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.     

Decentralised consensus-based formation tracking of multiple differential drive robots

This article investigates the control problem for formation tracking of multiple nonholonomic robots under distributed manner which means each robot only needs local information exchange. A class of general state and input transform is introduced to convert the formation-tracking issue of multi-robot systems into the consensus-like problem with time-varying reference. The distributed observer-based protocol with nonlinear dynamics is developed for each robot to achieve the consensus tracking of the new system, which namely means a group of nonholonomic mobile robots can form the desired formation configuration with its centroid moving along the predefined reference trajectory. The finite-time stability of observer and control law is analysed rigorously by using the Lyapunov direct method, algebraic graph theory and matrix analysis. Numerical examples are finally provided to illustrate the effectiveness of the theory results proposed in this paper.     

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.     

Marching control based on the leader-followers scheme and formation graphs

This paper analyzes the case of marching control, where a leader robot follows a desired trajectory, while the whole group reaches a formation pattern established by a formation graph. To guarantee that the group preserves the desired formation and follows the marching path simultaneously, two approaches are given, based on the feedback of the velocity of the desired trajectory or the velocity of some robots. The main result establishes that for both approaches and any well-defined formation graph, there is convergence to the formation and the marching path. The analysis addresses the cases of omnidirectional robots and the extension to unicycle-type robots. The performance of the control strategies is shown some numerical simulations and real-time experiments.     

Gradual spatial pattern formation of homogeneous robot group

This paper proposes a gradual formation of a spatial pattern for a homogeneous robot group. The autonomous formation of spatial pattern is one of key technologies for the advancement of cooperative robotic systems because a pattern formation can be regarded as function differentiation of a multi-agent system. When multiple autonomous robots without a given local task cooperatively work for a global objective, the function differentiation is the first and indispensable step. For example, each member of cooperative insects or animals can autonomously recognize own local tasks through mutual communication with local members. There were a lot of papers that reported a spatial pattern formation of multiple robots, but the global information was supposed to be available in their approaches. It is however almost impractical assumption for a small robot to be equipped with an advanced sensing system for global localization due to robot’s scale and sensor size. The local information-based algorithm for the pattern formation is desired even if each robot is not equipped with a global localization sensor.We therefore propose a gradual pattern formation algorithm, i.e., a group of robots improves complexity of their pattern from to a simple pattern to a goal pattern like a polygon. In the algorithm, the Turing diffusion-driven instability theory is used so that it could differentiate roles of each robot in a group based only on local information. In experiment, we demonstrate that robots can make a few polygon patterns from a circle pattern by periodically differentiating robot’s roles into a vertex or a side. We show utilities of the proposed gradual pattern formation algorithm for multiple autonomous robots based on local information through some experiments.     

A switched-system approach to formation control and heading consensus for multi-robot systems

This paper proposes a novel, hybrid and decentralized, switched-system approach for formation and heading consensus control of mobile robots under switching communication topology, including collision avoidance capability. The set of robots consists of nonholonomic wheeled mobile robots and can include a teleoperated UAV. The key feature of this approach is a virtual graph, which is derived by adding a set of relative translation vectors to the real graph of the multiple robots. Our approach results in the robots in the real graph moving to the desired formation and achieving heading consensus while the virtual robots on the virtual graph reach pose consensus. If any robot detects a nearby obstacle or other robot, the robot will temporarily move along an avoidance vector, which is perpendicular and positively projected onto the attractive vector, such that collision is avoided while minimally deviating from its formation control path. Experimental results are provided by two different research groups to demonstrate the effectiveness of our approach. These experiments extend the theoretical development by introducing a teleoperated quadrotor as a leader robot of the multi-robot systems. The same control law works for the extended system, with no modifications.     

