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.     

Finite time distributed distance‐constrained shape stabilization and flocking control for d‐dimensional undirected rigid formations

Most of the existing results on distributed distance‐constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non‐collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

基于一致性的小型四旋翼机群自主编队分布式运动规划

设计一种小型四旋翼无人机群起飞后自主形成正多边形编队的分布式运动规划方法.在四旋翼无人机的串级控制系统框架下,分布式编队控制器以简化agent模型为基础,同时采用平均一致性算法和有领导一致性算法,共同产生各无人机位置与偏航角的期望轨迹.讨论了达成最终协调目标队形的拓扑条件,并给出一种基于有向Hamilton环的通信拓扑设计方案.最后通过数值仿真验证了所提出算法的有效性.     

Formation control of multiple elliptic agents with limited sensing ranges

This paper presents a design of cooperative controllers that force a group of N mobile agents with an elliptic shape and limited sensing ranges to perform a desired formation and that guarantee no collisions between any agents in the group. The desired formation can be stabilized at feasible reference trajectories with bounded time derivatives. The formation control design is based on explicit algebraic separation conditions between ellipses, root conditions of cubic polynomials, the Lyapunov direct method, and smooth or p‐times differentiable step functions. These functions are incorporated into novel potential functions to solve the collision avoidance problem without the need for switchings despite the agents' limited sensing ranges. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.      

Coordination control of multiple ellipsoidal agents with collision avoidance and limited sensing ranges

This paper contributes a design of cooperative controllers that force N mobile agents with an ellipsoidal shape and a limited sensing range to track desired trajectories and to avoid collision between them. A separation condition for ellipsoidal agents is first derived. Smooth step functions are then introduced. These functions and the separation condition between the ellipsoidal agents are embedded in novel pairwise collision avoidance functions to design coordination controllers. The proposed control design guarantees (1) smooth coordination controllers despite the agents’ limited sensing ranges, (2) no collision between any agents, (3) asymptotical stability of desired equilibrium set, and (4) instability of all other undesired critical sets of the closed loop system.     

Formation control of underactuated ships with elliptical shape approximation and limited communication ranges

Based on the recent theoretical development for formation control of multiple fully actuated agents with an elliptical shape in Do (2012), this paper develops distributed controllers that force a group of $N$ underactuated ships with limited communication ranges to perform a desired formation, and guarantee no collisions between any ships in the group. The ships are first fitted to elliptical disks for solving collision avoidance. A coordinate transformation is then proposed to introduce an additional control input, which overcomes difficulties caused by underactuation and off-diagonal terms in the system matrices. The control design relies on potential functions with the separation condition between elliptical disks and the smooth or $p$-times differentiable step functions embedded in.     

多智能体沿多条给定路径编队运动的有向协同控制

研究了在有向通信连接下二阶积分器描述的多智能体沿多条给定路径编队运动的控制器设计及其稳定性分析问题. 智能体的动态和指定路径都是在固定直角坐标系下描述的. 通过引入路径函数来设计路径跟踪控制, 根据路径函数与弧长的关系来设计编队控制律, 使得多智能体沿期望路径的位置和速度在规定队形下达到一致. 利用图论证明, 当通信拓扑对应的有向图具有全局可达点时, 设计的编队控制系统是渐近稳定的. 本文设计的有向协同控制律可以应用于区域的信息优化采集.     

Distributed tracking of a non-minimally rigid formation for multi-agent systems

The objective of this paper is to design distributed control algorithms for a multi-agent system such that a rigid formation can be achieved asymptotically and the agents can finally move with a desired velocity. In particular, it is assumed that the formation is not necessarily minimally rigid, and the desired velocity is available to only a subset of the agents. Estimators are constructed for the agents to estimate the desired velocity, which are further used to design the control inputs of the agents. The proposed control algorithms consist of a formation acquisition term which depends on a potential function and the rigidity matrix, and a velocity estimation term. To deal with non-minimal rigidity, the centre manifold theorem is exploited to prove the stability of the resulting system. Simulation results are also provided to show the effectiveness of the proposed control algorithms.     

