Research On Affine Transformation Based Distributed Formation Control Technology Of Multi-Agent Systems

Along with the gradually developed networked communication,sensing equip-ment,and artificial intelligence,research topics on multi-agent systems have demon-strated broad application prospects in civil or military fields.Inspired and derived by swarming self-organized movements,consensus control of multi-agent systems has also faced unprecedented theoretical challenges.Nowadays,multi-agent formation control contains two subtasks:formation shape control and formation maneuver con-trol,which is a deeply concerned research hotspot and difficulty in the realm of consen-sus control.In the increasingly complex application environment,the use of traditional multi-agent formation control strategy is restricted from many aspects.Therefore,it is very important to design a kind of formation control strategy with better environmental adaptability for its practical application prospects.Based on directed graphs,this thesis studies a series of affine formation control problems for multi-agent systems.The main contents and contributions are summarized as follows:First,this thesis defines a novel k-reachable directed graphs based on leader-follower networks,and analyzes a signed Laplacian matrix with positive and negative weights.Then,a definition of affine localizability is given according to the network localizability and affine transformation,and two sufficient and necessary conditions in arbitrary dimensions are also provided and proved.Second,in continuous or discrete time domains respectively,this thesis tackles single and double-integrator multi-agent systems.Only by injecting prescribed time-invariant or time-varying references inside the target formation into the leaders,and designing the distributed affine formation maneuver control laws for the followers,the whole formation can achieve stable affine formation shapes and maneuvers.Third,if in arbitrary dimensions the dynamical leaders can be described as polyno-mial trajectories inside the target formation,this thesis then proposes a distributed PIn affine formation maneuver control scheme for the arbitrary order integrator followers.Meanwhile,state estimators for the inaccessible leader states are designed,and small-?theorem in the frequency domain is used to analyze the non-uniform time delays and give the upper delay bound.Fourth,this thesis proposes a two-layer hybrid affine formation control strategy for Euler-Lagrange multi-agent systems,designs distributed finite-time sliding-mode estimators for unknown formation information,and adopts integral barrier Lyapunov functions to constrain the velocities.In addition,based on the relation between the affine transformation and convexity,this thesis devises a scalable time-varying multi-layer convex formation shapes to enclose and track a dynamical target and introduces artificial potential functions to achieve the collision avoidance.Lastly,if the terminal states of the heterogeneous linear leaders can converge to the desired target formation positions,this thesis then designs a distributed PI-type affine formation control strategy for heterogeneous linear followers and utilizes the integral term to eliminate the steady-state errors induced by the leaders.The robustness of proposed control laws is also verified by injecting bounded external disturbances.Besides,only partial network connection information is known in advance,this thesis uses an adaptive algorithm to achieve the affine formation.