Circulation of curves using vector fields: Actual robot experiments in 2D and 3D workspaces

Different robotic tasks can be solved by controlling a robot to circulate along curves. These include, for example, border inspection and surveillance, multirobot manipulation, and pattern generation. In a previous, work we have proposed a vector field approach for robot convergence and circulation along time-varying curves embedded in N-dimensional spaces. In the present work we instantiate this approach for three-dimensional spaces and, for the first time, show the efficacy of this method to control actual robots. Besides new theoretical analysis when constant speed control is applied, we present experimental results with aerial (quadrotors) and ground (differential-driven) robot.