The leader-follower formation control of nonholonomic mobile robots

In this paper, the leader-waypoint-follower formation is constructed based on relative motion states of nonholonomic mobile robots. Since the robots’ velocities are constrained, we proposed a geometrical waypoint in cone method so that the follower robots move to their desired waypoints effectively. In order to form and maintain the formation of multi-robots, we combine stable tracking control method with receding horizon (RH) tracking control method. The stable tracking control method aims to make the robot’s state errors stable and the RH tracking control method guarantees that the convergence of the state errors tends toward zero efficiently. Based on the methods mentioned above, the mobile robots formation can be maintained in any trajectory such as a straight line, a circle or a sinusoid. The simulation results based on the proposed approaches show each follower robot can move to its waypoint efficiently. To validate the proposed methods, we do the experiments with nonholonomic robots using only limited on-board sensor information.     

移动机器人的队形控制及其主动避障

在这篇论文中, 我们利用一个统一的算法框架来解决移动机器人的队形控制和主动避障问题, 使得编队中的从机器人在避开障碍物的同时, 能够与被跟踪的主机器人保持期望的相对距离或相对方位. 在现有的关于主—从跟踪编队控制的文献中, 为了实现对主机器人快速准确的跟踪, 从机器人在跟踪控制时需要主机器人在惯性坐标系下的绝对运动速度作为队形跟踪控制器的输入. 然而, 在一些环境中, 主机器人的绝对运动状态很难获得. 这里, 我们将利用主—从机器人之间的相对速度来建立机器人编队系统的运动学模型. 基于这个模型的编队控制方法将不再需要测量主机器人的绝对运动速度. 进一步地, 上述的建模和控制方法被扩展为一个移动机器人的动态避障方法, 该方法利用机器人与障碍物之间相对运动状态作为避障控制器的信息输入. 利用由三个非完整移动机器人组成的多机器人系统, 验证了所提出编队控制方法的有效性.     

Asymptotic Adaptive Neural Network Tracking Control of Nonholonomic Mobile Robot Formations

In this paper, asymptotically stable control laws are developed for leader–follower based formation control using backstepping in order to accommodate the dynamics of the robots and the formation. First, a kinematic controller is developed around control strategies for single mobile robots and the idea of virtual leaders. The virtual leader is replaced with a physical mobile robot leader, and an auxiliary velocity control law is developed in order to prove the global asymptotic stability of the followers which in turn allows the local asymptotic stability of the entire formation. A novel approach is taken in the development of the dynamical controller such that the torque control inputs for the follower robots include the dynamics of the follower robot as well as the dynamics of its leader, and two cases are considered—the case when the robot dynamics are known and the case when they are unknown. In the first case, a robust adaptive control term is utilized to account for unmodeled dynamics. For the latter, a robust adaptive term is augmented with a NN control law to achieve asymptotic tracking performance in contrast with most NN controllers where a bounded tracking error result is shown. Additionally, the NN approximation error is assumed to be a function of tracking errors instead of a constant upper bound, which is commonly found in the literature. The stability of the follower robots as well as the entire formation is demonstrated in each case using Lyapunov methods and numerical results are provided.     

不确定环境下多机器人的动态编队控制

提出了一种不确定环境下多机器人的动态编队控制方法．通过队形参数矩阵确立多机器人之间的相对 位置关系,将全局队形控制问题转化为跟随机器人离轴点对虚机器人（与领航机器人运动方向一致,且对领航机器 人保持期望的相对距离和观测方位角）离轴点的跟踪．基于建立的跟随机器人和领航机器人之间的误差跟踪系统模 型设计相应控制律实现队形保持,并提出了防止机器人与障碍物及其它机器人碰撞的避障策略．仿真结果表明了所 提方法的可行性和有效性．     

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.     

Generalized measuring-worm algorithm: high-accuracy mapping and movement via cooperating swarm robots

Recently, many extensive studies have been conducted on robot control via self-positioning estimation techniques. In the simultaneous localization and mapping (SLAM) method, which is one approach to self-positioning estimation, robots generally use both autonomous position information from internal sensors and observed information on external landmarks. SLAM can yield higher accuracy positioning estimations depending on the number of landmarks; however, this technique involves a degree of uncertainty and has a high computational cost, because it utilizes image processing to detect and recognize landmarks. To overcome this problem, we propose a state-of-the-art method called a generalized measuring-worm (GMW) algorithm for map creation and position estimation, which uses multiple cooperating robots that serve as moving landmarks for each other. This approach allows problems of uncertainty and computational cost to be overcome, because a robot must find only a simple two-dimensional marker rather than feature-point landmarks. In the GMW method, the robots are given a two-dimensional marker of known shape and size and use a front-positioned camera to determine the marker distance and direction. The robots use this information to estimate each other’s positions and to calibrate their movement. To evaluate the proposed method experimentally, we fabricated two real robots and observed their behavior in an indoor environment. The experimental results revealed that the distance measurement and control error could be reduced to less than 3 %.     

