An Improved Algorithm in Shortest Path Planning for a Tethered Robot

There is vast amount of literature focusing on motion planning for general robots. However, the same studies for tethered robots have not been investigated much. While a robot navigates in an environment with obstacles, it may meet some problems, such as a lack of power supply, or losing its wireless communication connection. If a robot is attached to a flexible tether, it can obtain sufficient power supply and stable communication through the tether. Following [1], the shortest path planning problem for a tethered robot can be described as follows. Let E be a planar environment which consists of disjoint polygonal obstacles of n total vertices, s be the start point, and t be the destination point in the environment. Suppose a robot, modeled as a point, is attached to an anchor point u by a tether of length L. The initial configuration of the tether is considered as a polyline X of k total vertices from s to u. The goal is to find the shortest path from s to t subject to the tether length constraint. In this paper, we assume that (1) neither the robot nor any part of the tether can enter the interior of any obstacle, and (2) the robot can cross the tether, i.e., the tether can be self intersecting. First, we consider two different models of the shortest path planning problem. In the first model, the tether is automatically retracted and is kept taut, i.e., the tether is always the shortest path in its homotopy equivalent class. In the second model, the tether can only be retracted while the robot back-