Yongcan Cao

An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination

This paper reviews some main results and progress in distributed multi-agent coordination, focusing on papers published in major control systems and robotics journals since 2006. Distributed coordination of multiple vehicles, including unmanned aerial vehicles, unmanned ground vehicles, and unmanned underwater vehicles, has been a very active research subject studied extensively by the systems and control community. The recent results in this area are categorized into several directions, such as consensus, formation control, optimization, and estimation. After the review, a short discussion section is included to summarize the existing research and to propose several promising research directions along with some open problems that are deemed important for further investigations.

Distributed Coordinated Tracking With Reduced Interaction via a Variable Structure Approach

A distributed coordinated tracking problem is solved via a variable structure approach when there exists a dynamic virtual leader who is a neighbor of only a subset of a group of followers, all followers have only local interaction, and only partial measurements of the states of the virtual leader and the followers are available. In the context of coordinated tracking, we focus on both consensus tracking and swarm tracking algorithms. In the case of first-order kinematics, we propose a distributed consensus tracking algorithm without velocity measurements under both fixed and switching network topologies. In particular, we show that distributed consensus tracking can be achieved in finite time. The algorithm is then extended to achieve distributed swarm tracking without velocity measurements. In the case of second-order dynamics, we first propose two distributed consensus tracking algorithms without acceleration measurements when the velocity of the virtual leader is varying under, respectively, a fixed and switching network topology. In particular, we show that the proposed algorithms guarantee at least global exponential tracking. We then propose a distributed consensus tracking algorithm and a distributed swarm tracking algorithm when the velocity of the virtual leader is constant. When the velocity of the virtual leader is varying, distributed swarm tracking is solved by using a distributed estimator. For distributed consensus tracking, a mild connectivity requirement is proposed by adopting an adaptive connectivity maintenance mechanism in which the adjacency matrix is defined in a proper way. Similarly, a mild connectivity requirement is proposed for distributed swarm tracking by adopting a connectivity maintenance mechanism in which the potential function is defined in a proper way. Several simulation examples are presented as a proof of concept.

Leaderless and Leader-Following Consensus With Communication and Input Delays Under a Directed Network Topology

In this paper, time-domain (Lyapunov theorems) and frequency-domain (the Nyquist stability criterion) approaches are used to study leaderless and leader-following consensus algorithms with communication and input delays under a directed network topology. We consider both the first-order and second-order cases and present stability or boundedness conditions. Several interesting phenomena are analyzed and explained. Simulation results are presented to support the theoretical results.

Distributed Containment Control for Multiple Autonomous Vehicles With Double-Integrator Dynamics: Algorithms and Experiments

This brief studies distributed containment control for double-integrator dynamics in the presence of both stationary and dynamic leaders. In the case of stationary leaders, we propose a distributed containment control algorithm and study conditions on the network topology and the control gains to guarantee asymptotic containment control in any dimensional space. In the case of dynamic leaders, we study two cases: leaders with an identical velocity and leaders with nonidentical velocities. For the first case, we propose two distributed containment control algorithms to solve, respectively, asymptotic containment control under a switching directed network topology and finite-time containment control under a fixed directed network topology. In particular, asymptotic containment control can be achieved for any dimensional space if the network topology is fixed and for only the 1-D space if the network topology is switching. For the second case, we propose a distributed containment control algorithm under a fixed network topology where the communication patterns among the followers are undirected and derive conditions on the network topology and the control gains to guarantee asymptotic containment control for any dimensional space. Both simulation results and experimental results on a multi-robot platform are provided to validate some theoretical results.

Distributed containment control with multiple stationary or dynamic leaders in fixed and switching directed networks