Leader–follower formation control of nonholonomic mobile robots based on a bioinspired neurodynamic based approach

This paper investigates the leader–follower formation control problem for nonholonomic mobile robots based on a bioinspired neurodynamics based approach. The trajectory tracking control for a single nonholonomic mobile robot is extended to the formation control for multiple nonholonomic mobile robots based on the backstepping technique, in which the follower can track its real-time leader by the proposed kinematic controller. An auxiliary angular velocity control law is proposed to guarantee the global asymptotic stability of the followers and to further guarantee the local asymptotic stability of the entire formation. Also a bioinspired neurodynamics based approach is further developed to solve the impractical velocity jumps problem. The rigorous proofs are given by using Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.     

分数阶多机器人的领航–跟随型环形编队控制

针对多机器人系统的环形编队控制复杂问题,提出一种基于分数阶多机器人的环形编队控制方法,应用领航–跟随编队方法来控制多机器人系统的环形编队和目标包围,通过设计状态估测器,实现对多机器人的状态估计.由领航者获取系统中目标状态的信息,跟随者监测到领航者的状态信息并完成包围环绕编队控制,使多机器人系统形成对动态目标的目标跟踪.根据李雅普诺夫稳定性理论和米塔格定理,得到多机器人系统环形编队控制的充分条件,实现对多机器人系统对目标物的包围控制,通过对一组多机器人队列的目标包围仿真,验证了该方法的有效性.     

基于二阶运动学模型的移动机器人主从跟踪系统的鲁棒控制

In this paper, we study the problem of modeling and controlling leader-follower formation of mobile robots. First, a novel kinematics model for leader-follower robot formation is formulated based on the relative motion states between the robots and the local motion of the follower robot. Using this model, the relative centripetal and Coriolis accelerations between robots are computed directly by measuring the relative and local motion sensors, and utilized to linearize the nonlinear system equations. A formation controller, consisting of a feedback linearization part and a sliding mode compensator, is designed to stabilize the overall system including the internal dynamics. The control gains are determined by solving a robustness inequality and assumed to satisfy a cooperative protocol that guarantees the stability of the zero dynamics of the formation system. The proposed controller generates the commanded acceleration for the follower robot and makes the formation control system robust to the effect of unmeasured acceleration of the leader robot. Furthermore, a robust adaptive controller is developed to deal with parametric uncertainty in the system. Simulation and experimental results have demonstrated the effectiveness of the proposed control method.     

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.     

Coordinated transportation of a single object by two nonholonomic mobile robots

We propose a decentralized control algorithm for transporting a single object by two nonholonomic mobile robots. One of the robots acts as a leader, whose trajectory is planned by itself or defined previously, whereas the other robot, referred to as a follower, follows the leader by keeping a constant distance from the leader. The follower can also avoid obstacles while following the leader without any absolute information about their position. Furthermore, the two mobile robots can realize an omnidirectional motion of the object when the leader broadcasts some simple information to the follower. Some simulation results show a good performance by the proposed decentralized control algorithm. This work was presented, in part, at the Seventh International Symposium on Artificial Life and Robotics, Oita, Japan, January 16–18, 2002.     

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.     

含驱动器动力学的移动机器人编队自适应控制

针对含有驱动器及编队动力学的多非完整移动机器人编队控制问题,基于领航者-跟随者[l-ψ]控制结构,通过反步法设计了一种将运动学控制器与驱动器输入电压控制器相结合的新型控制策略。采用径向基神经网络（RBFNN）对跟随者及领航者动力学非线性不确定部分进行在线估计,并通过自适应鲁棒控制器对神经网络建模误差进行补偿。该方法不但解决了移动机器人编队控制的参数与非参数不确定性问题,同时也确保了机器人编队在期望队形下对指定轨迹的跟踪;基于Lyapunov方法的设计过程,保证了控制系统的稳定与收敛;仿真结果表明了该方法的有效性。     

Robust formation control without velocity measurement of the leader robot

In this paper a control problem of leader–follower motion coordination of multiple nonholonomic mobile robots is addressed and subsequently in the proposed scheme, a reference trajectory generated based on the information from the leader is tracked by the follower robots. To alleviate demanded information on the leader, specifically to eliminate the measurement requirement or estimation of the leader's velocity and dynamics, a virtual vehicle is constructed whereby its trajectory converges to the reference trajectory of the follower. Trajectory tracking controller is then designed to allow the follower robot to track the virtual vehicle using neural network approximation, in combination with the backstepping and Lyapunov direct design technique and finally the performance and effectiveness of the controller is verified throughout the experiments.     

