Reactively Following Equidistant Curves with Singularities by an Underactuated Nonholonomic Mobile Robot
Alexey S. Matveev, V. Chernov · 2023
An underactuated nonholonomic Dubins-vehicle-like robot with a lower-limited turning radius travels in a plane with unknown objects. In its local frame, the robot has access to the nearest point(s) in the union of the objects. The robot has to approach and escort them, with maintaining a given distance to the currently nearest object, so that all objects are enclosed inside the robot's path. The targeted equidistant curve to the objects may contain parts that cannot be perfectly traced due to excessive contortion and singularities. So the task is compulsorily reframed as that of finding, approaching and repeatedly tracing an approximation of the equidistant curve that is featured by a certain degree of optimality among those trackable by the robot. A computationally inexpensive navigation law is presented that solves this mission. Nonlocal convergence of this law is justified by mathematically rigorous results and is confirmed by computer simulation tests and experiments with real robots.