Robot formation control and navigation using artificial potential functions and panel method

In this thesis, potential flow calculations are used to develop collision free navigation algorithms for a robot swarm. The well known panel method in fluid mechanics is used to solve the governing equations for inviscid incompressible potential flow around rigid objects with tangency boundary conditions, providingthe robots with safe trajectories to the target. In addition, artificial potential functions are used to force the swarm to achieve a predefined geometrical shape. Two kinds of algorithms are developed, offline and online algorithms. In the off-line algorithm the environment is assumed to be previously known, and experimental results are obtained using e-puck mini-robots navigating in an environment with complex shaped obstacles. In the online algorithm, three KheperaIII robots are equiped with laser scanners which are used to detect the obstacles in the environment. Then, a real-time panel method is used to calculatethe streamlines of the potential flow around the complex shaped rigid objects, providing the robots with safe trajectories to the target. The swarm of robots is also forced to keep a desired formation during navigation using potential functions. Potential flow algorithms provide navigation with smooth paths to thetarget. The algorithm can be used in dynamic environments in real-time as the changes in the medium are detected. Finally, a method based on relative position sensing is developed to minimize the error in the algorithms.