In this paper, we study the problem of distributed containment control of a group of mobile autonomous agents with multiple stationary or dynamic leaders under both fixed and switching directed network topologies. First, when the leaders are stationary and all followers share an inertial coordinate frame, we present necessary and sufficient conditions on the fixed or switching directed network topology such that all followers will ultimately converge to the stationary convex hull formed by the stationary leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is fixed, we partition the (nonsymmetric) Laplacian matrix and explore its properties to derive the convergence results. When the directed network topology is switching, the commonly adopted decoupling technique based on the Kronecker product in a high-dimensional space can no longer be applied and we hence present an important coordinate transformation technique to derive the convergence results. The proposed coordinate transformation technique also has potential applications in other high-dimensional distributed control scenarios and might be used to simplify the analysis of a high-dimensional system to that of a one-dimensional system when the decoupling technique based on the Kronecker product cannot be applied. Second, when the leaders are dynamic and all followers share an inertial coordinate frame, we propose a distributed tracking control algorithm without velocity measurements. When the directed network topology is fixed, we derive conditions on the network topology and the control gain to guarantee that all followers will ultimately converge to the dynamic convex hull formed by the dynamic leaders for arbitrary initial states in a space of any finite dimension. When the directed network topology is switching, we derive conditions on the network topology and the control gain such that all followers will ultimately converge to the minimal hyperrectangle that contains the dynamic leaders and each of its hyperplanes is normal to one axis of the inertial coordinate frame in any high-dimensional space. We also show via some counterexamples that it is, in general, impossible to find distribute containment control algorithms without velocity measurements to guarantee that all followers will ultimately converge to the convex hull formed by the dynamic leaders under a switching network topology in a high-dimensional space. Simulation results are presented as a proof of concept.

Decentralized finite-time sliding mode estimators and their applications in decentralized finite-time formation tracking

In this paper, a simple but efficient framework is proposed to achieve finite-time decentralized formation tracking of multiple autonomous vehicles with the introduction of decentralized sliding mode estimators. First, we propose and study both first-order and second-order decentralized sliding mode estimators. In particular, we show that the proposed first-order decentralized sliding mode estimator can guarantee accurate position estimation in finite time and the proposed second-order decentralized sliding mode estimator can guarantee accurate position and velocity estimation in finite time. Then the decentralized sliding mode estimators are employed to achieve decentralized formation tracking of multiple autonomous vehicles. In particular, it is shown that formation tracking can be achieved for systems with both single-integrator kinematics and double-integrator dynamics in finite time. By using the decentralized sliding mode estimators, many formation tracking/flying scenarios can be easily decoupled into two subtasks, that is, decentralized sliding mode estimation and vehicle desired state tracking, without imposing a stringent condition on the information flow. Finally, several simulation results are presented as a proof of concept.

Optimal Linear-Consensus Algorithms: An LQR Perspective

Laplacian matrices play an important role in linear-consensus algorithms. This paper studies optimal linear-consensus algorithms for multivehicle systems with single-integrator dynamics in both continuous-time and discrete-time settings. We propose two global cost functions, namely, interaction-free and interaction-related cost functions. With the interaction-free cost function, we derive the optimal (nonsymmetric) Laplacian matrix by using a linear-quadratic-regulator-based method in both continuous-time and discrete-time settings. It is shown that the optimal (nonsymmetric) Laplacian matrix corresponds to a complete directed graph. In addition, we show that any symmetric Laplacian matrix is inverse optimal with respect to a properly chosen cost function. With the interaction-related cost function, we derive the optimal scaling factor for a prespecified symmetric Laplacian matrix associated with the interaction graph in both continuous-time and discrete-time settings. Illustrative examples are given as a proof of concept.

Brief paper: 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.

Distributed Coordination of Networked Fractional-Order Systems

This paper studies the distributed coordination of networked fractional-order systems over a directed interaction graph. A general fractional-order coordination model is introduced by summarizing three different cases: 1) fractional-order agent dynamics with integer-order coordination algorithms; 2) fractional-order agent dynamics with fractional-order coordination algorithms; and 3) integer-order agent dynamics with fractional-order coordination algorithms. We show sufficient conditions on the interaction graph and the fractional order such that coordination can be achieved using the general model. The coordination equilibrium is also explicitly given. In addition, we characterize the relationship between the number of agents and the fractional order to ensure coordination. Furthermore, we compare the convergence speed of coordination for fractional-order systems with that for integer-order systems. It is shown that the convergence speed of the fractional-order coordination algorithms can be improved by varying the fractional orders with time. Finally, simulation results are presented as a proof of concept.

Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction

In this article, we study two sampled-data-based discrete-time coordination algorithms for multi-vehicle systems with double-integrator dynamics under dynamic directed interaction. For both algorithms, we derive sufficient conditions on the interaction graph, the damping gain and the sampling period to guarantee coordination by using the property of infinity products of stochastic matrices. When the conditions on the damping gain and the sampling period are satisfied, the first algorithm guarantees coordination on positions with a zero final velocity if the interaction graph has a directed spanning tree jointly while the second algorithm guarantees coordination on positions with a constant final velocity if the interaction graph has a directed spanning tree at each time interval. Simulation results are presented to show the effectiveness of the theoretical results.