Fuzzy Policy Reinforcement Learning in Cooperative Multi-robot Systems

A multi-agent reinforcement learning algorithm with fuzzy policy is addressed in this paper. This algorithm is used to deal with some control problems in cooperative multi-robot systems. Specifically, a leader-follower robotic system and a flocking system are investigated. In the leader-follower robotic system, the leader robot tries to track a desired trajectory, while the follower robot tries to follow the reader to keep a formation. Two different fuzzy policies are developed for the leader and follower, respectively. In the flocking system, multiple robots adopt the same fuzzy policy to flock. Initial fuzzy policies are manually crafted for these cooperative behaviors. The proposed learning algorithm finely tunes the parameters of the fuzzy policies through the policy gradient approach to improve control performance. Our simulation results demonstrate that the control performance can be improved after the learning.     

Symmetry position/force hybrid control for cooperative object transportation using multiple humanoid robots

A symmetry position/force hybrid control framework for cooperative object transportation tasks with multiple humanoid robots is proposed in this paper. In a leader-follower type cooperation, follower robots plan their biped gaits based on the forces generated at their hands after a leader robot moves. Therefore, if the leader robot moves fast (rapidly pulls or pushes the carried object), some of the follower humanoid robots may lose their balance and fall down. The symmetry type cooperation discussed in this paper solves this problem because it enables all humanoid robots to move synchronously. The proposed framework is verified by dynamic simulations.     

A decentralized control system for cooperative transportation by multiple non-holonomic mobile robots

In this paper, we propose a decentralized control system for transporting a single object by multiple non-holonomic mobile robots. Each agent used in the proposed system has two arms, which can steer around a joint offset from the centre point between two driving wheels. One of these mobile robots acts as a leader, who is assumed to be able to plan and to manipulate the omnidirectional motion of the object by using a resolved velocity control. Other robots, referred to as followers, cooperatively transport the object by keeping a constant relative position with the object using a simple PI control. Different from conventional leader–follower type systems that transport an object by multiple robots in coordination, the present followers can plan an action based on their local coordinate and need no absolute positional information. In addition, as a special case, a system consisting of only two robots is introduced, in which the follower robot not only has an arm length controller to follow the leader but also has a fuzzy controller as an avoidance controller to avoid obstacles or a posture controller to keep a desired posture of the object. Simulation results are given to demonstrate the good performance of the proposed systems.     

利用方位角信息的移动机器人编队控制

本文以移动机器人为研究对象,仅利用方位角信息实现多智能体系统的编队控制.为实现大规模编队和队形的缩放控制,智能体被分为领航者、第1跟随者以及其余跟随者.首先,考虑智能体之间相对位置信息难以精确测量的情形,设计仅用方位角信息的估计算法获得准确的相对位置;然后,基于获得的相对位置信息设计第1跟随者的控制算法,使得第一跟随者与领航者之间的位置收敛到理想约束位置以控制整个队形的规模;接着,设计其余跟随者的控制算法使得各智能体之间的方位角达到理想约束角度,从而形成理想编队队形.最后通过数值和ROS仿真实验验证算法的有效性.     

Formation control of mobile robots with obstacle avoidance based on GOACM using onboard sensors

This paper deals with the problem of formation control for nonholonomic mobile robots under a cluttered environment. When the obstacles are not detected, the follower robot calculates its waypoint to track, based on the leader robot’s state. The proposed geometric obstacle avoidance control method (GOACM) guarantees that the robot avoids the static and dynamic obstacles using onboard sensors. Due to the difficulty for the robot to simultaneously get overall safe boundary of an obstacle in practice, a safe line, which is perpendicular to the obstacle surface, is used instead of the safe boundary. Since GOACM is executed to find a safe waypoint for the robot, GOACM can effectively cooperate with the formation control method. Moreover, the adaptive controllers guarantee that the trajectory and velocity tracking errors converge to zero with the consideration of the parametric uncertainties of both kinematic and dynamic models. Simulation and experiment results present that the robots effectively form and maintain formation avoiding the obstacles.     

电驱移动机器人多变量固定时间连续编队控制

针对扰动下电驱动非完整移动机器人固定时间编队控制问题,通过引入包含驱动器动力学的领航者-跟随者状态空间动力学模型,分两步对编队控制器进行了设计。对领航者跟随者编队运动学模型进行了多变量固定时间控制设计。在动力学层面,为实现扰动下的速度跟踪,通过辅助输入设计了一种跟随者机器人多变量超螺旋固定时间连续电压控制器。所提算法使机器人编队克服了跟随者机器人所受干扰,确保了跟随者机器人与领航者在固定时间达到期望队形,跟随者在固定时间内跟随期望速度,设计的连续控制消除了开关控制的抖振现象。通过参数设计提前给定系统收敛的固定时间,与系统初始状态无关。基于Lyapunov方法进行了系统稳定性分析。通过仿真对算法进行了验证。