Avoiding the local-minimum problem in multi-agent systems with limited sensing and communication

In this paper, we consider a control problem for nonholonomic multi-agent systems in which agents and obstacles operate within a circular-shaped work area. We assume that agents only have limited sensing and communication ranges. We propose a novel control scheme using potential functions that drives agents from the initial to the goal configuration while avoiding collision with other agents, obstacles, and the boundary of the work area. The control scheme employs an avoidance strategy that ensures that the agents are never trapped at local minima that are typically encountered with most potential function-based approaches. A numerical simulation is presented to demonstrate the validity and effectiveness of the proposed control scheme.     

Formation and obstacle avoidance control for multiagent systems

This paper considers the problems of formation and obstacle avoidance for multiagent systems.The objective is to design a term of agents that can reach a desired formation while avoiding collision with obstacles.To reduce the amount of information interaction between agents and target,we adopt the leader-follower formation strategy.By using the receding horizon control (RHC),an optimal problem is formulated in terms of cost minimization under constraints.Information on obstacles is incorporated online as sensed in a limited sensing range.The communication requirements between agents are that the followers should obtain the previous optimal control trajectory of the leader to each update time.The stability is guaranteed by adding a terminal-state penalty to the cost function and a terminal-state region to optimal problem.Finally,simulation studies are provided to verify the effectiveness of the proposed approach.     

Optimal Control of Underactuated Nonholonomic Mechanical Systems

In this paper, we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, underactuated mechanical systems. In particular, we aim to minimize the norm-squared of the control input to move the system from an initial to a terminal state. We consider systems evolving on general manifolds. The class of nonholonomic systems we study in this paper includes, in particular, wheeled-type vehicles, which are important for many robotic locomotion systems. The two special aspects of this optimal control problem are the nonholonomic constraints and underactuation. Nonholonomic constraints restrict the evolution of the system to a distribution on the manifold. The nonholonomic connection is used to express the constrained equations of motion. Many robotic systems are underactuated since control inputs are usually applied through the robot's internal configuration space only. While we do not consider symmetries with respect to group actions in this paper, the fact that the system is underactuated is taken into account in our problem formulation. This allows one to compute reaction forces due to any inputs applied in directions orthogonal to the constraint distribution. We illustrate our ideas by considering a simple example on a three-dimensional manifold, including obstacle avoidance using the method of navigation functions.     

A geometric approach to target convergence and obstacle avoidance of a nonstandard tractor‐trailer robot

In this article, a solution to target convergence and obstacle avoidance problem of an underactuated nonstandard n‐trailer robot is proposed. With a new geometric approach, we propose autonomous velocity and steering angle controllers for the car‐like tractor robot such that the tractor‐trailer system moves from an initial position to a designated target. The proposed method simultaneously takes into account the dynamics constraints of the system and also ensures that the robot avoids any fixed obstacles on its way to the target. We also generalize the results to control the motion of the nonstandard n‐trailer system with an arbitrary number of passive trailers, a mathematically challenging nonlinear underactuated system, given that the angular velocity of a trailer is dependent on the angular velocity of the preceding trailer. The effectiveness of the new geometric approach and the stabilizing control inputs is verified using computer simulations.     

一类欠驱动机械系统的动态及其稳定控制

Abstract The control of underactuated mechanical systems is very complex for the loss of its control inputs. The model of underactuated mechanical systems in a potential field is built with Lagrangian method and its structural properties are analyzed in detail. A stable control approach is proposed for the class of underactuated mechanical systems. This approach is applied to an unde ractuated double-pendulum-type overhead crane and the simulation results illustrate the correctness of dynamics analysis and validity of the proposed control algorithm.     

Safe Autonomous Agent Formation Operations Via Obstacle Collision Avoidance

In this paper, we consider the problem of flocking and shape‐orientation control of multi‐agent systems with inter‐agent and obstacle collision avoidance. We first consider the problem of forcing a set of autonomous agents to form a desired formation shape and orientation while avoiding inter‐agent collision and collision with convex obstacles, and following a trajectory known to only one of the agents, namely the leader of the formation. Then we build upon the solution given to this problem and solve the problem of guaranteeing obstacle collision avoidance by changing the size and the orientation of the formation. Changing the size and the orientation of the formation is helpful when the agents want to go through a narrow passage while the existing size or orientation of the formation does not allow this. We also propose collision avoidance algorithms that temporarily change the shape of the formation to avoid collision with stationary or moving nonconvex obstacles. Simulation results are presented to show the performance of the proposed control laws.     

Interconnection and damping assignment passivity‐based control of a class of underactuated mechanical systems with dynamic friction

This paper considers the extension of the interconnection and damping assignment passivity‐based control methodology for a class of underactuated mechanical systems with dynamic friction. We present a new damping assignment approach to compensate friction by means of a nonlinear observer. Friction at the actuated joints is assumed to be captured by a bristle deflection model: the Dahl model. Based on the Lyapunov direct method we show that, under some conditions, the overall closed‐loop system is stable and, by invoking the theorem of Barbashin–Krasovskii, we arrive to asymptotic stability conditions. Experiments with an underactuated mechanical system, the Furuta pendulum, show the effectiveness of the proposed scheme when friction is compensated. Copyright © 2010 John Wiley & Sons, Ltd.     

