Multirobot Relative Localization and Formation Control Using Interior Angle Measurements

Interrobot relative localization using accessible local measurements is crucial for various multirobot missions in a GPS-denied environment. Due to its importance, it is meaningful to complement existing localization methods, commonly based on distances or bearings between robots. Here, we propose a continuous relative localization approach using interior angle measurements for multirobot systems in 2-D. Each robot measures those angles formed with neighboring robots. First, for a minimum three-robot case, we show that the interrobot relative positions can be directly calculated from the robots’ interior angles, the time derivative of interior angles, and interrobot relative velocities, under the condition that the derivative of the interior angle intersected by the two neighboring robots is nonzero. To avoid this singularity case caused by a zero derivative of the interior angle at some instants, we propose a dynamical relative position estimator relying on the same three types of measurements. Using the estimated relative positions, a control law is designed to achieve a desired triangular formation specified by desired interrobot relative positions. For the case where the system consists of more than three robots, the multirobot relative localization is achieved in a directed and triangulated manner. The effects of measurement noise and robots’ collinearity on the relative localization are also discussed. Finally, simulations and experiments are conducted to validate the proposed approach.