Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology

This paper investigates two kinds of different consensus strategies for multi-vehicle systems with a time-varying reference velocity under directed communication topology, where the systems are modeled by double-integrator dynamics. For the fixed communication topology case, we provide a necessary and sufficient condition for all the vehicles with reference velocity to reach consensus by the use of a new graphic methodology. We then extend this method to deal with the general case, that is, both the communication topologies and weighting factors are dynamically changing. In particular, it is shown that all the vehicles can reach consensus even though the dynamically changing interaction topology may not have a globally reachable node.     

Distributed output feedback stationary consensus of multi-vehicle systems in unknown environments

In the traditional distributed consensus of multi-vehicle systems, vehicles agree on velocity and position using limited information exchange in their local neighborhoods. Recently, distributed leaderless stationary consensus has been proposed in which vehicles agree on a position and come to a stop. The proposed stationary consensus schemes are based on all vehicles'' access to their own absolute velocity measurements, and they do not guarantee this collective behavior in the presence of disturbances that persistently excite vehicles'' dynamics. On the other hand, traditional distributed disturbance rejection leaderless consensus algorithms may result in an uncontrolled increase in the speed of multi-vehicle system. In this paper, we propose a dynamic relative-output feedback leaderless stationary algorithm in which only a few vehicles have access to their absolute measurements. We systematically design the distributed algorithm by transforming this problem into a static feedback robust control design challenge for the low-order modified model of vehicles with fictitious modeling uncertainties. We further propose dynamic leader-follower stationary consensus algorithms for multi-vehicle systems with a static leader, and find closed-form solutions for the consensus gains based on design matrices and communication graph topology. Finally, we verify the feasibility of these ideas through simulation studies.     

On Consensus Algorithms for Double-Integrator Dynamics

This note considers consensus algorithms for double-integrator dynamics. We propose and analyze consensus algorithms for double-integrator dynamics in four cases: 1) with a bounded control input, 2) without relative velocity measurements, 3) with a group reference velocity available to each team member, and 4) with a bounded control input when a group reference state is available to only a subset of the team. We show that consensus is reached asymptotically for the first two cases if the undirected interaction graph is connected. We further show that consensus is reached asymptotically for the third case if the directed interaction graph has a directed spanning tree and the gain for velocity matching with the group reference velocity is above a certain bound. We also show that consensus is reached asymptotically for the fourth case if and only if the group reference state flows directly or indirectly to all of the vehicles in the team.      

Distributed discrete-time coordinated tracking with a time-varying reference state and limited communication

This paper studies a distributed discrete-time coordinated tracking problem where a team of vehicles communicating with their local neighbors at discrete-time instants tracks a time-varying reference state available to only a subset of the team members. We propose a PD-like discrete-time consensus algorithm to address the problem under a fixed communication graph. We then study the condition on the communication graph, the sampling period, and the control gain to ensure stability and give the quantitative bound of the tracking errors. It is shown that the ultimate bound of the tracking errors is proportional to the sampling period. The benefit of the proposed PD-like discrete-time consensus algorithm is also demonstrated through comparison with an existing P-like discrete-time consensus algorithm. Simulation results are presented as a proof of concept.     

Stabilization of sets with application to multi-vehicle coordinated motion

In this paper, we develop stability and control design framework for time-varying and time-invariant sets of nonlinear dynamical systems using vector Lyapunov functions. Several Lyapunov functions arise naturally in multi-agent systems, where each agent can be associated with a generalized energy function which further becomes a component of a vector Lyapunov function. We apply the developed control framework to the problem of multi-vehicle coordinated motion to design distributed controllers for individual vehicles moving in a specified formation. The main idea of our approach is that a moving formation of vehicles can be characterized by a time-varying set in the state space, and hence, the problem of distributed control design for multi-vehicle coordinated motion is equivalent to the design of stabilizing controllers for time-varying sets of nonlinear dynamical systems. The control framework is shown to ensure global exponential stabilization of multi-vehicle formations. Finally, we implement the feedback stabilizing controllers for time-invariant sets to achieve global exponential stabilization of static formations of multiple vehicles.     

