Xiwang Dong

Time-Varying Formation Control for Unmanned Aerial Vehicles: Theories and Applications

Formation control analysis and design problems for unmanned aerial vehicle (UAV) swarm systems to achieve time-varying formations are investigated. To achieve predefined time-varying formations, formation protocols are presented for UAV swarm systems first, where the velocities of UAVs can be different when achieving formations. Then, consensus-based approaches are applied to deal with the time-varying formation control problems for UAV swarm systems. Necessary and sufficient conditions for UAV swarm systems to achieve time-varying formations are proposed. An explicit expression of the time-varying formation center function is derived. In addition, a procedure to design the protocol for UAV swarm systems to achieve time-varying formations is given. Finally, a quadrotor formation platform, which consists of five quadrotors is introduced. Theoretical results obtained in this brief are validated on the quardrotor formation platform, and outdoor experimental results are presented.

Formation Control for High-Order Linear Time-Invariant Multiagent Systems With Time Delays

Formation control problems for high-order linear time-invariant multiagent systems with time delays are investigated. First, a general time-varying formation control protocol is proposed. Then, based on consensus approaches, necessary and sufficient conditions for multiagent systems to achieve a given time-varying formation are presented. An explicit expression of the time-varying formation reference function is also given. It is shown that the motion modes of the formation reference can be specified. Furthermore, necessary and sufficient conditions for formation feasibility are proposed. An approach to expand the feasible formation set and an algorithm to design the protocol for multiagent systems to achieve time-varying formations are provided, respectively. Finally, numerical simulations are presented to demonstrate theoretical results.

Time-Varying Formation Tracking for Second-Order Multi-Agent Systems Subjected to Switching Topologies With Application to Quadrotor Formation Flying

Time-varying formation tracking analysis and design problems for second-order Multi-Agent systems with switching interaction topologies are studied, where the states of the followers form a predefined time-varying formation while tracking the state of the leader. A formation tracking protocol is constructed based on the relative information of the neighboring agents. Necessary and sufficient conditions for Multi-Agent systems with switching interaction topologies to achieve time-varying formation tracking are proposed together with the formation tracking feasibility constraint based on the graph theory. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation, and the stability of the proposed approach is proved using the common Lyapunov stability theory. The obtained results are applied to solve the target enclosing problem of a multiquadrotor unmanned aerial vehicle (UAV) system consisting of one leader (target) quadrotor UAV and three follower quadrotor UAVs. A numerical simulation and an outdoor experiment are presented to demonstrate the effectiveness of the theoretical results.

Formation-containment control for high-order linear time-invariant multi-agent systems with time delays ☆

Formation-containment control problems for high-order linear time-invariant multi-agent systems with directed interaction topologies are dealt with. Firstly, protocols are presented for leaders and followers respectively to drive the states of leaders to realize the predefined time-varying formation and propel the states of followers to converge to the convex hull formed by the states of leaders. Then formation-containment problems of multi-agent systems are transformed into asymptotic stability problems and an explicit expression of the formation reference function is derived. Sufficient conditions for multi-agent systems to achieve formation-containment are proposed. Furthermore, necessary and sufficient conditions for multi-agent systems to achieve containment and time-varying formation are presented respectively as special cases. An approach to determine the gain matrices in the protocols is given. It is shown that containment problems, formation control problems, consensus problems and consensus tracking problems can all be treated as special cases of formation-containment problems. Finally, numerical simulations are provided to demonstrate theoretical results.

Practical consensus for high-order linear time-invariant swarm systems with interaction uncertainties, time-varying delays and external disturbances

Practical consensus problems for general high-order linear time-invariant swarm systems with interaction uncertainties and time-varying external disturbances on directed graphs are investigated in this article. A dynamic consensus protocol with non-uniform time-varying delays is adopted to deal with the practical consensus problem. Using state space decomposition, practical consensus problems of a swarm system are converted into stability problems of a disagreement subsystem. Based on the Lyapunov–Krasovskii functional approach and the linear matrix inequality technique, sufficient conditions for swarm systems to achieve practical consensus are proposed where the time-varying external disturbance can be in L 2 or L ∞. Numerical simulations are presented to demonstrate theoretical results.

