Time-varying formation tracking of multiple manipulators via distributed finite-time control

Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the time-varying formation tracking for multiple manipulator systems (MMSs) under fixed and switching directed graphs with a dynamic leader, whose acceleration cannot change too fast. An explicit mathematical formulation of time-varying formation is developed based on the related practical applications. A class of extended inverse dynamics control algorithms combining with distributed sliding-mode estimators are developed to address the aforementioned problem. By invoking finite-time stability arguments, several novel criteria (including sufficient criteria, necessary and sufficient criteria) for global finite-time stability of MMSs are established. Finally, numerical experiments are presented to verify the effectiveness of the theoretical results

Robust time-varying formation design for multi-agent systems with disturbances: Extended-state-observer method

Robust time-varying formation design problems for second-order multi-agent systems subjected to external disturbances are investigated. Firstly, by constructing an extended state observer, the disturbance compensation is estimated, which is a critical term in the proposed robust time-varying formation control protocol. Then, an explicit expression of the formation center function is determined and impacts of disturbance compensations on the formation center function are presented. With the formation feasibility conditions, robust time-varying formation design criteria are derived to determine the gain matrix of the formation control protocol by utilizing the algebraic Riccati equation technique. Furthermore, the tracking performance and the robustness property of multi-agent systems are analyzed. Finally, the numerical simulation is provided to illustrate the effectiveness of theoretical results.Comment: 14 pages, 5 figure

Distributed average tracking for multiple reference signals with general linear dynamics

This technical note studies the distributed average tracking problem for multiple time-varying signals with general linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In distributed fashion, a pair of continuous algorithms with, respectively, static and adaptive coupling strengths are designed. Based on the boundary layer concept, the proposed continuous algorithm with static coupling strengths can asymptotically track the average of the multiple reference signals without chattering phenomenon. Furthermore, for the case of algorithms with adaptive coupling strengths, the average tracking errors are uniformly ultimately bounded and exponentially converge to a small adjustable bounded set. Finally, a simulation example is presented to show the validity of the theoretical results

Task-space coordinated tracking of multiple heterogeneous manipulators via controller-estimator approaches

This paper studies the task-space coordinated tracking of a time-varying leader for multiple heterogeneous manipulators (MHMs), containing redundant manipulators and nonredundant ones. Different from the traditional coordinated control, distributed controller-estimator algorithms (DCEA), which consist of local algorithms and networked algorithms, are developed for MHMs with parametric uncertainties and input disturbances. By invoking differential inclusions, nonsmooth analysis, and input-to-state stability, some conditions (including sufficient conditions, necessary and sufficient conditions) on the asymptotic stability of the task-space tracking errors and the subtask errors are developed. Simulation results are given to show the effectiveness of the presented DCEA.Comment: 17 pages, 7 figures, Journal of the Franklin Institut

Fully Distributed Flocking with a Moving Leader for Lagrange Networks with Parametric Uncertainties

This paper addresses the leader-follower flocking problem with a moving leader for networked Lagrange systems with parametric uncertainties under a proximity graph. Here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching. In the proximity graph, the neighbor relationship is defined according to the relative distance between each pair of agents. Each follower is able to obtain information from only the neighbors in its proximity, involving only local interaction. We consider two cases: i) the leader moves with a constant velocity, and ii) the leader moves with a varying velocity. In the first case, a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower. In the second case, a distributed discontinuous adaptive control algorithm and estimator are proposed. Then the algorithm is extended to be fully distributed with the introduction of gain adaptation laws. In all proposed algorithms, only one-hop neighbors' information (e.g., the relative position and velocity measurements between the neighbors and the absolute position and velocity measurements) is required, and flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly. Numerical simulations are presented to illustrate the theoretical results

Coordination of Multi-Agent Systems under Switching Topologies via Disturbance Observer Based Approach

In this paper, a leader-following coordination problem of heterogeneous multi-agent systems is considered under switching topologies where each agent is subject to some local (unbounded) disturbances. While these unknown disturbances may disrupt the performance of agents, a disturbance observer based approach is employed to estimate and reject them. Varying communication topologies are also taken into consideration, and their byproduct difficulties are overcome by using common Lyapunov function techniques. According to the available information in difference cases, two disturbance observer based protocols are proposed to solve this problem. Their effectiveness is verified by simulations.Comment: 12 pages, 4 figures, 2 table

