Lyapunov Function Based Steering Law for Generalized Voronoi Diagram (GVD) Construction by a Mobile Robot

Motion planning of an autonomous robot in an unknown environment is a challenging task. The prerequisite of any motion planning task is collision avoidance. This paper aims on designing a steering control-law for constructing Generalized Voronoi Diagram (GVD) of an unknown environment. The GVD is a roadmap which offers a maximum clearance path and hence a reliable method to avoid collisions. The GVD comprises of edges and nodes. The GVD node is considered a primary feature of topological localization. This paper proposes a modification in the steering control law for smooth tracing of GVD edge using curvature information at closest points on the obstacle. The proposed modification leads the mobile robot to reach the unknown GVD node. This modification is necessary without which the robot leaves a GVD edge and traces another GVD edge bypassing the GVD node. The modification is suggested based on the geometry of the GVD construction. The proposed steering law is verified using simulations. The simulation result shows that the mobile robot reaches the GVD node with an accuracy of ±0.001 unit distance.