Feasible Formation Set Research Articles

Time-Varying Formation for General Linear Multiagent Systems Over Directed Topologies: A Fully Distributed Adaptive Technique

In this paper, the time-varying formation problem is studied under directed topologies. An adaptive approach is utilized to develop a fully distributed formation controller for general linear multiagent systems. To achieve distributed time-varying formations, a feasible formation set is proposed by proposing some conditions. By using adaptive techniques, the main contribution of this paper is that a fully distributed formation algorithm is designed for achieving time-varying formation under directed graphs, which relies only on the local measurements without requiring any global information. By analyzing the Lyapunov stability, the proposed fully distributed formation algorithm can ensure the multiagent systems achieving the goal of time-varying formations. To verify the theoretical results, some simulation examples are shown finally.

Time-varying output formation tracking of heterogeneous linear multi-agent systems with multiple leaders and switching topologies

This paper studies the time-varying output formation tracking problems for heterogeneous linear multi-agent systems with multiple leaders in the presence of switching directed topologies, where the agents can have different system dynamics and state dimensions. The outputs of followers are required to accomplish a given time-varying formation configuration and track the convex combination of leaders’ outputs simultaneously. Firstly, using the neighboring relative information, a distributed observer is constructed for each follower to estimate the convex combination of multiple leaders’ states under the influences of switching directed topologies. The convergence of the observer is proved based on the piecewise Lyapunov theory and the threshold for the average dwell time of the switching topologies is derived. Then, an output formation tracking protocol based on the distributed observer and an algorithm to determine the control parameters of the protocol are presented. Considering the features of heterogeneous dynamics, the time-varying formation tracking feasible constraints are provided, and a compensation input is applied to expand the feasible formation set. Sufficient conditions for the heterogeneous multi-agent systems with multiple leaders and switching directed topologies to achieve the desired time-varying output formation tracking under the designed protocol are proposed. Finally, simulation examples are given to validate the theoretical results.

Distributed fault-tolerant time-varying formation control for high-order linear multi-agent systems with actuator failures

This paper investigates the fault-tolerant time-varying formation control problems for high-order linear multi-agent systems in the presence of actuator failures. Firstly, a fully distributed formation control protocol is presented to compensate for the influences of both bias fault and loss of effectiveness fault. Using the adaptive online updating strategies, no global knowledge about the communication topology is required and the bounds of actuator failures can be unknown. Then an algorithm is proposed to determine the control parameters of the fault-tolerant formation protocol, where the time-varying formation feasible conditions and an approach to expand the feasible formation set are given. Furthermore, the stability of the proposed algorithm is proven based on the Lyapunov-like theory. Finally, two simulation examples are given to demonstrate the effectiveness of the theoretical results.

Time-varying formation control for general linear multi-agent systems with switching directed topologies

Time-varying formation analysis and design problems for multi-agent systems with general linear dynamics and switching directed interaction topologies are investigated. Different from the previous results, the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed. Firstly, necessary and sufficient conditions for general linear multi-agent systems with switching directed topologies to achieve time-varying formations are proposed, where a description of the feasible time-varying formation set and approaches to expand the feasible formation set are given. Then an explicit expression of the time-varying formation reference function is derived to describe the macroscopic movement of the whole formation. An approach to assign the motion modes of the formation reference is provided. Moreover, an algorithm consisting of four steps to design the formation protocol is presented. In the case where the given time-varying formation belongs to the feasible formation set, it is proven that by designing the formation protocol using the proposed algorithm, time-varying formation can be achieved by multi-agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold. Finally, numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

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

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.

Optimal Formation of Multirobot Systems Based on a Recurrent Neural Network.

The optimal formation problem of multirobot systems is solved by a recurrent neural network in this paper. The desired formation is described by the shape theory. This theory can generate a set of feasible formations that share the same relative relation among robots. An optimal formation means that finding one formation from the feasible formation set, which has the minimum distance to the initial formation of the multirobot system. Then, the formation problem is transformed into an optimization problem. In addition, the orientation, scale, and admissible range of the formation can also be considered as the constraints in the optimization problem. Furthermore, if all robots are identical, their positions in the system are exchangeable. Then, each robot does not necessarily move to one specific position in the formation. In this case, the optimal formation problem becomes a combinational optimization problem, whose optimal solution is very hard to obtain. Inspired by the penalty method, this combinational optimization problem can be approximately transformed into a convex optimization problem. Due to the involvement of the Euclidean norm in the distance, the objective function of these optimization problems are nonsmooth. To solve these nonsmooth optimization problems efficiently, a recurrent neural network approach is employed, owing to its parallel computation ability. Finally, some simulations and experiments are given to validate the effectiveness and efficiency of the proposed optimal formation approach.

Time‐varying formation control for high‐order linear swarm systems with switching interaction topologies

Time-varying formation control problems for high-order linear time-invariant swarm systems with switching interaction topologies are investigated. A general formation control protocol is proposed firstly. Then using a consensus based approach, necessary and sufficient conditions for swarm systems with switching interaction topologies to achieve a given time-varying formation are presented. An explicit expression of the time-varying formation reference function is given. It is revealed that the switching interaction topologies have no effect on the formation reference function and the motion modes of the formation reference can be specified. Furthermore, necessary and sufficient conditions for formation feasibility are presented. An approach to expand the feasible formation set is given and an algorithm to design the protocol for swarm systems with switching interaction topologies to achieve time-varying formations is provided. Finally, numerical simulations are presented to demonstrate theoretical results.

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.