Decentralized spatial partitioning algorithms for multi-vehicle systems based on the minimum control effort metric

We consider the problem of characterizing a spatial partition of the position space of a team of vehicles with linear time-varying kinematics. The generalized metric that determines the proximity relations between the vehicles and an arbitrary target point in the partition space is the minimum control effort required for each vehicle to reach the latter point with zero miss distance and exactly zero velocity at a prescribed final time. We show that the solution to the generalized Voronoi partitioning problem can be associated with a special class of spatial partitions known as affine diagrams. Because the combinatorial complexity of the affine diagrams is comparable to the one of the standard Voronoi diagrams, their computation does not pose a significant challenge in applications of multi-vehicle systems. Subsequently, we propose an algorithm for the computation of the spatial partition, which is decentralized in the sense that each vehicle can compute an approximation of its own cell independently from the other vehicles from the same team without utilizing a common spatial mesh. Numerical simulations that illustrate the theoretical developments are also presented.     

Leader-following consensus of single-integrator multi-agent systems under noisy and delayed communication

This paper proposes a leader-following consensus control for continuous-time single-integrator multi-agent systems with multiplicative measurement noises and time-delays under directed fixed topologies. Each agent in the team receives imprecise information states corrupted by noises from its neighbours and from the leader; these noises are depending on the agents’ relative states information. Moreover, the information states received are also delayed by constant or time-varying delays. An analysis framework based on graph theory and stochastic tools is followed to derive conditions under which the tracking consensus of a constant reference is achieved in mean square. The effectiveness of the proposed algorithms is proved through some simulation examples.     

A decomposition approach to multi-vehicle cooperative control

We use a decomposition approach to generate cooperative strategies for a class of multi-vehicle control problems. By introducing a set of tasks to be completed by the team of vehicles and a task execution method for each vehicle, we decompose the problem into a combinatorial component and a continuous component. The continuous component of the problem is captured by task execution, and the combinatorial component is captured by task assignment. In this paper, we present a solver for task assignment that generates near-optimal assignments quickly and can be used in real-time applications. To motivate our methods, we apply them to an adversarial game between two teams of vehicles. One team is governed by simple rules and the other by our algorithms. In our study of this game we found phase transitions, showing that the task assignment problem is most difficult to solve when the capabilities of the adversaries are comparable. Finally, we utilize our algorithms in a hierarchical model predictive control architecture with a variable replanning rate at each level to provide feedback in dynamically changing and uncertain environments.     

Robust discrete time dynamic average consensus

This paper deals with the problem of average consensus of a set of time-varying reference signals in a distributed manner. We propose a new class of discrete time algorithms that are able to track the average of the signals with an arbitrarily small steady-state error and with robustness to initialization errors. We provide bounds on the maximum step size allowed to ensure convergence to the consensus with error below the desired one. In addition, for certain classes of reference inputs, the proposed algorithms allow arbitrarily large step size, an important issue in real networks, where there are constraints in the communication rate between the nodes. The robustness to initialization errors is achieved by introducing a time-varying sequence of damping factors that mitigates past errors. Convergence properties are shown by the decomposition of the algorithms into sequences of static consensus processes. Finally, simulation results corroborate the theoretical contributions of the paper.     

Incremental computation of time-varying query expressions

We present and analyze algorithms for the incremental computation of time-varying queries in which selection predicates refer to the state of a clock. Such queries occur naturally in many situations where temporal data are processed. Incremental techniques for query computation have proven to be more efficient than other techniques in many situations. However, all existing incremental techniques for query computation assume that old query results remain valid if no intermediate changes are made to the underlying database. Unfortunately, this assumption does not hold for time-varying queries whose results may change just because time passes. In order to solve this problem, we introduce the notion of a superview which contains all current tuples that will eventually satisfy the selection predicate of a time-varying selection. Based on the notion of superview, we develop efficient algorithms for the incremental computation of time-varying selections. Our algorithms, combined with existing incremental algorithms, allow complex time-varying queries to benefit from the proven efficiency of incremental techniques. It is important to notice that without our algorithms, the existing algorithms for incremental computation would be useless for any time-varying query expression     

采用一致性算法与虚拟结构的多自主水下航行器编队控制

采用一致性算法与虚拟结构法研究了多自主水下航行器(AUV)小尺度编队控制问题.首先针对各自主水下航行器拥有不同虚拟领航者信息(参考信息)的情况,通过对各AUV拥有的不一致参考信息进行一致性协商而达到状态一致.其次,基于虚拟结构思想采用坐标变换将各AUV相对于虚拟领航者的相对位置转换为各自的期望位置,并设计了一种有限时间跟踪控制律以确保各AUV能在有限时间内跟踪上其期望轨迹,从而实现了多AUV的小尺度有限时间编队控制.最后仿真实验验证了控制策略的有效性.     

