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