Bounded Controllers for Formation Stabilization of Mobile Agents With Limited Sensing Ranges

A constructive method is presented to design bounded cooperative controllers that force a group of N mobile agents with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the agents. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, and are equal to infinity when a collision occurs. A p-times differential bump function is introduced and embedded into the potential functions to deal with the agent limited sensing ranges. An alternative to Barbalat's lemma is developed to analyze stability of the closed loop system. Extension to formation tracking is also addressed     

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.     

Coordinated circumnavigation by multiple agents under directed topology

ABSTRACT

This paper focuses on the coordinated circumnavigation problem for multiple agents with directed communication topology. All agents are required to be evenly spaced around a moving target, and orbit around it with prescribed radii and circular velocity. We divide the coordinated circumnavigation system into a cascaded system consisting of a standoff tracking subsystem and a spacing distribution subsystem. A tracking controller and an additional controller for the two subsystems are developed, respectively. The global uniform stability of the coordinated circumnavigation system is analysed using the cascaded control theory. The presented controllers render each individual agent circumnavigating the target with the desired requirements. More importantly, we show that the derived tracking controller is a general extension of existing controllers for single agent circumnavigation problem. Another feature of the proposed controllers is that the directed topology considered only needs to have a directed spanning tree. Furthermore, the proposed controllers take the velocity constraints into consideration, that is more rational for practical applications. Numerical simulations are provided to verify the effectiveness of the proposed methods.     

Mixed H∞ and passive control for linear switched systems via hybrid control approach

This paper investigates the mixed H_∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H_∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H_∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.     

Multi-Agent Formation Control Based on Bell-Shaped Potential Functions

In this paper we analyze stability properties of multi-agent control system with an artificial potential based on bell-shaped functions. In our approach attractive and repulsive forces created by potential gradient have the same form. This particular property allows definition of target formation that is parameter invariant. Due to the fact that agents are identical, the proposed structure of formation potential is invariant to the interchange of agents configurations, hence, target in which particular agent would eventually end up, depends only on formation initial condition. It has been demonstrated that stability analysis, given for stationary targets, applies to moving targets formation as well. We show that position of unwanted stable equilibria can be controlled by a single parameter that defines an elementary potential function. This fact has been used for synthesis of an adaptation algorithm, such that arrival of agents at required formation is guarantied. Simulation results, presented at the end of the paper, confirm correctness of the proposed control scheme.     

Robust Formation Control of Multiple Wheeled Mobile Robots

This paper considers formation control of a group of wheeled mobile robots with uncertainty. Decentralized cooperative robust controllers are proposed in two steps. In the first step, cooperative control laws are proposed for multiple kinematic systems with the aid of results from graph theory such that a group of robots comes into a desired formation. In the second step, cooperative robust control laws for multiple uncertain dynamic systems are proposed with the aid of backstepping techniques and the passivity properties of the dynamic systems such that multiple robots comes into a desired formation. Since communication delay is inevitable in cooperative control, its effect on the proposed controllers is analyzed. Simulation results show the effectiveness of the proposed controllers.     

Cooperative Target-centric Formation Control without Relative Velocity Measurements under Heterogeneous Networks

This paper proposes distributed control laws for a group of unmanned aerial vehicles (UAVs) to make and maintain a circular formation around a maneuvering target. The work considers usage of heterogeneous communication networks to achieve the desired formation. Two different scenarios are considered on velocity information. In both scenarios, it is assumed that each UAV has its own position and velocity measurements available to itself. However, the team is unable to exchange velocity information among themselves. In the first scenario, each agent uses its own position and velocity information in the consensus algorithm. In the second scenario, agents need only position information for the consensus algorithm. For both the approaches, each agent calculates a virtual estimate of target’s velocity from the received information and exchanges the estimate with its neighbors. The control algorithms are developed using heterogeneous communication networks to satisfy a communication bandwidth constraint. Three different communication networks are used to circulate position information, virtual estimates, and its time derivatives. The graphs representing communication networks are undirected and connected. Further, it is considered that there is at least one UAV (agent) receiving position, velocity, and acceleration information of the target. The agent receiving target’s position need not be the same agent which receives velocity and/or acceleration information of the maneuvering target. However, the target does not receive any information from any agent. Using Barbalat’s lemma, the stability of the target-centric formation of a group of UAVs is analyzed. The performance of the proposed laws are illustrated through numerical simulations.     

