2015/05/29 by Soumic Sarkar, Sarkar, Soumic, Indra Narayan Kar +1
Computer Science · Engineering · #Adaptive Control of Nonlinear Systems #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #Neural Networks Stability and Synchronization #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1505.08128
openalex publication_date 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half as opposed to the vector representation in Cartesian coordinate system. We first design a stable formation controller in an attempt to solve the formation control turned to stabilization problem and then find a collision avoidance controller in the transformed domain, respectively. Different linear transformations are used to facilitate the formation control task in a different way. For example Jacobi transformation is used to separate the shape control and trajectory control. The inverse of the transformation must have nonzero eigenvalues with both positive and negative real parts which may lead the system to instability. If the inverse of the transformation appears in closed loop then a diagonal stabilizing matrix is required to reassign the eigenvalues of the inverse of transformation in the right half of complex plane. The algorithm to find such stabilizing matrix is provided. We then define a matrix of potential in the actual domain which is the stepping stone to find a matrix of potential in the transformed domain. Thus collision avoidance controller can be designed directly in the transformed domain. The mathematical proof is given that both the actual and transformed system behaves identically. Simulation results are provided to support our claim.