Control of mechanical systems on Lie groups based on vertically transverse functions

The transverse function approach to control provides a unified setting to deal with practical stabilization and tracking of arbitrary trajectories for controllable driftless systems. Controllers derived from that approach offer advantages over those based on more classical techniques for control of nonholonomic systems. Nevertheless, its extension to more general classes, such as critical underactuated mechanical systems, is not immediate. The present paper explores a possible extension by developing a framework that allows one to cast point stabilization problems for (left-invariant) second-order systems on Lie groups, including simple mechanical systems. The approach is based on “vertical transversality,” a property exhibited by derivatives of transverse functions. In this paper, we lay out the theoretical foundations of our approach and present an example to illustrate some of its features. This work was partially funded by CONACYT under grants No. 66910 and 52914.     

Matching, linear systems, and the ball and beam

A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. In this paper, we describe one matching condition and an approach for finding all control laws that fit the condition. After an analysis of the resulting control laws for linear systems, we present the results from an experiment on a nonlinear ball and beam system.     

Dynamic Frontier-Led Swarming: Multi-Robot Repeated Coverage in Dynamic Environments

A common assumption of coverage path planning research is a static environment.Such environments require only a single visit to each area to achieve coverage.However,some real-world environments are characterised by the presence of unexpected,dynamic obstacles.They require areas to be revisited periodically to maintain an accurate coverage map,as well as reactive obstacle avoidance.This paper proposes a novel swarmbased control algorithm for multi-robot exploration and repeated coverage in envir...     

Finite-time coordination in multiagent systems using sliding mode control approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of agents described by fully actuated Euler–Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time. The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network. In addition, we discuss the case of switching communication topologies in multiagent systems. Finally, we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents.     

On simultaneous control of the energy and actuated variables of underactuated mechanical systems – example of the acrobot with counterweight

The energy-based control approach aiming to control both the total mechanical energy and actuated variables of underactuated mechanical systems has generated renewed interest in recent years. Different from the reports of successful applications of this approach, we investigate whether there exists an underactuated mechanical system for which we fail to control both the total mechanical energy and actuated variable(s) to some given desired values by studying a CWA (Counter-Weighted Acrobot), which is a modified Acrobot with its first link having a counterweight and only its second link being actuated. By analyzing globally the solution of the closed-loop system consisting of the CWA and the controller designed via the energy-based control approach, we show that unless the CWA is linearly controllable at the up–up equilibrium, where links 1 and 2 are in the upright position, the controller fails to achieve the goal of controlling the energy to the potential energy at the equilibrium and controlling the actuated joint variable to zero. We also provide corresponding results for the up–down, down–up, and down–down equilibriums of the CWA, where up and down denote that the link is in the upright and downward positions, respectively. We present numerical simulation results to validate the theoretical results.     

基于能量整形方案实现具有通讯时滞欠驱动Euler-Lagrange网络的一致性

本文主要基于能量整形方案研究具有通讯时滞网络化欠驱动Euler-Lagrange (EL)系统的一致性问题,通过利用阻尼注入和互连分配的无源控制(PBC)技术,在有向连通网络拓扑下提出了一个简单的分布式协议,来实现在无引导者和有引导者-跟随者两种情形下欠驱动EL网络的一致性. 本文提出的一致性能量整形方案的主要特点是有机地整合了系统欠驱动和驱动部分以及控制器三部分能量作为整个系统的总能量,这个总能量被利用作为一个合适的Lyapunov函数,它能够充分确保网络化欠驱动EL系统达到所期望的分布式一致性. 最后,通过由欠驱动EL网络所描述柔性关节机械臂系统的数值模拟,来分析通讯时滞对一致性的效应和验证所提出控制算法的正确性.     

A Stable Switched-System Approach to Collision-Free Wheeled Mobile Robot Navigation

This paper presents a novel switched-system approach for obstacle avoidance by mobile robots. This approach does not suffer from common drawbacks of existing methods, such as needing prior knowledge of obstacles, or local minima or chattering in control laws. We define an attractive and an avoidance vector in obstacle-free and obstacle-avoidance regions, respectively. Next, we define an unified velocity vector, which represents either the attractive vector or the avoidance vector, and drives the robot away from the obstacle and ultimately towards the goal. The avoidance vector differs from the repulsive vector commonly used in potential field approaches, rather it is defined always perpendicular to such a repulsive vector and projects positively onto the attractive vector. The unified velocity vector enables the use of a common Lyapunov function in analyzing the stability of the system under arbitrary switching. Novel switching rules are proposed for obstacles that can be well bounded by a circle in the local subset of SE(2). To better handle large, non-circular obstacles, a separate switching signal is proposed. Through the choice of switching rule, we investigate the chattering problem that can hinder some switching controllers. We present two control laws, one with bounded inputs and one with no bounds on inputs. We prove both control schemes are asymptotically stable and guide the robot to the goal while avoiding obstacles. To verify the effectiveness of the proposed approach, as well as compare the control laws and switching rules, several simulations and experiments have been conducted.     

