Relative Docking and Formation Control via Range and Odometry Measurements

This article studies the problem of distance-based relative docking of a single robot and formation control of multirobot systems. In particular, an integrated localization and navigation scheme is proposed for a robot to navigate itself to a desired relative position with respect to a fixed landmark at an unknown position, where only range and odometry measurements are used. By carefully embedding historical measurements into equilibrium conditions, we design an integrated estimation-control scheme to achieve the relative docking asymptotically. It is rigorously proved that the robot will converge to the desired docking position asymptotically provided that control gains are chosen to satisfy certain conditions. This scheme is further extended to multirobot systems to consider an integrated relative localization and formation control problem. Unlike widely used spatial cooperation in the existing literature, we propose to exploit both spatial and temporal cooperations for achieving formation control. It is proved that multirobot formation can be achieved with zero error for directed acyclic graphs. Several simulation examples are provided to validate our theoretical results.