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.     

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 tracking control of mobile robots via one-to-one time-varying communication

We solve the formation tracking control problem for mobile robots via linear control, under the assumption that each agent communicates only with one ‘leader’ robot and with one follower, hence forming a spanning-tree topology. We assume that the communication may be interrupted on intervals of time. As in the classical tracking control problem for non-holonomic systems, the swarm is driven by a fictitious robot which moves about freely and which is a leader to one robot only. Our control approach is decentralised and the control laws are linear with time-varying gains; in particular, this accounts for the case when position measurements may be lost over intervals of time. For both velocity-controlled and force-controlled systems, we establish uniform global exponential stability, hence consensus formation tracking, for the error system under a condition of persistency of excitation on the reference angular velocity of the virtual leader and on the control gains.     

Finite-time tracking control for multiple non-holonomic mobile robots based on visual servoing

This paper investigates finite-time tracking control problem of multiple non-holonomic mobile robots via visual servoing. It is assumed that the pinhole camera is fixed to the ceiling, and camera parameters are unknown. The desired reference trajectory is represented by a virtual leader whose states are available to only a subset of the followers, and the followers have only interaction. First, the camera-objective visual kinematic model is introduced by utilising the pinhole camera model for each mobile robot. Second, a unified tracking error system between camera-objective visual servoing model and desired reference trajectory is introduced. Third, based on the neighbour rule and by using finite-time control method, continuous distributed cooperative finite-time tracking control laws are designed for each mobile robot with unknown camera parameters, where the communication topology among the multiple mobile robots is assumed to be a directed graph. Rigorous proof shows that the group of mobile robots converges to the desired reference trajectory in finite time. Simulation example illustrates the effectiveness of our method.     

Computing collision-free motions for a team of robots using formation and non-holonomic constraints

This paper focuses on the collision-free motion of a team of robots moving in a 2D environment with formation and non-holonomic constraints. With the proposed approach one can simultaneously control the formation of the team and generate a safe path for each individual robot. The computed paths satisfy the non-holonomic constraints, avoid collisions, and minimize the task-completion time. The proposed approach, which combines techniques from mathematical programming and CAD, consists of two main steps: first, a global team path is computed and, second, individual motions are determined for each unit. The effectiveness of the proposed approach is demonstrated using several simulation experiments.     

Controlling Ensembles of Robots via a Supervisory Aerial Robot

We consider the task of controlling a large team of non-holonomic ground robots with an unmanned aerial vehicle in a decentralized manner that is invariant to the number of ground robots. The central idea is the development of an abstraction for the team of ground robots that allows the aerial platform to control the team without any knowledge of the specificity of individual vehicles. This happens in much the same way as a human operator can control a single robot vehicle by simply commanding the forward and turning velocities without a detailed knowledge of the specifics of the robot. The abstraction includes a gross model of the shape of the formation of the team, and information about the position and orientation of the team in the plane. We derive controllers that allow the team of robots to move in formation while avoiding collisions and respecting the abstraction commanded by the aerial platform. We propose strategies for controlling the physical spread of the ensemble of robots by splitting and merging the team based on distributed techniques. We provide simulation and experimental results using a team of indoor mobile robots and a three-dimensional, cable-controlled, parallel robot which serves as our indoor unmanned aerial platform.     

轮式移动机器人瞬态模型鲁棒自适应同步终端滑模编队控制

在轮式移动机器人协同编队问题中,如何保证移动机器人在追踪自身期望轨迹的同时,又能实现与其他机器人运动同步的问题对控制算法的设计提出了更高的要求.本文提出一种基于图论的鲁棒自适应同步终端滑模控制算法来解决这一问题.首先介绍了轮式移动机器人非线性运动学瞬态模型,该模型避免了一般运动学模型多输入耦合互相干扰的问题.然后根据交叉耦合误差设计同步控制算法实现运动同步,通过鲁棒控制对系统外部干扰进行抑制,自适应律保证切换增益实时调节.运用Lyapunov方法进行了稳定性分析,证明了系统追踪误差的收敛性.最后通过MATLAB仿真验证了所设计算法的有效性.     

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.     

