Signed Laplacian Based Formation Control For Distributed Multi-agent Systems

In recent years,with the rapid development of communication technology,sensor technology and artificial intelligence,a single agent no longer satisfies the complex actual demands.Cooperative control of multi-agent systems(MAS)arises at the historical moment.Formation control has rich application scenarios in cooperative control of multi-agent systems and also has huge theoretical challenges in understanding emergent group behavior mechanism.Therefore,formation control has quickly become one of the hot issues in the field of cooperative control of MAS.In actual applications,different application scenarios and task forms lead to different formation requirements of MAS.Similarly,different sensing and communication capabilities correspond to different formation control strategies.Therefore,it is of great significance to study formation control problems that adapt to a wider range of formation requirements or sensing capabilities.Laplacian matrix is an important mathematical tool for studying distributed formation control of MAS.This thesis mainly focuses on distributed formation control of MAS based on signed Laplacian matrix.The main research contents are summarized as follows:Firstly,finite-time and(almost)global stablization of rigid formation control problem based on signed Laplacian is studied.A unified control framework and a control strategy for finite-time and(almost)globally stablization of rigid formation in any dimensional space are proposed.The proposed control strategy can steer all agents to an affine formation with multiple degrees of freedom,which is demonstrated that it is globally stable in finite time.Meanwhile,all agents are proved to achieve a desired rigid formation with finite-time and(almost)globally stablization by selecting the least number of leader agents and satisfying their conditions of the steering law.Secondly,finite-time and global stablization of translational formation control problem based on signed Laplacian is studied.A unified control framework and a control strategy for finite-time and globally stable translational formation in any dimensional space are proposed.Under the proposed control strategy,all agents can be steered to a desired affine formation globally stably in finite time.Furthermore,all agents are proved to achieve a desired translational formation with finite-time and(almost)globally stablization by selecting the least number of leader agents and satisfying their conditions of the steering law.Thirdly,affine formation control problems of multi-agent systems based on the mixed measurements of distance and bearing are studied.Inspired by the first research based on mixed information formation control,it is the first time to extend the measurements of affine formation control from relative position measurements to mixed distance and bearing ones.A discontinuous eventtriggered approach for affine formation control based on MMB-MDS algorithm is proposed which provides a sufficient condition for relative localization.An elimination scheme of measurement errors is developed to improve robustness of the system.Besides,a discontinuous event-triggered mechanism is introduced to reduce the communication burden of the system.Under the proposed formation control strategy,all agents are converged to a desired affine formation asymptotically.Finally,distributed event-triggered affine formation control based on stiffness theory is studied.Sufficient conditions for relative localization of a sensor subgraph are given which can reconstruct relative positions from distance and bearing measurements.A distributed event-triggered formation control strategy with asynchronous sampling and estimation calculation is proposed to drive all agents to asymptotically converge to a desired affine formation.