Distributed Circle Formation Control Of Multi-agent Systems With Bounded Measurement Errors

Due to its extensive applications such as cooperative exploration,environmental monitoring,and search and rescue,cooperative control of multi-agent systems has attracted much attention of domestic and foreign scholars.As one of its research directions,more and more scholars begin to study the formation control of multi-agent systems.Circle formation control is a typical formation control problem.The control objective of the circle formation is to form the desired circle for all agents.At present,most of the recent research works on circle formation control are based on an assumption that each agent can perceive accurate information of its neighbors.However,in practical applications,the above assumption may not be satisfied because of the sensing noise and communication noise.Therefore,for multi-agent systems with first-order and second-order dynamics,this dissertation will study the circle formation control of mobile agents with bounded measurement errors.The measurement errors studied in this dissertation are bounded,and the agents only know the upper bounds of the measurement errors and do not know its specific formation or distribution.For the first-order multi-agent system with bounded measurement errors,a distributed circle formation control law is proposed in this dissertation.Then,the convergence of the control law is analyzed and the upper bound of formation errors is given by using algebraic graph theory,matrix theory and stability theory.In order to avoid collision among the agents,we further give the conditions of order preservation of the system.Finally,the effectiveness of the control law is verified by numerical simulations.In the first-order multiagent system,the control input of an agent is its speed in the physical sense.In practical applications,each agent has its own maximum rotating velocity,which means that the control input of each agent is always upper bounded.Therefore,this dissertation will further study the circle formation control of multi-agent systems with both measurement errors and input saturation.In this dissertation,a distributed control law based on the low gain control method is proposed to avoid the saturation of control input by selecting appropriate low gains.The corresponding convergence analysis and the upper bound of the formation errors of the multiagent system are also given.In practical physical applications,Newton's second law of motion is more appropriate to describe the motion properties of the mobile agents.Therefore,based on the study of first-order dynamic systems,the circle formation control problem of second-order multi-agent systems with measurement errors is studied in this dissertation.Different from the first-order system,in addition to the position errors,each agent cannot perceive the accurate velocity information of its neighbors,that is,the second-order multi-agent system studied has dual measurement errors.Under the influence of the dual measurement errors,the multi-agent system should be driven to a neighborhood of the desired formation and the velocity differences between the neighboring agents should be uniformly bounded under the proposed control law.Therefore,based on the research about the first-order system,this dissertation will apply bilinear transformation and other theoretical approaches to analyze the convergence of the control law,and further give the upper bound of the formation errors and the conditions to preserve the agents' spatial order during the formation task.