Multirobot Rendezvous With Visibility Sensors in Nonconvex Environments

This paper presents a coordination algorithm for mobile autonomous robots. Relying on distributed sensing, the robots achieve rendezvous, i.e., they move to a common location. Each robot is a point mass moving in a simply connected, nonconvex, unknown environment according to an omnidirectional kinematic model. It is equipped with line-of-sight limited-range sensors, i.e., it can measure the relative position of any object (robots or environment boundary) if and only if the object is within a given distance and there are no obstacles in between. The perimeter minimizing algorithm is designed using the notions of robust visibility, connectivity-preserving constraint sets, and proximity graphs. The algorithm provably achieves rendezvous if the interagent sensing graph is connected at any time during the evolution of the group. Simulations illustrate the theoretical results and the performance of the proposed algorithm in asynchronous setups and with measurement errors, control errors, and nonzero robot size. Simulations to illustrate the importance of visibility constraints and comparisons with the optimal centralized algorithm are also included.     

Sensor Fusion for Joint Kinematic Estimation in Serial Robots Using Encoder,Accelerometer and Gyroscope

Open-chain manipulator robots play an important role in the industry, since they are utilized in applications requiring precise motion. High-performance motion of a robot system mainly relies on adequate trajectory planning and the controller that coordinates the movement. The controller performance depends of both, the employed control law and the sensor feedback. Optical encoder feedback is the most used sensor for angular position estimation of each joint in the robot, since they feature accurate and low noise angular position measurements. However, it cannot detect mechanical imperfections and deformations common in open chain robots. Moreover, velocity and acceleration cannot be extracted from the encoder data without adding phase delays. Sensor fusion techniques are found to be a good solution for solving this problem. However, few works has been carried out in serial robots for kinematic estimation of angular position, velocity and acceleration, since the delays induced by the filtering techniques avoids its use as controller feedback. This work proposes a novel sensor-fusion-based feedback system capable of providing complete kinematic information from each joint in 4-degrees of freedom serial robot, with the contribution of a proposed methodology based on Kalman filtering for fusing the information from optical encoder, gyroscope and accelerometer appended to the robot. Calibration and experimentation are carried out for validating the proposal. The results are compared with another kinematic estimation technique finding that this proposal provides more information about the robot movement without adding state delays, which is important for being used as controller feedback.     

Nonlinear formation control of unicycle-type mobile robots

We investigate formation control of a group of unicycle-type mobile robots at the dynamics level with a little amount of inter-robot communication. A combination of the virtual structure and path-tracking approaches is used to derive the formation architecture. Each individual robot has only position and orientation available for feedback. For each robot, a coordinate transformation is first derived to cancel the velocity quadratic terms. An observer is then designed to globally exponentially/asymptotically estimate the unmeasured velocities. An output feedback controller is designed for each robot. The controller is designed in such a way that the path derivative is left as a free input to synchronize the robots’ motion. Simulations illustrate the soundness of the proposed controller.     

多机器人编队离散模型及队形控制稳定性分析

针对包含绕心运动情况下的多机器人编队进行离散建模,并利用该模型解决保持队形期望前端始终朝着编队前进方向的控制问题.以控制多机器人编队收敛到期望的队形并镇定到预设运动规律上为目标,定义了一类通信拓扑图,基于该类图提出了一种分布式协同控制算法.给出了该控制算法下编队系统渐进稳定的充分必要条件及反馈控制参数的收敛域.证明了在该充分必要条件下可实现编队收敛到期望的队形和预设运动规律上的目标.仿真实验表明,在该算法控制下多机器人编队较好地收敛到期望队形并按预设规律运动,且过程中始终保持队形期望前端朝着编队前进方向,进而验证了该算法的有效性和正确性.     

