Nageswara S. V. Rao

Robot navigation in unknown terrains using learned visibility graphs. Part I: The disjoint convex obstacle case

The problem of navigating an autonomous mobile robot through unexplored terrain of obstacles is discussed. The case when the obstacles are known has been extensively studied in literature. Completely unexplored obstacle terrain is considered. In this case, the process of navigation involves both learning the information about the obstacle terrain and path planning. An algorithm is presented to navigate a robot in an unexplored terrain that is arbitrarily populated with disjoint convex polygonal obstacles in the plane. The navigation process is constituted by a number of traversals; each traversal is from an arbitrary source point to an arbitrary destination point. The proposed algorithm is proven to yield a convergent solution to each path of traversal. Initially, the terrain is explored using a rather primitive sensor, and the paths of traversal made may be suboptimal. The visibility graph that models the obstacle terrain is incrementally constructed by integrating the information about the paths traversed so far. At any stage of learning, the partially learned terrain model is represented as a learned visibility graph, and it is updated after each traversal. It is proven that the learned visibility graph converges to the visibility graph with probability one when the source and destination points are chosen randomly. Ultimately, the availability of the complete visibility graph enables the robot to plan globally optimal paths and also obviates the further usage of sensors.

A 'retraction' method for learned navigation in unknown terrains for a circular robot

The authors consider the problem of learned navigation of a circular robot R, of radius delta (>or=0), through a terrain whose model is not a priori known. The authors consider two-dimensional finite-sized terrains populated by an unknown (but finite) number of simple polygonal obstacles. The number and locations of the vertices of each obstacle are unknown to R; R is equipped with a sensor system that detects all vertices and edges that are visible from its present location. The authors deal with two problems: the visit problem and the terrain model acquisition problem. In the visit problem, the robot is required to visit a sequence of destination points, and in the terrain model acquisition problem, the robot is required to acquire the complete model of the terrain. The authors present an algorithmic network framework for solving these two problems based on a retraction of the free space onto the Voronoi diagram of the terrain. >

On terrain acquisition by a point robot amidst polyhedral obstacles

The authors consider the problem of terrain model acquisition by a roving point placed in an unknown terrain populated by stationary polyhedral obstacles in two/three dimensions. The motivation for this problem is that after the terrain model is completely acquired, navigation from a source point to a destination point can be achieved along the collision-free paths. This can be done without the usage of sensors by applying the existing techniques for the find-path problem. In the paper, the point robot autonomous machine (PRAM) is used as a simplified abstract model for real-life roving robots. An algorithm is presented that enables PRAM to autonomously acquire the model of an unexplored obstacle terrain composed of an unknown number of polyhedral obstacles in two/three dimensions. In this method, PRAM undertakes a systematic exploration of the obstacle terrain with its sensor that detects all the edges and vertices visible from the present location, and builds the complete obstacle terrain model. >

Algorithmic framework for learned robot navigation in unknown terrains

A framework is presented that uses the same strategy to solve both the learned navigation and terrain model acquisition. It is shown that any abstract graph structure that satisfies a set of four properties suffices as the underlying structure. It is also shown that any graph exploration algorithm can serve as the searching strategy. The methods provide paths that keep the robot as far from the obstacles as possible. In some cases, these methods are preferable to visibility graph methods that require the robot to navigate arbitrarily close to the obstacles, which is hard to implement if the robot motions are not precise.<<ETX>>

Autonomous robot navigation in unknown terrains: incidental learning and environmental exploration

The navigation of autonomous mobile machines, which are referred to as robots, through terrains whose models are not known a priori is considered. The authors deal with point-sized robots in 2-D and 3-D (two- and three-dimensional) terrains and circular robots in 2-D terrains. The 2-D (or 3-D) terrains are finite-sized and populated by an unknown, but finite, number of simple polygonal (or polyhedral) obstacles. The robot is equipped with a sensor system that detects all vertices and edges that are visible from its present location. Two basic navigational problems are considered. In the visit problem, the robot is required to visit a sequence of destination points in a specified order, using the sensor system. In the terrain model acquisition problem, the robot is required to acquire the complete model of the terrain by exploring the terrain with the sensor. A framework that yields solutions to both the visit problem and the terrain model acquisition problem using a single approach is presented, and the algorithms are described. The approach consists of incrementally constructing, in an algorithmic manner, an appropriate geometric graph structure (1-skeleton), called the navigational course. A point robot employs the restricted visibility graph and the visibility graph as the navigational course in 2-D and 3-D cases, respectively. A circular robot uses the modified visibility graph. >

