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 and speed sensorless for the synchronisation of multi-robot systems

This paper investigates a synchronization approach to trajectory tracking of networked robotic systems while maintaining time-varying formations. The objective is to control networked robots to track a desired trajectory while synchronizing their behaviors. Combining trajectory tracking and synchronization algorithms, the developed approach uses a cross-coupling technical to create interconnections for mutual synchronization of robots. The main objective of distributed approach is to generate an emerging behavior using only local information interactions. First, a distributed scheme is developed to achieve the networked robots synchronization on undirected graph. Then, the leaderless synchronized tracking problem in the case when only position measurements are available, will be presented. For both cases: In the presence of the velocity feedback or in its absence, the controller, designed by incorporating the cross-coupling technical into a sliding mode control architecture, successfully guarantees asymptotic convergence to zero of both position tracking and synchronization errors simultaneously. The Lyapunov-based approach has been used to establish the multi-robot systems asymptotic stability. A real-time software simulator is developed to visualize the synchronized behaviors. Based on LabVIEW integrated development environment (IDE), a developed human-machine-interface (HMI) allows its user to control, in real time, the networked robots. Simulation and experimental results are provided to demonstrate performances of the proposed control schemes.     

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.     

Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots

In this paper, we investigate the output consensus problem of tracking a desired trajectory for a class of systems consisting of multiple nonlinear subsystems with intrinsic mismatched unknown parameters. The subsystems are allowed to have non-identical dynamics, whereas with similar structures and the same yet arbitrary system order. And the communication status among the subsystems can be represented by a directed graph. Different from the traditional centralized tracking control problem, only a subset of the subsystems can obtain the desired trajectory information directly. A distributed adaptive control approach based on backstepping technique is proposed. By introducing the estimates to account for the parametric uncertainties of the desired trajectory and its neighbors’ dynamics into the local controller of each subsystem, information exchanges of online parameter estimates and local synchronization errors among linked subsystems can be avoided. It is proved that the boundedness of all closed-loop signals and the asymptotically consensus tracking for all the subsystems’ outputs are ensured. A numerical example is illustrated to show the effectiveness of the proposed control scheme. Moreover, the design strategy is successfully applied to solve a formation control problem for multiple nonholonomic mobile robots.     

Trajectory design and control for aggressive formation flight with quadrotors

In this work we consider the problem of controlling a team of micro-aerial vehicles moving quickly through a three-dimensional environment while maintaining a tight formation. The formation is specified by shape vectors which prescribe the relative separations and bearings between the robots. To maintain the desired shape, each robot plans its trajectory independently based on its local information of other robot plans and estimates of states of other robots in the team. We explore the interaction between nonlinear decentralized controllers, the fourth-order dynamics of the individual robots, time delays in the network, and the effects of communication failures on system performance. Simulations as well as an experimental evaluation of our approach on a team of quadrotors suggests that suitable performance is maintained as the formation motions become increasingly aggressive and as communication degrades.     

Global Output Tracking Control of Flexible Joint Robots via Factorization of the Manipulator Mass Matrix

This paper investigates the problem of global output feedback tracking control of flexible joint robots. Despite the fact that only link position and actuator position are available from measurements, the proposed controller ensures that the link position globally tracks the desired trajectory while keeping all the remaining signals bounded. The controller development uses a partial state-feedback linearization technique combined with the integrator backstepping control design method whereas a filter and an observer are utilized to remove the requirement of link and actuator velocity measurements. Partial state-feedback linearization of robot dynamics is performed by factoring the manipulator mass matrix into a quadratic form involving an integrable root matrix. The applicability of the proposed general design methodology is illustrated by an example of flexible joint planar robots. Numerical results for a two-link flexible joint planar robot are also provided.      

Formation Control of Swarm Robots with Multiple Proximity Distance Sensors

This study deals with the formation control problem of swarm robots using position sensitive detector (PSD) proximity distance sensors based on light-emitting diodes (LEDs). These proximity distance sensors are lightweight and quickly responsive, and are expected to enhance the mobility and flexibility of swarm robots. However, as each sensor has a narrow detection angle, the formation control problem becomes more difficult than when wide-directional distance sensors (such as cameras and laser rangefinders) are used. To overcome this difficulty, we design a two-part motion controller that controls both position and attitude. The attitude controller is necessary for continuous detection of other robots through the narrow detection angles. The designed controller is distributed in the sense that it requires only information on measured values of each robot’s own sensors. Next, we derive an appropriate sensor arrangement (positions and detection angles) that achieves the desired formation pattern. Finally, the effectiveness of the proposed method is demonstrated in an experiment performed by six omni-wheeled robots equipped with LED-based PSD proximity distance sensors.     

Aggressive Longitudinal Aircraft Path Tracking Using Nonlinear Control

We study the problem of converting a trajectory tracking controller to a path tracking controller for a nonlinear non-minimum phase longitudinal aircraft model. The solution of the trajectory tracking problem is based on the requirement that the aircraft follows a given time parameterized trajectory in inertial frame. In this paper we introduce an alternative nonlinear control design approach called path tracking control. The path tracking approach is based on designing a nonlinear state feedback controller that maintains a desired speed along a desired path with closed loop stability. This design approach is different from the trajectory tracking approach where aircraft speed and position are regulated along the desired path. The path tracking controller regulates the position errors transverse to the desired path but it does not regulate the position error along the desired path. First, a trajectory tracking controller, consisting of feedforward and static state feedback, is designed to guarantee uniform asymptotic trajectory tracking. The feedforward is determined by solving a stable noncausal inversion problem. Constant feedback gains are determined based on LQR with singular perturbation approach. A path tracking controller is then obtained from the trajectory tracking controller by introducing a suitable state projection.     