Vision-based hybrid control scheme for autonomous parking of a mobile robot

This paper presents a novel vision-based hybrid controller for parking of mobile robots. Parking or docking is an essential behavioral unit for autonomous robots. The proposed hybrid controller comprises a discrete event controller to change the direction of travel and a pixel error-driven proportional controller to generate motion commands to achieve the continuous motion. At the velocity control level, the robot is driven using a built-in PID control system. The feedback system uses image plane measurements in pixel units to perform image-based visual servoing (IBVS). The constraints imposed due to the non-holonomic nature of the robot and the limited field of view of the camera are taken into account in designing the IBVS-based controller. The controller continuously compares the current view of the parking station against the reference view until the desired parking condition is achieved. A comprehensive analysis is provided to prove the convergence of the proposed method. Once the parking behavior is invoked, the robot has the ability to start from any arbitrary position to achieve successful parking given that initially the parking station is in the robot's field of view. As the method is purely based on vision the hybrid controller does not require any position information (or localization) of the robot. Using the Pioneer 3AT robot, several experiments are carried out to authenticate the method. The experimental system has the ability to achieve the parking state and align laterally within ±0.5 cm of the target pose.     

Switching control approach for stable navigation of mobile robots in unknown environments

This paper presents a stable switching control strategy for the parking problem of non-holonomic mobile robots. First, it is proposed a positioning-orientation switching controller for the parking problem. With this strategy robot backwards motions are avoided and the robot heading is always in the direction of the goal point facilitating the obstacle handling. Second, the avoidance of unexpected obstacles is considered in a reactive way by following the contour of the obstacles. Next, the stability of the switching parking/obstacle-avoider controller is analyzed showing stability under reasonable conditions. Finally, the good performance and the feasibility of this approach are shown through several experimental results.     

A Behavioral Adaptive Fuzzy controller of multi robots in a cluster space

Cooperation between autonomous robot vehicles holds several promising advantages like robustness, adaptability, configurability, and scalability. Coordination between the different robots and the individual relative motion represent both the main challenges especially when dealing with formation control and maintenance. Cluster space control provides a simple concept for controlling multi-agent formation. In the classical approach, formation control is the unique task for the multi-agent system. In this paper, the development and application of a novel Behavioral Adaptive Fuzzy-based Cluster Space Control (BAFC) to non-holonomic robots is presented. By applying a fuzzy priority control approach, BAFC deals with two conflicting tasks: formation maintenance and target following. Using priority rules, the fuzzy approach is used to adapt the controller and therefore the behavior of the system, taking into accounts the errors in the formation states and the target following states. The control approach is easy to implement and has been implemented in this paper using SIMULINK real-time platform. The communication between the different agents and the controller is established through Wi-Fi link. Both simulation and experimental results demonstrate the behavioral response where the robot performs the higher priority tasks first. This new approach shows a great performance with a lower control signal when benchmarked with previously known results in the literature.     

Tracking Control of Multiple Mobile Robots: A Case Study of Inter‐Robot Collision‐Free Problem

ABSTRACT Tracking control problem of multiple mobile robots is considered. Our system is composed of a reference and two follower robots of unicycle type, which have their own priority numbers. The purpose is to control the two followers so that the reference is tracked with arbitrary desired clearance and also to avoid an inter‐robot collision, which can occur randomly during the control process subjected to communication range limitation. We introduce two switching controllers and appropriately using their convergence properties leading to the collision‐free movement. Simulation results prove efficiency of our control techniques.     

PDC Control Design for Non-holonomic Wheeled Mobile Robots with Delayed Outputs

This paper presents a new technique for tracking-error model-based Parallel Distributed Compensation (PDC) control for non-holonomic vehicles where the outputs (measurements) of the system are delayed and the delay is constant. Briefly, this technique consists of rewriting the kinematic error model of the mobile robot tracking problem into a TS fuzzy representation and finding a stabilizing controller by solving LMI conditions for the tracking-error model. The state variables are estimated by nonlinear predictor observer where the outputs are delayed by a constant delay. To illustrate the efficiency of the proposed approach a comparison between the TS fuzzy observer and the nonlinear predictor observer is shown. For this study the reference trajectory is built by taking into account the acceleration limits of the mobile robot. All experiments are implemented on simulation and the real-time platform.     

基于滚动时域优化的轮式移动机器人路径跟踪问题研究

轮式移动机器人是典型的非完整约束系统. 本文基于滚动时域控制策略研究轮式移动机器人的路径跟踪问题. 为了既能够保证移动机器人渐近收敛到期望轨迹, 又能够保证在线求解的优化问题的滚动可行性, 参考轨迹 被选为优化问题中的终端等式约束. 仿真结果验证了所提出的控制策略的有效性.     

