Vector field for curve tracking with obstacle avoidance.

In this work, we extend a recently proposed methodology to construct artificial vector fields for robot navigation in n-dimensional spaces to track and circulate time-varying curves. Now, we incorporate the ability to deviate from obstacles that might be static or dynamic by constructing a collision-free vector field. It can be considered a reactive approach in which the obstacles can be locally sensed and then circumnavigated at a fixed distance. The novel vector field that allows the circumnavigation of obstacles and the traversal of a target curve is built upon the consideration of the closest points on the obstacles, which can assume a generic shape, and the closest point on the curve. To validate our method, we present ROS-based computational simulations and real-world experiments with a wheeled robot and a UAV quadcopter.