A Cooperative receding horizon controller for multivehicle uncertain environments

We consider a setting where multiple vehicles form a team cooperating to visit multiple target points and collect rewards associated with them. The team objective is to maximize the total reward accumulated over a given time interval. Complicating factors include uncertainties regarding the locations of target points and the effectiveness of collecting rewards, differences among vehicle capabilities, and the fact that rewards are time-varying. We propose a receding horizon (RH) controller suitable for dynamic and uncertain environments, where combinatorially complex assignment algorithms are infeasible. The control scheme dynamically determines vehicle trajectories by solving a sequence of optimization problems over a planning horizon and executing them over a shorter action horizon. This centralized scheme can generate stationary trajectories in the sense that they guide vehicles to target points, even though the controller is not explicitly designed to perform any discrete point assignments. This paper establishes conditions under which this stationarity property holds in settings that are analytically tractable, quantifies the cooperative properties of the controller, and includes a number of illustrative simulation examples.     

Coordination of networked systems on digraphs with multiple leaders via pinning control

It is well known that achieving consensus among a group of multi-vehicle systems by local distributed control is feasible if and only if all nodes in the communication digraph are reachable from a single (root) node. In this article, we take into account a more general case that the communication digraph of the networked multi-vehicle systems is weakly connected and has two or more zero-in-degree and strongly connected subgraphs, i.e. there are two or more leader groups. Based on the pinning control strategy, the feasibility problem of achieving second-order controlled consensus is studied. At first, a necessary and sufficient condition is given when the topology is fixed. Then the method to design the controller and the rule to choose the pinned vehicles are discussed. The proposed approach allows us to extend several existing results for undirected graphs to directed balanced graphs. A sufficient condition is proposed in the case where the coupling topology is variable. As an illustrative example, a second-order controlled consensus scheme is applied to coordinate the movement of networked multiple mobile robots.     

基于多车辆集群的多编队一致性协议

针对车道减少路段下的车辆通行问题,提出了一个基于多车辆集群的多编队横向和纵向一致性协议.该协议既保证集群内领导车、跟随车状态的一致性,又保证集群间领导车状态的一致性,使得集群所有车辆能够通过车道减少路口.利用Routh稳定理论和Lyapunov方法,对控制协议进行一致性和稳定性分析.仿真实验结果验证了所提横向和纵向协议能够使得多车辆集群收敛一致,并且在满足不同车辆换道比例的情况下能够提高道路吞吐量、减少总通行时间.     

Experimental validation of collective circular motion for nonholonomic multi-vehicle systems

This paper presents the experimental validation of a recently proposed decentralized control law, for the collective circular motion of a team of nonholonomic vehicles about a virtual reference beacon. The considered control strategy ensures global asymptotic stability in the single-vehicle case and local asymptotic stability in the multi-vehicle scenario. The main contribution of this work is to evaluate the performance of the proposed algorithm in the presence of a number of uncertainty sources naturally arising in a real-world environment. Both static and moving reference beacons are considered, in a low-cost experimental framework based on the LEGO MINDSTORMS technology. The adopted setup features good scalability and is versatile enough to be adopted for the evaluation of different control strategies. At the same time, it represents a challenging testbed, exhibiting several issues that have to be faced in real-world applications.     

Editorial of special issue on unmanned aerial vehicles (UAVs)

