In several applications in robotics, including monitoring, mapping, and surveillance, robots must follow closed curves with several different shapes determined by the application. In this paper, it is proposed a methodology for robot navigation in tasks where the robot path can be specified by the intersection of level sets of given functions. Besides the path, the control law is also defined by a vector field created using these functions. The main contribution of this work is the computation of n-dimensional vector fields and the proofs that a holonomic robot controlled by this vector field converges and circulates the specified curve. The paper also shows that the resulting field is continuous and can be modified to maintain constant robot speed, an important characteristic for controlling airplane based aerial robots. Finally, it is shown a numerical technique, based on the weighted sum of radial basis functions, for the construction of the functions that determine the robot path. Simulations with a nonholonomic mobile robot subject to localization errors illustrate the potential of the method to drive several types of robots.
Mobile robots; navigation; implicit functions; limit cycles
