Continuum Deformation of Multi-Agent Systems Under Directed Communication Topologies

Abstract

A leader follower model has recently been proposed for homogeneous deformation of a multi-agent system (MAS) in ℝn. Researchers have shown how a desired homogeneous transformation can be designed by choosing proper trajectories for n + 1 leader agents and can be learned by every follower through local communication. However, existing work requires every follower to communicate with n + 1 adjacent agents, where communication between every two adjacent followers is constrained to be bidirectional. These requirements limit the total allowable number of agents, so an arbitrary number of agents may not be able to acquire a desired homogeneous mapping by local interaction. Additionally, if followers are not allowed to communicate with more than n + 1 neighboring agents, the convergence rate of actual positions to the desired positions (defined by a homogeneous transformation) may not be sufficiently high. The system may then considerably deviate from the desired configuration during transition. The main contribution of this article is to address these two issues, where each follower is considered to be a general linear system. It will be proven that followers can acquire desired positions prescribed by a homogeneous mapping in the presence of disturbance and measurement noise by applying a new finite-time reachability model under either fixed or switching topologies, if: (i) communication among followers is defined by a directed and strongly connected subgraph, (ii) each follower applies a consensus protocol with communication weights that are consistent with the positions of the agents in the initial configuration, and (iii) every follower i is allowed to communicate with mi≥n+1 local agents. With this strategy, an MAS with an arbitrary number of agents with linear dynamics can acquire a desired homogeneous mapping in the presence of disturbance and measurement noise, where convergence rate can be enhanced by increasing the number of communication links.

Multi-UAV Continuum Deformation Flight Optimization in Cluttered urban environments

“…A leading triangle configurationT n is called a valid deformation, if 1) P l,n is defined by Eqs. (18) and (19) and 2) Constraint Eqs. (9), (16a), and (16b) are all satisfied.…”

“…A flexible virtual structure formulation is also studied in [9]. Consensus [10][11][12], containment [13,14], and continuum deformation [15][16][17][18][19] are decentralized multi-agent coordination approaches. Consensus is perhaps the most common approach for formation and cooperative control.…”

Continuum Deformation of a Multiple Quadcopter Payload Delivery Team without Inter-Agent Communication

“…, N } defines follower index numbers. Elements of the Jacobian matrix Q and rigid-body displacement vector D can be uniquely related to leaders' positions by [30][31][32]…”

“…Note that the matrix [I 2 ⊗ L 0 I 2 ⊗ 1 2 ] is nonsingular if leader positions satisfy the following rank condition [30][31][32]:…”

Experimental Evaluation of Continuum Deformation with a Five Quadrotor Team

“…Shared state data is weighted based on a reference configuration. Continuum deformation stability is analyzed in [7], while coordination under switching communication topologies is studied in [8]. Characterization of the homogeneous transformation and safety guarantees are key features of continuum deformation.…”