text: We study the problem of visibility-based exploration, reconstruction and surveillance in the context of supervised learning. Using a level set representation of data and information, we train a convolutional neural network to determine vantage points that maximize visibility. We show that this method drastically reduces the on-line computational cost and determines a small set of vantage points that solve the problem. This enables us to efficiently produce highly-resolved and topologically accurate maps of complex 3D environments. We present realistic simulations on 2D and 3D urban environments.
  @cite_22: We introduce a new approach for exploration based on the concept of frontiers, regions on the boundary between open space and unexplored space. By moving to new frontiers, a mobile robot can extend its map into new territory until the entire environment has been explored. We describe a method for detecting frontiers in evidence grids and navigating to these frontiers. We also introduce a technique for minimizing specular reflections in evidence grids using laser-limited sonar. We have tested this approach with a real mobile robot, exploring real-world office environments cluttered with a variety of obstacles. An advantage of our approach is its ability to explore both large open spaces and narrow cluttered spaces, with walls and obstacles in arbitrary orientation.
  @cite_32: A combustion apparatus comprises a combustor liner forming a combustion chamber, and a swirler for introducing a fuel gas into the combustion chamber in the form of a swirl. The combustor liner has an air film forming device provided on the wall thereof and capable of forming a film of cooling air on the inner peripheral wall of the combustor liner so as to protect the combustor liner from the hot combustion gas in the combustion chamber. The air film forming means is formed such that the flowing direction of the air forming the film becomes the same direction as the swirling direction of the combustion gas, so that the film of the cooling air is not broken by the hot combustion gas.
  @cite_3: We present an algorithm for interpolating the visible portions of a point cloud that are sampled from opaque objects in the environment. Our algorithm projects point clouds onto a sphere centered at the observing locations and performs essentially non-oscillatory (ENO) interpolation to the projected data. Curvatures of the occluding objects can be approximated and used in many ways. We show how this algorithm can be incorporated into novel algorithms for mapping an unknown environment.
  @cite_23: Autonomous robotic systems (observers) equipped with range sensors must be able to discover their surroundings, in an initially unknown environment, for navigational purposes. We present an implementation of a recent environment- mapping algorithm [1] based on Essentially Non-oscillatory (ENO) interpolation [2]. An economical cooperative control tank-based platform [3] is used to validate our algorithm. Each vehicle on the test-bed is equipped with a flexible caterpillar drive, range sensor, limited onboard computing, and wireless communication.
  @cite_10: The context of this work is the exploration of unknown polygonal environments with obstacles. Both the outer boundary and the boundaries of obstacles are piecewise linear. The boundaries can be nonconvex. The exploration problem can be motivated by the following application. Imagine that a robot has to explore the interior of a collapsed building, which has crumbled due to an earthquake, to search for human survivors. It is clearly impossible to have a knowledge of the building's interior geometry prior to the exploration. Thus, the robot must be able to see, with its onboard vision sensors, all points in the building's interior while following its exploration path. In this way, no potential survivors will be missed by the exploring robot. The exploratory path must clearly reflect the topology of the free space, and, therefore, such exploratory paths can be used to guide future robot excursions (such as would arise in our example from a rescue operation).
summary: For the exploration problem, a class of approaches pick new vantage points along shadow boundaries (aka frontiers), the boundary between free and occluded regions @cite_22 . propose a frontier-based approach for 2D polygonal environments which requires @math views, where @math is the number of reflex angles @cite_10 . For general 2D environments, @cite_3 @cite_23 @cite_32 use high order ENO interpolation to estimate curvature, which is then used to determine how far past the horizon to step. However, it is not necessarily optimal to pick only points along the shadow boundary, e.g. when the map is a star-shaped polygon @cite_10 .