Motion planning in an unknown polygonal environment with sounded performance guarantee

We consider the navigation problem of a robot from a starting point S to a target point T inside an unknown polygonal environment. The robot knows the directions of the points S and T and it can detect the walls of the environment through its tactile sensors. We present a competitive strategy for the robot to reach the target T. The path length generated by the robot is ⩽4.5d(κ-1)(κ+2)×d, where, κ=3^(d/2-1) and d is the L₁ distance between S and T