Position estimation and formation control using distance and partial state measurements

This paper presents a distributed formation control strategy for multi-agent systems (MASs) and explores a position observer using distance measurements and partial state measurements. By leveraging infinitesimally rigid framework and matrix decomposition techniques, we pinpoint the position states that require direct measurements for satisfying local weak observability of MASs. Subsequently, by utilizing distance and partial position state measurements, we construct distributed observers to estimate positions in a global coordinate system encompassing all agents. The controller employs the gradient laws to preserve formation rigidity, facilitate collision avoidance, and ensure network connectivity. Additionally, proportional feedback is utilized to guide the agents toward desired global reference positions. Our analysis, based on the Lyapunov method, establishes the local asymptotic convergence of formation control and estimate errors, and derives lower bounds for control and observation feedback gains. To validate the effectiveness of our control method, we conduct some numerical simulations in a 3D space.