Near-Optimal Sensor-Based Navigation in an Environment Cluttered with Simple Shapes

Abstract

For the last decade, many sensor-based path-planning algorithms have been proposed. In all the algorithms, the convergence of a mobile robot to a destination is theoretically ensured if a path to the destination exists. However, due to no information of obstacle shape and location, a mobile robot basically takes a very long path to its destination. To overcome this drawback in this paper, we consider how a mobile robot selects its direction to follow when encountering an obstacle. Then, the result is as follows: a mobile robot should select a tangential direction to avoid a circular obstacle, whose absolute angle against the goal directions is smaller. The obstacle avoidance procedure is very simple. Therefore, by adding it into good classic sensor-based path-planning algorithms Class1 and Bug2, we get near-optimal algorithms Simple(Class1) and Simple(Bug2). In this paper, we firstly ascertain that Simple(Class1) and Simple(Bug2) always select slightly longer paths than the path generated by the optimal (model-based) path-planning algorithm. Secondly, we describe that Simple(Class1) and Simple(Bug2) always select extremely shorter paths than paths generated by Class1 and Bug2. The near-optimality and the superiority are given by theoretical proofs in an uncertain 2-D environment with circular obstacles. Thirdly, we theoretically investigate whether the near-optimality and the superiority are still kept or not in an uncertain environment with square, rectangular, elliptic, or triangular obstacles. Finally based on simulation and experiment results, we conclude that Simple(Class1) and Simple(Bug2) keep the near-optimality and the superiority in an environment with simple shapes as obstacles.