Intelligent Robust Tracking Controls for Holonomic and Nonholonomic Mechanical Systems Using Only Position Measurements

Intelligent robust tracking control designs are proposed in this paper for both uncertain holonomic and nonholonomic mechanical systems. A unified and systematic procedure, that is based on an adaptive fuzzy (or neural network) system and a linear observer, is employed to derive the controllers for these two constrained mechanical systems. Adaptive fuzzy-based (or neural network-based) position feedback tracking controllers can be constructed such that all the states and signals of the closed-loop systems are bounded and the tracking error locally converges to a small region around zero. Only position measurements are required for feedback. The implementation of the fuzzy (or neural network) basis functions depends only on the desired reference information and so once a set of desired trajectories is given, the required basis functions can be explicitly preassigned. Consequently, the intelligent robust position feedback tracking controllers developed here possess the properties of computational simplicity and easy implementation. Finally, simulation examples are presented to demonstrate the effectiveness of the proposed control algorithms.     

基于SO(3)的多四旋翼无人机编队协同控制

针对多四旋翼无人机系统的编队飞行问题,提出了基于特殊正交群SO(3)的协同控制设计方法.在给出编队空间队形和通信拓扑描述后,建立了多四旋翼无人机系统SO(3)控制模型.由于SO(3)与传统俯仰/偏航/滚转三通道模型具有不同的结构,文中进一步研究了SO(3)中无人机之间相对误差的表示方法,设计了适用于多飞行器的SO(3)控制器实现对编队和姿态的协同控制.推力控制器用于调节无人机的位置与速度,并在此基础上构造旋转矩阵形式的姿态协同指令.文中相应设计了SO(3)姿态控制器用于实现指令跟踪,最后从理论上对协同稳定性进行了分析.提出的控制方法能够使得多四旋翼无人机形成期望的队形,并且保持姿态一致进行稳定飞行.仿真结果验证了本文方法的有效性.     

Distributed adaptive output consensus control of second-order systems containing unknown non-linear control gains

In this paper, we address the output consensus problem of tracking a desired trajectory for a group of second-order agents on a directed graph with a fixed topology. Each agent is modelled by a second-order non-linear system with unknown non-linear dynamics and unknown non-linear control gains. Only a subset of the agents is given access to the desired trajectory information directly. A distributed adaptive consensus protocol driving all agents to track the desired trajectory is presented using the backstepping technique and approximation technique of Fourier series (FSs). The FS structure is taken not only for tracking the non-linear dynamics but also the unknown portion in the controller design procedure, which can avoid virtual controllers containing the uncertain terms. Stability analysis and parameter convergence of the proposed algorithm are conducted based on the Lyapunov theory and the algebraic graph theory. It is also demonstrated that arbitrary small tracking errors can be achieved by appropriately choosing design parameters. Though the proposed work is applicable for second-order non-linear systems containing unknown non-linear control gains, the proposed controller design can be easily extended to higher-order non-linear systems containing unknown non-linear control gains. Simulation results show the effectiveness of the proposed schemes.     

Adaptive force and position control of manipulators

The article presents simple methods for the design of adaptive force and position controllers for robot manipulators within the hybrid control architecture. The force controller is composed of an adaptive PID feedback controller, an auxiliary signal, and a force feedforward term, and achieves tracking of desired force setpoints in the constraint directions. The position controller consists of adaptive feedback and feedforward controllers as well as an auxiliary signal, and accomplishes tracking of desired position trajectories in the free directions. The controllers are capable of compensating for dynamic cross-couplings that exist between the position and force control loops in the hybrid control architecture. The adaptive controllers do not require knowledge of the complex dynamic model or parameter values of the manipulator or the environment. The proposed control schemes are computationally fast and suitable for implementation in online control with high sampling rates. The methods are applied to a two-link manipulator for simultaneous force and position control. Simulation results confirm that the adaptive controllers perform remarkably well under different conditions.