Path-following control of a mobile robot in the presence of actuator constraints

In this paper, we present a control law for a non-holonomic mobile robot that achieves path following. In the path-following problem, the objective is to control the angular velocity of the robot so that the robot tracks a given reference trajectory. In this paper, we propose a control law that achieves path following in the presence of a constraint on the angular velocity. By applying the proposed control law, the robot can track the reference trajectory even if the distance from the initial position of the robot and the reference trajectory is arbitrary large. Further, we extend the control law so that the linear velocity of the robot becomes small when the robot passes through corners. By using the control algorithm, we can prevent the angular velocity of the robot becoming extremely large when the robot passes through corners. Numerical examples are provided to illustrate the effectiveness of the proposed methods.     

Scalable formation control in stealth with limited sensing range

In this paper, a protocol and a control law are designed for a single robot so that a team of such robots can interact and cooperate to reach the displacements from an eligible reference formation. Each robot is equipped with displacement sensors of limited sensing ranges. Communication channels are assumed to be unavailable to the team, and each robot works in stealth mode. The team is scalable such that new robots can be recruited, and existing robots can be dismissed. In order for the team size to be scalable, the extended formation based on relative displacement is established as the reference formation. Thus, using the extended formation as a reference, the control law and the protocol could be flexible. As potential conflicts deflect the robot team from the desired formation, the control law is designed to expose the conflicts to the involved neighboring robots such that the protocol can resolve them. A numerical example is given to illustrate how an extended formation is designed, and a simulation example is conducted to demonstrate the performance and merits of the proposed techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Formation control of underactuated bio-inspired snake robots

This paper considers formation control of snake robots. In particular, based on a simplified locomotion model, and using the method of virtual holonomic constraints, we control the body shape of the robot to a desired gait pattern defined by some pre-specified constraint functions. These functions are dynamic in that they depend on the state variables of two compensators which are used to control the orientation and planar position of the robot, making this a dynamic maneuvering control strategy. Furthermore, using a formation control strategy we make the multi-agent system converge to and keep a desired geometric formation, and enforce the formation follow a desired straight line path with a given speed profile. Specifically, we use the proposed maneuvering controller to solve the formation control problem for a group of snake robots by synchronizing the commanded velocities of the robots. Simulation results are presented which illustrate the successful performance of the theoretical approach.     

Vision-Based Localization for Leader–Follower Formation Control

This paper deals with vision-based localization for leader–follower formation control. Each unicycle robot is equipped with a panoramic camera that only provides the view angle to the other robots. The localization problem is studied using a new observability condition valid for general nonlinear systems and based on the extended output Jacobian. This allows us to identify those robot motions that preserve the system observability and those that render it nonobservable. The state of the leader–follower system is estimated via the extended Kalman filter, and an input-state feedback control law is designed to stabilize the formation. Simulations and real-data experiments confirm the theoretical results and show the effectiveness of the proposed formation control.      

Learning optimal trajectories for non-holonomic systems

Many advanced robotic systems are subject to non-holonomic constraints, e.g. wheeled mobile robots, space manipulators and multifingered robot hands. Steering these mechanisms between configurations in the presence of perturbations is a difficult problem. In fact, the divide et impera strategy (first plan a trajectory, then track it by feedback) has a fundamental drawback in this case: due to the peculiar control properties of non-holonomic systems, smooth feedback cannot provide tracking of the whole trajectory. As a result, it would be necessary to give up either accuracy in the final positioning or predictability of the actual motion. We pursue here a different approach which does not rely on a separation between planning and control. Based on the learning control paradigm, a robust steering scheme is devised for systems which can be put in chained form, a canonical structure for non-holonomic systems. By overparametrizing the control law, other performance goals can be met, typically expressed as cost functions to be minimized along the trajectory. As a case study, we consider the generation of robust optimal trajectories for a car-like mobile robot, with criteria such as total length, maximum steering angle, distance from workspace obstacles, or error with respect to an offline planned trajectory.     

Robust finite-time containment control for high-order multi-agent systems with matched uncertainties under directed communication graphs

In this paper, we study the robust finite-time containment control problem for a class of high-order uncertain nonlinear multi-agent systems modelled as high-order integrator systems with bounded matched uncertainties. When relative state information between neighbouring agents is available, an observer-based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite-time containment control problem under general directed communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding-mode controllers are employed together with the distributed finite-time observers. It is shown that robust finite-time containment control can still be achieved in this situation. An application in the coordination of multiple non-holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies.