Abstract-This paper considers what can be accomplished using a mobile robot that has limited sensing. For navigation and mapping, the robot has only one sensor, which tracks the directions of depth discontinuities. There are no coordinates, and the robot is given a motion primitive that allows it to move toward discontinuities. The robot is incapable of performing localization or measuring any distances or angles. Nevertheless, when dropped into an unknown planar environment, the robot builds a data structure, called the Gap Navigation Tree, which enables it to navigate optimally in terms of Euclidean distance traveled. In a sense, the robot is able to learn the critical information contained in the classical shortest-path roadmap, although surprisingly it is unable to extract metric information. We prove these results for the case of a point robot placed into a simply connected, piecewise-analytic planar environment. The case of multiply connected environments is also addressed, in which it is shown that further sensing assumptions are needed. Due to the limited sensor given to the robot, globally optimal navigation is impossible; however, our approach achieves locally optimal (within a homotopy class) navigation, which is the best that is theoretically possible under this robot model.

No abstract

In this paper we address the problem of finding time-optimal search paths in known environments. In particular, we address the problem of searching a known environment for an object whose unknown location is characterized by a known probability density function (PDF). With this formulation, the time required to find the object is a random variable induced by the choice of search path together with the PDF for the object's location. The optimization problem we consider is that of finding the path that minimizes the expected value of the time required to find the object. As the complexity of the problem precludes finding an exact optimal solution, we propose a two-level, heuristic approach to finding the optimal search path. At the top level, we use a decomposition of the workspace based on critical curves to impose a qualitative structure on the solution trajectory. At the lower level, individual segments of this trajectory are refined using local numerical optimization methods. We have implemented the algorithm and present simulation results for the particular case when the object's location is specified by the uniform PDF.

In this paper, we present techniques that allow one or multiple mobile robots to efficiently explore and model their environment. While much existing research in the area of Simultaneous Localization and Mapping (SLAM) focuses on issues related to uncertainty in sensor data, our work focuses on the problem of planning optimal exploration strategies. We develop a utility function that measures the quality of proposed sensing locations, give a randomized algorithm for selecting an optimal next sensing location, and provide methods for extracting features from sensor data and merging these into an incrementally constructed map.We have also provide an efficient algorithm driven by our utility function. This algorithm is able to explore several steps ahead without incurring too high a computational cost. We have compared that exploration strategy with a totally greedy algorithm that optimizes our utility function with a one-step-look ahead.The planning algorithms which have been developed operate using simple but flexible models of the robot sensors and actuator abilities. Techniques that allow implementation of these sensor models on top of the capabilities of actual sensors have been provided.All of the proposed algorithms have been implemented either on real robots (for the case of individual robots) or in simulation (for the case of multiple robots), and experimental results are given.

Three-dimensional (3D) object reconstruction is the process of building a 3D model of a real object. This task is performed by taking several scans of an object from different locations (views). Due to the limited field of view of the sensor and the object's self-occlusions, it is a difficult problem to solve. In addition, sensor positioning by robots is not perfect, making the actual view different from the expected one. We propose a next best view (NBV) algorithm that determines each view to reconstruct an arbitrary object. Furthermore, we propose a method to deal with the uncertainty in sensor positioning. The algorithm fulfills all the constraints of a reconstruction process, such as new information, positioning constraints, sensing constraints and registration constraints. Moreover, it improves the scan's quality and reduces the navigation distance. The algorithm is based on a search-based paradigm where a set of candidate views is generated and then each candidate view is evaluated to determine which one is the best. To deal with positioning uncertainty, we propose a second stage which re-evaluates the views according to their neighbours, such that the best view is that which is within a region of the good views. The results of simulation and comparisons with previous approaches are presented.