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.     

Formation Control and Tracking for Co-operative Robots with Non-holonomic Constraints

This paper mainly addresses formation control problem of non-holonomic systems in an optimized manner. Instead of using linearization to solve this problem approximately, we designed control laws with guaranteed global convergence by leveraging nonlinear transformations. Under this nonlinear transformation, consensus of non-holonomic robots can be converted into a stabilization problem, to which optimal treatment applies. This concept is then extended to the formation control and tracking problem for a team of robots following leader-follower strategy. A trajectory generator prescribes the feasible motion of virtual reference robot, a decentralized control law is used for each robot to track the reference while maintaining the formation. The asymptotic convergence of follower robots to the position and orientation of the reference robot is ensured using the Lyapunov function which is also generated using chained form differential equations. In order to witness the efficacy of the scheme, simulations results are presented for Unicycle and Car-like 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。     

Using Sensor Morphology for Multirobot Formations

In formation-maintenance (formation control) tasks, robots maintain their relative position with respect to their peers, according to a desired geometric shape. Previous work has examined formation-maintenance algorithms, based on formation control graphs, that ensure the theoretical stability of the formation. However, an exponential number of stable controllers exists. Thus a key question is how to select (construct) a formation controller that optimizes desired properties, such as sensor usage. We present a novel representation of the sensing capabilities of robots in formations, using a monitoring multigraph. We first show that graph-theoretic techniques can then be used to efficiently compute optimal sensing policies that maintain a given formation, while minimizing sensing costs. In particular, separation-bearing (distance-angle) control targets are automatically constructed for each individual robot in the formation, taking into account its specific sensor morphology. Then, we present a protocol allowing control graphs to be switched on line, to allow robots to adjust to sensory failures. We report on results from comprehensive experiments with physical and simulated robots. The results show that the use of the dynamic protocol allows formations of real robots to move significantly faster and with greater precision, while reducing the number of formation failures, due to sensor limitations. We also evaluate the sensitivity of our approach to communication reliability, and discuss opportunities and challenges raised by our approach.     

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。     

Synchronization Control for a Swarm of Unicycle Robots: Analysis of Different Controller Topologies

This paper proposes a nonlinear synchronization controller for a swarm of unicycle robots performing a cooperative task, i.e., following a desired trajectory per robot while maintaining a prescribed formation. The effect of communication between robots is analyzed and several network topologies are investigated, e.g., all‐to‐all, ring type, undirected, among others. The stability analysis of the closed loop system is provided using the Lyapunov method. Experiments with four unicycle robots are presented to validate the control law and communication analysis. Accumulated errors over the experiment time are presented in order to determine which topology is most efficient.     

Precision Synchronization Motion Trajectory Tracking Control of Multiple Pneumatic Cylinders

This paper deals with the synchronized motion trajectory tracking control problem of multiple pneumatic cylinders. An adaptive robust synchronization controller is developed by incorporating the cross‐coupling technology into the integrated direct/indirect adaptive robust control (DIARC) architecture. The position synchronization error and the trajectory tracking error of each cylinder are combined to construct the so‐called coupled position error. The proposed adaptive robust synchronization controller is designed with the feedback of this coupled position error and is composed of two parts: an on‐line parameter estimation algorithm and a robust control law. The former is employed to obtain accurate estimates of model parameters for reducing the extent of parametric uncertainties, while the latter is utilized to attenuate the effects of parameter estimation errors, unmodelled dynamics, and external disturbances. Theoretically, both the position synchronization and trajectory tracking errors will achieve asymptotic convergence simultaneously. Moreover, the effectiveness of the proposed controller is verified by the extensive experimental results performed on a two‐cylinder pneumatic system.     

On controlling robots with redundancy

Recently there has been considerable interest in increasing the applicability and utility of robots by developing manipulators which possess kinematic and/or actuator redundancy. This paper presents a unified approach to controlling these redundant robots. The proposed control system consists of two subsystems: an adaptive position controller which generates the Cartesian-space control force FR^m required to track the desired end-effector position trajectory, and an algorithm that maps this control input to a robot joint torque vector TRⁿ. The F → T map is constructed so that the robot redundancy (kinematic and/or actuator) is utilized to improve the performance of the robot. The control scheme does not require knowledge of the complex robot dynamic model or parameter values for the robot or the payload. As a result, the controller is very general and is computationally efficient for on-line implementation. Computer simulation results are given for a kinematically redundant robot, for a robot with actuator redundancy, and for a robot which possesses both kinematic and actuator redundancy. In each case the results demonstrate that accurate end-effector trajectory tracking and effective redundancy utilization can be achieved simultaneously with the proposed scheme.     

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.     

Finite‐time formation control of multiple nonholonomic mobile robots

This paper considers finite‐time formation control problem for a group of nonholonomic mobile robots. The desired formation trajectory is represented by a virtual dynamic leader whose states are available to only a subset of the followers and the followers have only local interaction. First of all, a continuous distributed finite‐time observer is proposed for each follower to estimate the leader's states in a finite time. Then, a continuous distributed cooperative finite‐time tracking control law is designed for each mobile robot. Rigorous proof shows that the group of mobile robots converge to the desired geometric formation pattern in finite time. At the same time, all the robots can track the desired formation trajectory in finite time. Simulation example illustrates the effectiveness of our method. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.