Output containment control for swarm systems with general linear dynamics: A dynamic output feedback approach ☆

Abstract Output containment control problems for high-order linear time-invariant swarm systems under directed interaction topologies are investigated using a dynamic output feedback approach. Firstly, to propel the outputs of followers to converge to the convex hull formed by the outputs of leaders, a dynamic output containment protocol is presented. Then necessary and sufficient conditions for swarm systems to achieve output containment are proposed. To ensure the scalability of the criteria, a sufficient condition which only includes two linear matrix inequality constraints independent of the number of agents is further presented. Moreover, an approach independent of the number of agents is proposed to determine the gain matrices in the dynamic output containment protocols. Finally, numerical simulations are presented to demonstrate theoretical results.

Time-varying output formation control for high-order linear time-invariant swarm systems

Formation control of swarm systems has gained considerable attention from scientific communities due to its potential applications in various areas. In practical applications, the dynamics of each agent may be of high order and only the outputs of all agents are required to achieve time-varying formations. Therefore, this paper focuses on time-varying output formation control problems for high-order linear time-invariant swarm systems with directed interaction topologies. A general output formation protocol is proposed based on the relative outputs of neighboring agents. Necessary and sufficient conditions for swarm systems to achieve time-varying output formations are presented using a consensus based approach. An explicit expression of the output formation reference function is given. For a swarm system, whether or not a desired output formation is feasible is a crucial problem. Based on partial stability theory, necessary and sufficient conditions for output formation feasibility are derived. Approaches to expand the feasible time-varying output formation set and an algorithm to design the protocol for swarm systems to achieve time-varying output formation are presented respectively. Finally, theoretical results are demonstrated by numerical simulations.

Distributed adaptive time-varying formation for multi-agent systems with general high-order linear time-invariant dynamics☆

Abstract This paper studies distributed time-varying formation control problems for general high-order linear time-invariant (LTI) multi-agent systems using an adaptive based approach. Firstly, a time-varying formation control protocol is constructed by the states of neighboring agents, which the adaptive gain scheduling technique is employed to estimate the coupling weights between neighboring agents. Different from the existing results on formation control, the formation can be specified by piecewise continuously differentiable vectors and no global information about the interaction topologies is required. Then an algorithm with two steps is presented to design the distributed adaptive formation control protocol, where a description of the feasible time-varying formation set is given. The stability of the algorithm is proved using the Lyapunov theory. It is shown that if the predefined time-varying formation belongs to the feasible formation set and each agent is stabilizable, then time-varying formation can be achieved by general high-order LTI multi-agent systems using the distributed adaptive formation protocol designed in the proposed algorithm. Finally, numerical examples are given to demonstrate the effectiveness of the theoretical results.

Necessary and sufficient conditions for average formation tracking of second-order multi-agent systems with multiple leaders☆

Abstract Average formation tracking problems for second-order multi-agent systems with multiple leaders and directed interaction topologies are studied, where the states of followers form a predefined time-varying formation while tracking the average state of the multiple leaders. An average formation tracking protocol is constructed using neighboring relative information, where only part of the followers which are named as well-informed ones are required to obtain the information of the multiple leaders. New properties of the Laplacian matrix are derived under the assumption that for each uninformed follower, there exists at least one directed path from a well-informed follower to it. Necessary and sufficient conditions for second-order multi-agent systems with multiple leaders to achieve average formation tracking are proposed by utilizing the properties of the Laplacian matrix. An approach to design the average formation tracking protocol is presented by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems, average tracking problems and consensus tracking problems for second-order multi-agent systems with one or multiple targets/leaders. An application example in multiple vehicles enclosing is provided to demonstrate the effectiveness of the theoretical results.

Output formation-containment analysis and design for general linear time-invariant multi-agent systems ☆

Abstract Output formation-containment control problems for general linear time-invariant multi-agent systems with directed topologies are dealt with. Output formation-containment means that the outputs of leaders achieve the predefined formation, and at the same time the outputs of followers converge to the convex hull formed by the outputs of leaders. Firstly, static output protocols are presented for leaders and followers respectively. Then output formation-containment problems of multi-agent systems are transformed into asymptotic stability problems. Sufficient conditions with less computation complexity are proposed for multi-agent systems to achieve the output formation-containment. An explicit expression for the time-varying output formation reference function is derived to describe the macroscopic movement of the whole output formation-containment. Explicit expressions to describe the relationship among the outputs of followers, the time-varying output formation for the leaders and the output formation reference are derived. It is proven that the outputs of followers not only converge to the convex hull formed by those of leaders but also achieve certain time-varying formation specified by the convex combination of the desired output formation for the leaders. Moreover, an approach to determine the gain matrices in the protocols is given for multi-agent systems to achieve the output formation-containment. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results.