Cooperative Control of Multiple Nonholonomic Mobile Agents

This paper considers two cooperative control problems for nonholonomic mobile agents. In the first problem, we discuss the design of cooperative control laws such that a group of nonholonomic mobile agents cooperatively converges to some stationary point under various communication scenarios. Dynamic control laws for each agent are proposed with the aid of $sigma $-processes and results from graph theory. In the second problem, we discuss the design of cooperative control laws such that a group of mobile agents converges to and tracks a target point which moves along a desired trajectory under various communication scenarios. By introducing suitable variable transformations, cooperative control laws are proposed. Since communication delay is inevitable in cooperative control, in each of the above cooperative control problems, we analyze the effect of delayed communication on the proposed controllers. As applications of the proposed results, formation control of wheeled mobile robots is discussed. It is shown that our results can be successfully used to solve formation control problem. To show effectiveness of the proposed approach, simulation results are included.      

On consensus algorithms of multiple uncertain mechanical systems with a reference trajectory

This paper considers the consensus problem of multiple uncertain mechanical systems with a desired trajectory as an agreement vector. In the consensus problem, a desired trajectory is available to a portion of a group of mechanical systems. Distributed adaptive/robust control laws are proposed such that the state of each system asymptotically converges to the desired trajectory with the aid of information interchange between systems. Simulation results show effectiveness of the proposed controllers.     

一种编队控制的动态调整与规划方法

This article is concerned with cooperative control problems in formation of mobile robots under the nonholonomic constraints that certain geometrical constraints are imposed on multiple mobile robots throughout their travel. For this purpose, a new method of motion control for formation is presented, which is based on the dynamic regulation and scheduling scheme. It is attractive for its adaptability to the formation structure and desired trajectory. The quality of formation keeping can be evaluated by the instantaneous errors of formation offset and spacing distance. Some kinematics laws are developed to regulate and maintain the formation shape. Simulation results and data analysis show the validity of the proposed approach for a group of robots.     

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.     

Distributed tracking control of uncertain mechanical systems with velocity constraints

This paper considers the leader‐following control problem of multiple mechanical systems with uncertainty and velocity constraints. So as to deal with the velocity constraints, a reduction procedure is applied to transform the model of each system to a cascaded system. With the aid of the cascade structure of each system and the properties of linear time‐varying systems, distributed robust feedback controllers are proposed such that the state of each follower system asymptotically converges to the state of a leader system with the aid of neighbors' information. So as to reduce the cost of the communication between systems, an event‐triggered leader‐following control problem is also considered, and event‐triggered distributed controllers are proposed. As an application of the proposed results, formation control of wheeled mobile robots is considered, and distributed controllers are obtained with the aid of the results in Theorems 1 and 2. Simulation results show the effectiveness of the proposed results. Copyright © 2017 John Wiley & Sons, Ltd.     

Distributed tracking control of networked chained systems

This paper considers distributed tracking control of multiple nonholonomic chained systems using neighbours’ information. With the aid of the cascade structure of each system and properties of persistently excited signals, distributed state feedback tracking controllers and distributed output feedback tracking controllers are proposed such that the tracking errors exponentially converge to zero. To show applications of the proposed results, formation control of wheeled mobile robots is considered. Distributed controllers are obtained with the aid of the proposed theorems. Simulation results verify the effectiveness of the proposed results.     

Distributed observer-based cooperative control of multiple nonholonomic mobile agents

In this article, cooperative output feedback control of a group of nonholonomic mobile agents is considered. Distributed observer-based cooperative control laws are proposed with the aid of Lyapunov techniques and results from graph theory. Robustness of the stability of the closed-loop systems with the proposed control laws is considered. The effectiveness of the proposed controllers is verified by simulation results.     

Practical Formation Control of Multiple Unicycle-Type Mobile Robots with Limited Sensing Ranges

This paper presents a design of cooperative controllers that force a group of N unicycle-type mobile robots with limited sensing ranges to perform a desired tight formation and that guarantee no collisions between any robots in the group. The desired formation can be stabilized at any reference trajectories with bounded time derivatives. The formation control design is based on several nonlinear coordinate changes, the transverse function approach, the backstepping technique, the Lyapunov direct method, and smooth or p −times differentiable step functions. These functions are introduced and incorporated into novel potential functions to solve the collision avoidance problem without the need of switchings despite of the robots’ limited sensing ranges. The proposed formation control system is applied to solve a gradient climbing problem.     

Distributed Consensus of Multiple Nonholonomic Mobile Robots

Consensus problems of multiple nonholonomic mobile robots are considered in this paper. These problems are simplified into consensus problems of two subsystems based on structure of nonholonomic mobile robots. Linear distributed controllers are constructed respectively for these two subsystems thanks to the theory of nonautonomous cascaded systems. Consensus of multiple nonholonomic mobile robots has been realized using the methodology proposed in this paper no matter whether the group reference signal is persistent excitation or not. Different from previous research on cooperative control of nonholonomic mobile robots where the consensus problem under persistent exciting reference has received a lot of attention, this paper reports the first consensus result for multiple nonholonomic mobile robots whose group reference converges to zero. Simulation results using Matlab illustrate the effectiveness of the proposed controllers in this paper.      

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.     

Neural adaptive PID formation control of car-like mobile robots without velocity measurements

A virtual leader–follower formation control of a group of car-like mobile robots is addressed in this paper. First, the kinematic and dynamic models of car-like robots are transformed into a second-order leader–follower formation model which inherits all structural properties of the robot dynamic model. Then, a new observer-based proportional–integral-derivative formation controller is proposed to force that all robots construct a desired formation with respect to a predefined virtual leader. To improve the formation tracking and observation performance, the integral action is incorporated into the design of the observer–controller scheme. Adaptive robust and neural network techniques are also employed to compensate uncertain parameters, unmodeled dynamics, and external disturbances. Lyapunov’s direct method is utilized to show that the formation tracking and observation errors are semi-globally uniformly ultimately bounded. Then, the proposed controller is extended to the leader–follower formation of a team of tractor–trailer systems. Finally, simulation results illustrate the efficiency of the proposed controller.     

Adaptive Distributed Fault-tolerant Formation Control for Multi-robot Systems under Partial Loss of Actuator Effectiveness

This paper presents an adaptive distributed fault-tolerant formation control for multi-robot systems. Both the kinematics and dynamics of differential wheeled mobile robots are considered. In particular, the problem caused by actuator faults is investigated. Based on dynamic surface control techniques, adaptive formation controllers can be obtained under a directed communication network. The closed-loop stability is guaranteed by using Lyapunov stability analysis such that all followers can exponentially converge to a leader-follower formation pattern. Simulation and experimental results illustrate that the desired formation pattern can be preserved for a group of wheeled robots subject to unknown uncertainties and actuator faults.     

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.     

Cooperative adaptive consensus tracking for multiple nonholonomic mobile robots

This paper addresses the cooperative adaptive consensus tracking for a group of multiple nonholonomic mobile robots, where the nonholonomic robot model is assumed to be a canonical vehicle having two actuated wheels and one passive wheel. By integrating a kinematic controller and a torque controller for the nonholonomic robotic system, a cooperative adaptive consensus tracking strategy is developed for the uncertain dynamic models using Lyapunov-like analysis in combination with backstepping approach and sliding mode technique. A key feature of the developed adaptive consensus tracking algorithm is the introduction of a directed network topology into the control constraints based on algebraic graph theory to characterise the communication interaction among robots, which plays an important role in realising the cooperative consensus tracking with respect to a specific common reference trajectory. Furthermore, a novel framework is proposed for developing a unified methodology for the convergence analysis of the closed-loop control systems, which can fully ensure the desired adaptive consensus tracking for multiple nonholonomic mobile robots. Subsequently, illustrative examples and numerical simulations are provided to demonstrate and visualise the theoretical results.     

一种多非完整移动机器人分布式编队控制方法

本文研究了多非完整移动机器人编队控制算法。在该算法中,参考轨迹被视为虚拟领导者,只有部分机器人可以接收到领导者信息,机器人之间只能进行局部信息交互。利用坐标变换将机器人系统的编队问题转化为变换后系统的一致性问题,在持续激励的条件下,设计了一种分布式控制算法,通过图论与Lyapunov 理论证明了该分布式控制算法可以使移动机器人队伍指数收敛于期望队形,并使队形的几何中心指数收敛到参考轨迹。最后,数值仿真验证了该控制算法的有效性。     

多动态目标的多机器人协同环航控制

主要研究了多个非完整机器人对多个动态目标的协同环航控制问题;首先,针对多目标护航任务,建立目标扩展圆形构型,以期完成紧密目标保卫任务;其次,针对护航机器人,通过利用自身及相邻节点的位置与方位信息及所包围的动态目标的中心位置及扩展半径设计分布式时变圆形编队控制协议,实现预定几何分布下的机器人环航编队设计;其中,通过引入虚拟信号变量设计期望的速度及角速度控制律,利用反步技术提出了一种新的考虑时变护航半径的分布式控制策略;在对目标节点速度的温和假设下,所提出的编队控制器可以驱动多护航机器人渐近收敛到以多目标中心的圆上,同时维持一个预定的几何编队配置;Lyapunov分析证明了所有的误差都可以渐进稳定到原点,数值仿真核实了所构建的控制方案的可行性。     

Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory

In this paper, the distributed formation control problem for multiple nonholonomic mobile robots using consensus-based approach is considered. A transformation is given to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem. Distributed control laws are developed for achieving the formation control objectives: a group of nonholonomic mobile robots at least exponentially converge to a desired geometric pattern with its centroid moving along the specified reference trajectory. Rigorous proofs are provided by using graph, matrix , and Lyapunov theories. Simulations are also given to verify the effectiveness of the theoretical results.     

From Trajectory Tracking Control to Leader–Follower Formation Control

Abstract

This work investigates the leader–follower formation control of multiple nonholonomic mobile robots. First, the formation control problem is converted into a trajectory tracking problem and a tracking controller based on the dynamic feedback linearization technique drives each follower robot toward its corresponding reference trajectory in order to achieve the formation. The desired orientation for each follower is selected such that the nonholonomic constraint of the robot is respected, and thus the tracking of the reference trajectory for each follower is feasible. An adaptive dynamic controller that considers the actuators dynamics in the design procedure is proposed. The dynamic model of the robots includes the actuators dynamics in order to obtain the velocities as control inputs instead of torques or voltages. Using Lyapunov control theory, the tracking errors are proven to be asymptotically stable and the formation is achieved despite the uncertainty of the dynamic model parameters. In order to assess the proposed control laws, a ROS-framework is developed to conduct real experiments using four ROS-enabled mobile robots TURTLEBOTs. Moreover, the leader fault problem, which is considered as the main drawback of the leader–follower approach, is solved under ROS. An experiment is conducted where in order to overcome this problem, the desired formation and the leader role are modified dynamically during the experiment.     

Distributed Control of Nonholonomic Robots Without Global Position Measurements Subject to Unknown Slippage Constraints

This paper studies the fully distributed formation control problem of multi-robot systems without global position measurements subject to unknown longitudinal slippage constraints.It is difficult for robots to obtain accurate and stable global position information in many cases,such as when indoors,tunnels and any other environments where GPS(global positioning system)is denied,thus it is meaningful to overcome the dependence on global position information.Additionally,unknown slippage,which is hard to avoid for wheeled robots due to the existence of ice,sand,or muddy roads,can not only affect the control performance of wheeled robot,but also limits the application scene of wheeled mobile robots.To solve both problems,a fully distributed finite time state observer which does not require any global position information is proposed,such that each follower robot can estimate the leader’s states within finite time.The distributed adaptive controllers are further designed for each follower robot such that the desired formation can be achieved while overcoming the effect of unknown slippage.Finally,the effectiveness of the proposed observer and control laws are verified by simulation results.     

Adaptive control strategies for cooperative dual-arm manipulators

The article describes three strategies for adaptive control of cooperative dual-arm robots. In the position-position control strategy, the adaptive controllers ensure that the end-effector positions of both arms track desired trajectories in Cartesian space despite unknown time-varying interaction forces exerted through the load. In the position-hybrid control strategy, the adaptive controller of one arm controls end-effector motions in the free directions and applied forces in the constraint directions; while the adaptive controller of the other arm ensures that the end-effector tracks desired position trajectories. In the hybrid-hybrid control strategy, the adaptive controllers ensure that both end-effectors track reference position trajectories while simultaneously applying desired forces on the load. In all three control strategies, the coupling effects between the arms through the load are treated as “disturbances” which are rejected by the adaptive controllers while following desired commands in a common frame of reference. The adaptive controllers do not require the complex mathematical model of the arm dynamics or any knowledge of the arm dynamic parameters or the load parameters such as mass and stiffness. The controllers have simple structures and are computationally fast for on-line implementation with high sampling rates. Simulation results are given to illustrate the proposed adaptive control strategies.