Sensor-based exploration for planar two-identical-link robots

We present a new roadmap based on a generalized Voronoi graph for two-identical-link mobile robots to explore an unknown planar environment. It is called the L-2-generalized Voronoi graph and is defined in terms of workspace distance measurements using only sensor-provided information, with the robot having the maximum distance from obstacles, and is therefore optimum in a point of view for exploration and obstacle avoidance. The configuration of the robot possesses four degrees of freedom, and hence the roadmap is one-dimensional in an unknown configuration space 2xT2. The L-2-generalized Voronoi graph is not always connected, and so is connected with an additional structure called the (LR)-R-2-edge, where the robot is tangent to a GVD structure with the same orientation for the two links. This roadmap is termed L-2 hierarchical generalized Voronoi graph. The L-2 hierarchical generalized Voronoi graph includes two structures: the L-2 hierarchical generalized Voronoi graph and the (LR)-R-2 edge. Although the condition of two identical links looks somewhat constraining, the L-2 hierarchical generalized Voronoi graph is still worth pursuing because the case is very common in the engineering environment.