itself and its neighbors. The projection algorithm is applied to guarantee that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the consensus errors converge to zero asymptotically. Simulation results on multiple two-link planar elbow manipulators are provided to illustrate the performance of the proposed algorithms.

Distributed robust consensus tracking control of higher-order nonlinear systems

In this paper, a multi-agent consensus problem has been considered with a dynamic leader and fixed communication topology. Each follower node is modeled by a higher-order nonlinear systems with unknown nonlinear dynamics and an unknown disturbance. The leader node is also a higher-order nonlinear system. Only a part of the networked group has access to the information of the leader. And a distributed robust consensus controller is designed to ensure all the follower nodes synchronize to the trajectory of the leader node exponentially. Meanwhile, a smooth and time-varying sliding mode controller is presented to eliminate chattering phenomenon. The stability of the proposed methods is proved rigorously. Simulation results confirm the effectiveness of the proposed methods.

Trajectory Tracking of Nonholonomic Mobile Robots via Discrete-Time Sliding Mode Controller Based on Uncalibrated Visual Servoing

This paper considers the problem of trajectory tracking of nonholonomic mobile robots based on uncalibrated visual servoing. A prerecorded image sequence or a video taken by the pin-hole camera is used to define a desired trajectory for the mobile robot. First, a novel discrete-time model is present based on visual servoing. And then the discrete-sliding mode controller is designed for the model associated with uncertain parameter. The asymptotic convergence of the tracking errors is proved rigorously. Finally, simulation results confirm the effectiveness of the proposed methods.

Distributed consensus control for second-order nonlinear multi-agent systems with unknown control directions and position constraints

Abstract This paper investigates the leaderless consensus problem in the presence of unknown control directions and position constraints under directed graph. Based on the Nussbaum-gain technique and Barrier Lyapunov functions, the position-constrained consensus protocol is proposed for the multi-agent systems with unknown control directions. The proposed protocol ensures that all the signals in the closed-loop system are globally bounded and the consensus errors asymptotically converge to zero. Moreover, during the process of consensus, the trajectory of the position state of each agent is contained in the open interval which can be chosen arbitrarily in advance. A simulation example is given to demonstrate the effectiveness of the proposed control protocol.