Robot navigation in unknown generalized polygonal terrains using vision sensors

This paper considers the problem of navigating a point robot in an unknown two-dimensional terrain populated by disjoint generalized polygonal obstacles. A generalized polygon consists of a connected sequence of circular arcs and straight-line segments. The terrain model is not known a priori, but the robot is equipped with a vision sensor. A discrete vision sensor detects all visible (from a single position) portions of the obstacle boundaries in a single scan operation. The navigation problem deals with moving the robot through the terrain from a source position to a destination position, and the terrain model acquisition problem deals with autonomously building a model of the terrain. A complete solution to either problem is shown to require an infinite number of scan operations in cusp regions formed by a pair of convex and concave obstacle edges. Either problem is considered solved with a precision /spl epsiv/ if the points that have not been scanned are those in a cusp region with a clearance less than /spl epsiv/ from two obstacle edges. Three methods are proposed to solve both problems with a precision /spl epsiv/ based on extensions of the generalized visibility graph, the generalized Voronoi diagram, and the trapezoidal decomposition. Then simplified versions of these structures are proposed to exactly solve the navigation and terrain model acquisition problems using a continuous vision sensor that detects all visible obstacle boundaries as the robot navigates along a path. >

Robot navigation in an unexplored terrain

Navigation planning is one of the most vital aspects of an autonomous mobile robot. Robot navigation for completely known terrain has been solved in many cases. Comparatively less research dealing with robot navigation in unexplored obstacle terrain has been reported in the literature. In recent times this problem has been addressed by adding learning capability to a robot. The robot explores terrain using sensors as it navigates, and builds a terrain model in an incremental manner. In this article we present concurrent algorithms for robot navigation in unexplored terrain. The performance of the concurrent algorithms is analyzed in terms of planning time, travel time, scanning time, and update time. The analysis reveals the need for an efficient data structure to store an obstacle terrain model in order to reduce traversal time, and also to incorporate learning. A modified adjacency list is proposed as a data structure for storing a spatial graph that represents an obstacle terrain. The time complexities of the algorithms that access, maintain, and update the spatial graph are estimated, and the effectiveness of the implementation is illustrated.

The visit problem: visibility graph-based solution

An algorithm to navigate a point robot through a sequence of destination points amid unknown stationary polygonal obstacles in a two-dimensional terrain is presented. The algorithm implements learning in the course of building a global terrain model by integrating the sensor information obtained during navigation. This global model is used in planning future navigational paths. This approach prevents the robot from making localized detours, and results in better navigation, in an average case, than obtained using algorithms without learning. The proposed algorithms are implemented in the C language on a simulator for a HERMIES-II robot running on an IBM PC.<<ETX>>

Algorithms for recognizing planar polygonal configurations using perspective images

A simplified abstraction of the problem of recognizing planar arrangements of objects using camera pictures taken from unknown positions is considered. A set of polygons in planes is called a planar polygonal configuration. Given perspective images P and Q corresponding to planar polygonal configurations, the matching problem is to determine if P and Q correspond to the same configuration. An optimal theta (n log n) time algorithm is presented to solve this problem, where n is the total number of vertices of polygons in each image. The algorithm is obtained by combining ideas of cross ratios, which are well known to be invariant under perspective projections, and the first fundamental theorem of perspective projections. This algorithm has been implemented and tested with satisfactory results. >

Building heaps in parallel

We present O(log n) time parallel algorithms for constructing a heap of a set of n elements, chosen from a total order, using EREW PRAM and hypercube of at most [2n/log n] processors.