On the Synchronization of Second-Order Nonlinear Systems with Communication Constraints

This paper studies the synchronization problem of second-order nonlinear multi-agent systems with intermittent communication in the presence of irregular communication delays and possible information loss. The control objective is to steer all systems' positions to a common position with a prescribed desired velocity available to only some leaders. Based on the small-gain framework, we propose a synchronization scheme relying on an intermittent information exchange protocol in the presence of time delays and possible packet dropout. We show that our control objectives are achieved with a simple selection of the control gains provided that the directed graph, describing the interconnection between all systems (or agents), contains a spanning tree. The example of Euler-Lagrange systems is considered to illustrate the application and effectiveness of the proposed approach.Comment: 21 pages, 8 figures. Submitted for journal publicatio

Multi-Agent Distributed Coordination Control: Developments and Directions

In this paper, the recent developments on distributed coordination control, especially the consensus and formation control, are summarized with the graph theory playing a central role, in order to present a cohesive overview of the multi-agent distributed coordination control, together with brief reviews of some closely related issues including rendezvous/alignment, swarming/flocking and containment control.In terms of the consensus problem, the recent results on consensus for the agents with different dynamics from first-order, second-order to high-order linear and nonlinear dynamics, under different communication conditions, such as cases with/without switching communication topology and varying time-delays, are reviewed, in which the algebraic graph theory is very useful in the protocol designs, stability proofs and converging analysis. In terms of the formation control problem, after reviewing the results of the algebraic graph theory employed in the formation control, we mainly pay attention to the developments of the rigid and persistent graphs. With the notions of rigidity and persistence, the formation transformation, splitting and reconstruction can be completed, and consequently the range-based formation control laws are designed with the least required information in order to maintain a formation rigid/persistent. Afterwards, the recent results on rendezvous/alignment, swarming/flocking and containment control, which are very closely related to consensus and formation control, are briefly introduced, in order to present an integrated view of the graph theory used in the coordination control problem. Finally, towards the practical applications, some directions possibly deserving investigation in coordination control are raised as well.Comment: 28 pages, 8 figure

Observer-Based Distributed Leader-Follower Tracking Control: A New Perspective and Results

Leader-follower tracking control design has received significant attention in recent years due to its important and wide applications. Considering a multi-agent system composed of a leader and multiple followers, this paper proposes and investigates a new perspective into this problem: can we enable a follower to estimate the leader's driving input and leverage this idea to develop new observer-based tracking control approaches? With this motivation, we develop an input-observer-based leader-follower tracking control framework, which features distributed input observers that allow a follower to locally estimate the leader's input toward enhancing tracking control. This work first studies the first-order tracking problem. It then extends to the more sophisticated case of second-order tracking and considers a challenging situation when the leader's and followers' velocities are not measured. The proposed approaches exhibit interesting and useful advantages as revealed by a comparison with the literature. Convergence properties of the proposed approaches are rigorously analyzed. Simulation results further illustrate the efficacy of the proposed perspective, framework and approaches.Comment: International Journal of Control 201

Containment Control of Second-order Multi-agent Systems Under Directed Graphs and Communication Constraints

The distributed coordination problem of multi-agent systems is addressed in this paper under the assumption of intermittent communication between agents in the presence of time-varying communication delays. Specifically, we consider the containment control problem of second-order multi-agent systems with multiple dynamic leaders under a directed interconnection graph topology. Also, communication between agents is performed only at some discrete instants of time in the presence of irregular communication delays and packet dropout. First, we present distributed control algorithms for double integrator dynamics in the full and partial state feedback cases. Then, we propose a method to extend our results to second-order systems with locally Lipschitz nonlinear dynamics. In both cases, we show that the proposed approach leads to our control objectives under sufficient conditions relating the characteristics of the communication process and the control gains. We also show that our approach can be applied to solve various similar coordination problems in multi-agent systems under the same communication constraints. The effectiveness of the proposed control schemes is illustrated through some examples and numerical simulations.Comment: Modified version. Paper submitted for publicatio