Obstacle avoidance of robotic formations based on fluid mechanical modeling

This paper is on obstacle avoidance of swarms of robots moving in certain geometric planar formations. Focus is given to a particular obstacle avoidance approach, which is based on the fluid mechanical principle known as the Circle Theorem. Considering the motion region as a fictitious fluid environment surrounding the obstacles, fluid streamlines are calculated which correspond to unique smooth paths that a robot or a robotic formation can follow without colliding with the obstacles. The design and analysis are initially performed assuming simple integrator dynamics for each agent, and later extended for more realistic non-holonomic unicycle dynamic agent models, with the help of proportional integral (PI) control. The fluid dynamics based designs developed for obstacle avoiding motion control of agents, moving in a prescribed rigid formation are novel, and successfully tested via an extensive set of simulations. Application of the developed designs for motion control of unmanned aerial vehicle (UAV) formations under the constraint of constant speed is also presented.