UAVs have witnessed unprecedented levels of growth during the last decade. Projections and predictions suggest that during the next 5-10 years growth will continue to rapidly increase, while the spectrum of UAV utilization will be dominated by civil and public domain applications, ranging from search and rescue, emergency response, disaster management, infrastructure monitoring and protection, precision agriculture, surveillance and reconnaissance, cartography, etc. This special issue on UAVs consists of six invited and peer reviewed papers. The main focus of the issue is on multi-UAV teams, a research area that has attracted attention due to the fact that a team of unmanned vehicles may accomplish, collectively, tasks that may be difficult or impossible by a single UAV to complete. The first four papers focus on: Flocking control of a fleet of UAVs; distributed output feedback stationary consensus of multi-vehicle systems in unknown environments; consensus controller for multi-UAV navigation; and ranging-aided relative navigation of multi-platforms. Collectively, these four papers offer insight to the state of the art in this important topic. The fifth paper on nonlinear robust control of a quadrotor helicopter with finite time convergence addresses challenges related to UAV navigation/control, while the last paper on experimental evaluation of a real-time GPU-based pose estimation system for autonomous landing of rotary wing UAVs introduces a comprehensive methodology that is suitable for real-time autonomous takeoff and landing from stationary and moving ground platforms.     

Collective circular motion of multi-vehicle systems

This paper addresses a collective motion problem for a multi-agent system composed of nonholonomic vehicles. The aim of the vehicles is to achieve circular motion around a virtual reference beacon. A control law is proposed, which guarantees global asymptotic stability of the circular motion with a prescribed direction of rotation, in the case of a single vehicle. Equilibrium configurations of the multi-vehicle system are studied and sufficient conditions for their local stability are given, in terms of the control law design parameters. Practical issues related to sensory limitations are taken into account. The transient behavior of the multi-vehicle system is analyzed via numerical simulations.     

Collective Motion From Consensus With Cartesian Coordinate Coupling

Collective motions including rendezvous, circular patterns, and logarithmic spiral patterns can be achieved by introducing Cartesian coordinate coupling to existing consensus algorithms. We study the collective motions of a team of vehicles in 3-D by introducing a rotation matrix to an existing consensus algorithm for double-integrator dynamics. It is shown that the network topology, the damping gain, and the value of the Euler angle all affect the resulting collective motions. We show that when the nonsymmetric Laplacian matrix has certain properties, the damping gain is above a certain bound, and the Euler angle is below, equal, or above a critical value, the vehicles will eventually rendezvous, move on circular orbits, or follow logarithmic spiral curves lying on a plane perpendicular to the Euler axis. In particular, when the vehicles eventually move on circular orbits, the relative radii of the orbits (respectively, the relative phases of the vehicles on their orbits) are equal to the relative magnitudes (respectively, the relative phases) of the components of a right eigenvector associated with a critical eigenvalue of the nonsymmetric Laplacian matrix. Simulation results are presented to demonstrate the theoretical results.      

Optimal partitioning for multi-vehicle systems using quadratic performance criteria

We consider the problem of characterizing a generalized Voronoi diagram that is relevant to a special class of area assignment problems for multi-vehicle systems. It is assumed that the motion of each vehicle is described by a second order mechanical system with time-varying linear or affine dynamics. The proposed generalized Voronoi diagram encodes information regarding the proximity relations between the vehicles and arbitrary target points in the plane. These proximity relations are induced by an anisotropic (generalized) distance function that incorporates the vehicle dynamics. In particular, the generalized distance is taken to be the minimum control effort required for the transition of a vehicle to an arbitrary target point with a small terminal speed at a fixed final time. The space we wish to partition corresponds to the union of all the terminal positions that can be attained by each vehicle using finite control effort. Consequently, the partition space has lower dimension than the state space of each vehicle. We show that, in the general case, the solution to the proposed partitioning problem can be associated with a power Voronoi diagram generated by a set of spheres in a five-dimensional Euclidean space for the computation of which efficient techniques exist in the relevant literature.     

On the Generation of Trajectories for Multiple UAVs in Environments with Obstacles

This paper presents a methodology based on a variation of the Rapidly-exploring Random Trees (RRTs) that generates feasible trajectories for a team of autonomous aerial vehicles with holonomic constraints in environments with obstacles. Our approach uses Pythagorean Hodograph (PH) curves to connect vertices of the tree, which makes it possible to generate paths for which the main kinematic constraints of the vehicle are not violated. These paths are converted into trajectories based on feasible speed profiles of the robot. The smoothness of the acceleration profile of the vehicle is indirectly guaranteed between two vertices of the RRT tree. The proposed algorithm provides fast convergence to the final trajectory. We still utilize the properties of the RRT to avoid collisions with static, environment bound obstacles and dynamic obstacles, such as other vehicles in the multi-vehicle planning scenario. We show results for a set of small unmanned aerial vehicles in environments with different configurations.