多机器人主—从行星式编队控制

研究了二阶积分器描述的多机器人主—从行星式编队控制问题,提出了将多机器人编队分解为每个机器人对各自具有时变速度的虚拟机器人的跟踪控制,使得每个机器人相对于虚拟机器人的位置与速度跟踪误差收敛为零且彼此不相碰撞,此时编队系统收敛到理想队形.在统一的算法框架下,分别实现了跟随者以领航者为中心的公转运动编队(revolution formation,RF)模式和跟随者与领航者保持期望距离、期望速度的编队(desiredformation,DF)模式.公转运动编队(RF)模式适用于异构多机器人系统的环境探索任务;保持期望距离、期望速度的编队(DF)模式适用于自主水下机器人(AUV)、无人机(UAV)等合作与协调任务.应用李亚普诺夫稳定性理论对控制算法的稳定性进行了分析,并通过计算机仿真验证了该方法的有效性.     

Anonymous graph exploration without collision by mobile robots

Considering autonomous mobile robots moving on a finite anonymous graph, this paper focuses on the Constrained Perpetual Graph Exploration problem (CPGE). That problem requires each robot to perpetually visit all the vertices of the graph, in such a way that no vertex hosts more than one robot at a time, and each edge is traversed by at most one robot at a time. The paper states an upper bound k on the number of robots that can be placed in the graph while keeping CPGE solvability. To make the impossibility result as strong as possible (no more than k robots can be initially placed in the graph), this upper bound is established under a strong assumption, namely, there is an omniscient daemon that is able to coordinate the robots movements at each round of the synchronous system. Interestingly, this upper bound is related to the topology of the graph. More precisely, the paper associates with each graph a labeled tree that captures the paths that have to be traversed by a single robot at a time (as if they were a simple edge). The length of the longest of these labeled paths reveals to be the key parameter to determine the upper bound k on the number of robots.     

任意初始位置机器人领航跟随型迭代学习编队

针对移动机器人编队形成与队形保持问题,提出了一种适用于任意初始位置条件下的迭代学习编队控制算法。采用领航-跟随型编队法,仅利用领航者的运动轨迹和期望的编队队形推导出跟随者的参考航迹,引入迭代学习控制（Iterative Learning Control,ILC）方法,设计跟随者的控制律,使跟随者随着每次迭代调节自身的线速度和角速度,与领航者一起以期望编队队形工作;引入对初始位置的学习,即同时进行编队队形的学习和编队初始位置的学习。解决了任意初始位置的多移动机器人形成并保持期望编队队形的问题。并在理论上分析了控制算法的可行性,仿真结果验证了控制算法的有效性。     

Nonlinear formation control strategies for agents without relative measurements under heterogeneous networks

This paper proposes cooperative control protocols for a group of unmanned vehicles to make a stable formation around a maneuvering target. The control protocols are proposed on the basis of heterogeneous communication networks, which represents more challenging and generalized situations. Two different scenarios are considered. Separate control protocols are developed for each case. In both scenarios, agents do not have relative position, velocity, and acceleration measurements as feedback. In the first scenario, each agent uses its own position and velocity measurement in a consensus algorithm. In the second scenario, each agent needs only its own position information for the consensus algorithm. For both protocols, agents compute virtual estimates of a target's position and velocity and exchange these among the neighbors. Three different communication networks are used for exchanging two virtual estimates calculated by each agent and a time derivative of one virtual estimate. Each interagent communication network is represented by a fixed, undirected, and connected graph. Furthermore, it is considered that at least one agent receives the position, velocity, and acceleration information of the maneuvering target. It is not necessary that the agent receiving the target's position and the agent receiving the velocity and/or the acceleration information of the target be the same. However, the target does not receive any information about any agent. Stability of the formation is analyzed by using Barbalat's lemma. It is also shown that, despite the large difference in received information, the acceleration of the agents remains bounded for all time. The performance of the proposed formation control protocols is illustrated through numerical simulations.     

Decentralized behavior-based formation control of multiple robots considering obstacle avoidance

This paper proposes a decentralized behavior-based formation control algorithm for multiple robots considering obstacle avoidance. Using only the information of the relative position of a robot between neighboring robots and obstacles, the proposed algorithm achieves formation control based on a behavior-based algorithm. In addition, the robust formation is achieved by maintaining the distance and angle of each robot toward the leader robot without using information of the leader robot. To avoid the collisions with obstacles, the heading angles of all robots are determined by introducing the concept of an escape angle, which is related with three boundary layers between an obstacle and the robot. The layer on which the robot is located determines the start time of avoidance and escape angle; this, in turn, generates the escape path along which a robot can move toward the safe layer. In this way, the proposed method can significantly simplify the step of the information process. Finally, simulation results are provided to demonstrate the efficiency of the proposed algorithm.     