Novel potential-function-based control scheme for non-holonomic multi-agent systems to prevent the local minimum problem

In this paper, we consider a control problem of a non-holonomic multi-agent system. We assume that agents and obstacles are in a circular shaped work area. We propose a novel potential-function-based control scheme that drives agents from the initial to the goal configuration while avoiding collision with other agents, obstacles, and the boundary of the work area. The control scheme enables agents to avoid being trapped at local minima by forcing them to exit from the regions that may contain local minima. A numerical simulation is presented to demonstrate the validity of the proposed control scheme.     

多智能体系统输入约束下的一致性与轨迹规划研究

针对多智能体系统提出了一种分布式预测控制方法. 首先, 研究了有输入约束下的一致性问题. 其次, 对环境中有障碍物的多智能体轨迹规划进行了研究, 其中只有当障碍物进入智能体有限感知区域内时, 障碍物状态信息才能被获取. 基于预测控制方法, 设计了一种分布式控制算法来解决上面两个问题. 构造一个与每个智能体动力学相交互的代价函数, 设计相应最优控制问题, 从而实现优化控制算法. 智能体间交互信息是其邻居在上一时刻的最优控制状态. 系统稳定性可以通过构造代价函数中的一个终点状态控制器与最优控制问题中的一个终点状态区域来保证. 仿真研究表明所提方法的有效性.     

A Continuous Leader-following Consensus Control Strategy for a Class of Uncertain Multi-agent Systems

In this paper, we study the robust leader-following consensus problem for a class of multi-agent systems with unknown nonlinear dynamics and unknown but bounded disturbances. The control input of the leader agent is nonzero and not available to any follower agent. We first consider a class of high order chain integrator-type multi-agent systems. By employing the robust integral of the sign of the error technique, a continuous distributed control law is constructed using local information obtained from neighboring agents. Using Lyapunov analysis theory, we show that under a connected undirected information communication topology, the proposed protocol achieves semiglobal leader-following consensus. We then extend the approach to a class of more general uncertain multiagent systems. A numerical example is given to verify our proposed protocol.      

Control of cooperative manipulator-endowed systems under high-level tasks and uncertain dynamics

This paper considers the problem of distributed motion- and task-planning of multi-agent and multi-agent-object systems under temporal-logic-based tasks and uncertain dynamics. We focus on manipulator-endowed robotic agents that can interact with their surroundings. We present first continuous control algorithms for multi-agent navigation and cooperative object manipulation that exhibit the following properties. First, they are distributed in the sense that each agent calculates its own control signal from local interaction with the other agents and the environment. Second, they guarantee safety properties in terms of inter-agent collision avoidance and obstacle avoidance. Third, they adapt on-the-fly to dynamic uncertainties and are robust to exogenous disturbances. The aforementioned algorithms allow the abstraction of the underlying system to a finite-state representation. Inspired by formal-verification techniques, we use such a representation to derive plans for the agents that satisfy the given temporal-logic tasks. Various simulation results and hardware experiments verify the efficiency of the proposed algorithms.     

Power-shaping control of reaction systems: The CSTR case

Power-shaping control is a recent approach for the control of nonlinear systems based on the physics of the dynamical system. It rests on the formulation of the dynamics in the Brayton-Moser form. One of the main obstacles for using the power-shaping approach is to write the dynamics in the required form, since a partial differential equation system submitted to sign constraints has to be solved. This work comes within the framework of control design approaches that could possibly generate a closer link between the notions of energy that are specific to reaction systems as derived from thermodynamics concepts, and the dynamic system stability theory. The objective of this paper is to address the design of power-shaping control to reaction systems, and more particularly the step of solving the partial differential equation system. In order to illustrate the approach, we have selected the classical yet complex continuous stirred tank reactor (CSTR) as a case study. We show how using the power-shaping approach leads to a global Lyapunov function for the unforced exothermic CSTR. This Lyapunov function is then reshaped by means of a controller in order to stabilize the process at a desired temperature.     

Computing differential invariants of hybrid systems as fixedpoints

We introduce a fixedpoint algorithm for verifying safety properties of hybrid systems with differential equations whose right-hand sides are polynomials in the state variables. In order to verify nontrivial systems without solving their differential equations and without numerical errors, we use a continuous generalization of induction, for which our algorithm computes the required differential invariants. As a means for combining local differential invariants into global system invariants in a sound way, our fixedpoint algorithm works with a compositional verification logic for hybrid systems. With this compositional approach we exploit locality in system designs. To improve the verification power, we further introduce a saturation procedure that refines the system dynamics successively with differential invariants until safety becomes provable. By complementing our symbolic verification algorithm with a robust version of numerical falsification, we obtain a fast and sound verification procedure. We verify roundabout maneuvers in air traffic management and collision avoidance in train control and car control.