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.     

Cooperative localization and control of multiple heterogeneous robots using a string formation

This paper is on cooperative localization and control of multiple heterogeneous robots utilizing a string formation. This formation is preferred, since robots can move along a narrow passage utilizing this formation. Dead reckoning localization based on inertial measurement units leads to accumulated localization error. To avoid the error accumulation in dead reckoning localization, this paper introduces the last-move strategy for multiple heterogeneous robots. In the last-move strategy, a single robot is selected for maneuvering, and it turns on its bearing-range sensors for a short amount of time, in order to locate itself. While the selected robot moves, all other robots stop moving and perform as static landmarks for the moving robot. A robot may not maintain its desired course, in the case where environmental disturbance is severe. We thus develop a control strategy for avoiding obstacles while estimating the disturbance direction at a robot's location. To the best of our knowledge, this paper is novel in localization and control of a team of heterogeneous robots, considering the case where environmental disturbance is severe. The proposed localization process is energy-efficient, thus is suitable for practical applications. The performance of the proposed schemes is demonstrated utilizing MATLAB simulations.     

A Complete and Scalable Strategy for Coordinating Multiple Robots Within Roadmaps

This paper addresses the challenging problem of finding collision-free trajectories for many robots moving toward individual goals within a common environment. Most popular algorithms for multirobot planning manage the complexity of the problem by planning trajectories for robots individually; such decoupled methods are not guaranteed to find a solution if one exists. In contrast, this paper describes a multiphase approach to the planning problem that uses a graph and spanning tree representation to create and maintain obstacle-free paths through the environment for each robot to reach its goal. The resulting algorithm guarantees a solution for a well-defined number of robots in a common environment. The computational cost is shown to be scalable with complexity linear in the number of the robots, and demonstrated by solving the planning problem for 100 robots, simulated in an underground mine environment, in less than 1.5 s with a 1.5 GHz processor. The practicality of the algorithm is demonstrated in a real-world application requiring coordinated motion planning of multiple physical robots.     

A semiglobally stable output feedback PI2D regulator forrobot manipulators

Provides an answer to the long-standing question of designing asymptotically stable proportional plus integral regulators with only position feedback for robots with uncertain payload. It has previously been shown in Kelly (1993) and Ailon and Ortega (1993) that globally asymptotically stable set-point regulators for robot manipulators without velocity measurement can be obtained replacing the velocity feedback of a proportional plus derivative controller by a filtered position feedback. In these schemes, the only robot prior information required is the evaluation of the gravity forces at the reference (constant) position. This prior knowledge is used to shape the robot potential energy to have a unique minimum at the desired position. A mismatch in the estimation of the gravity forces leads to a position steady-state error. The authors' main contribution in this paper is to obviate the need of this prior information via the inclusion of two integral terms, around the position error and the filtered position, respectively. Semiglobal stability of the resulting control law is established     

Formation-containment control of second-order multi-agent systems with only sampled position data

This paper studies the formation-containment control problem of second-order multi-agent systems with only sampled position data. It is assumed that there exist interactions among leaders and the leaders’ neighbours are only leaders. Two different control protocols with only sampled position information are proposed for followers and leaders, respectively. By the algebraic graph theory and matrix theory, sufficient conditions are given to guarantee that the leaders achieve a desired formation and the followers asymptotically converge into the convex hull formed by the corresponding states of the leaders, i.e. the multi-agent systems achieve formation-containment. Moreover, an explicit expression of the formation position function is given for each leader. Finally, a numerical simulation is provided to illustrate the effectiveness of theoretical results.