From: AAAI-96 Proceedings. Copyright © 1996, AAAI (www.aaai.org). All rights reserved. r&grating Grid- pologica ile Sebastiau Thrunt~ tcomputer Science Department SInstitut fur Informatik Carnegie Mellon University Universitat Bonn Pittsburgh, PA 152 13 D-53 117 Bonn, Germany Abstract Recent research has produced two fundamental paradigms for modeling indoor robot environments: the grid-based Research on mobile robot navigation has produced two ma- (metric) paradigm and the topological paradigm. Grid- jor paradigms for mapping indoor environments: grid-based and topological. While grid-based methods produce accu- based approaches, such as those proposed by Moravec/Elfes rate metric maps, their complexity often prohibits efficient (Moravec 1988) and many others, represent environments planning and problem solving in large-scale indoor environ- by evenly-spaced grids. Each grid cell may, for exam- ments. Topological maps, on the other hand, can be used ple, indicate the presence of an obstacle in the correspond- much more efficiently, yet accurate and consistent topolog- ing region of the environment. Topological approaches, ical maps are considerably difficult to learn in large-scale such a those described in (Engelson & McDermott 1992; environments. Kortenkamp & Weymouth 1994; Kuipers & Byun 1990; This paper describes an approach that integrates both MatariC 1994; Pierce & Kuipers 1994), represent robot en- paradigms: grid-based and topological. Grid-based maps vironments by graphs. Nodes in such graphs correspond to are learned using artificial neural networks and Bayesian in- distinct situations, places, or landmarks (such as doorways). tegration. Topological maps are generated on top of the They are connected by arcs if there exists a direct path be- grid-based maps, by partitioning the latter into coherent tween them. regions. By combining both paradigms-grid-based and topological-, the approach presented here gains the best of Both approaches to robot mapping exhibit orthogonal both worlds: accuracy/consistency and efficiency. The pa- strengths and weaknesses. Occupancy grids are considerably per gives results for autonomously operating a mobile robot easy to construct and to maintain even in large-scale envi- equipped with sonar sensors in populated multi-room envi- ronments (Buhmann et al. 1995; Thrun & Bticken 1996). ronments. Since the intrinsic geometry of a grid corresponds directly to the geometry of the environment, the robot’s position within Introduction its model can be determined by its position and orientation To efficiently carry out complex missions in indoor environ- in the real world-which, as shown below, can be deter- ments, autonomous mobile robots must be able to acquire mined sufficiently accurately using only sonar sensors, in and maintain models of their environments. The task of ac- environments of moderate size. As a pleasing consequence, quiring models is difficult and far from being solved. The different positions for which sensors measure the same values following factors impose practical limitations on a robot’s (i.e., situations that look alike) are naturally disambiguated ability to learn and use accurate models: in grid-based approaches. This is not the case for topological approaches, which determine the position of the robot relative 1. Sensors. Sensors often are not capable to directly mea- to the model based on landmarks or distinct sensory features. sure the quantity of interest (such as the exact location of For example, if the robot traverses two places that look alike, obstacles). topological approaches often have difficulty determining if 2. Perceptual limitations. The perceptual range of most sensors is limited to a small range close to the robot. these places are the same or not (particularly if these places have been reached via different paths). Also, since sensory To acquire global information, the robot has to actively input usually depends strongly on the view-point of the robot, explore its environment. topological approaches may fail to recognize geometrically 3. Sensor noise. Sensor measurements are typically cor- rupted by noise, the distribution of which is often un- nearby places. known (it is rarely Gaussian). On the other hand, grid-based approaches suffer from their 4. Drift/slippage. Robot motion is inaccurate. Qdometric enormous space and time complexity. This is because the errors accumulate over time. resolution of a grid must be fine enough to capture every im- 5. Complexity and dynamics. Robot environments are portant detail of the world. Compactness in a key advantage complex and dynamic, making it principally impossible of topological representations. Topological maps are usu- to maintain exact models. ally more compact, since their resolution is determined by 6. Real-time requirements. Time requirements often de- the complexity of the environment. Consequently, they per- mand that the internal model must be simple and easily ac- mit fast planning, facilitate interfacing to symbolic planners cessible. For example, fine-grain CAD models are often and problem-solvers, and provide more natural interfaces for disadvantageous if actions must be generated in real-time. human instructions. Since topological approaches usually 944 Mobile Robots Grid-based approaches Topological approaches + easy to build, represent, and permits efficient planning, maintain low space complexity (res- + recognition of places (based on olution depends on the com- geometry) is non-ambiguous plexity of the environment) and view point-independent does not require accurate de- + facilitates computation of termination of the robot’s shortest paths position convenient represen- tation for symbolic planners, problem solvers, natural lan- guage interfaces - planning inefficient, space- difficult to construct and Figure 1: The robots used in our research: RHINO (University of consuming (resolution does not maintain in larger environ- Bonn), XAVIER, and AMELIA (both CMU). depend on the complexity of ments the environment) recognition of places (based manufacturer (Real World Interface, Inc.) as part of the reg- - requires accurate determina- on landmarks) often am- ular navigation software. tion of the robot’s position biguous, sensitive to the - poor interface for most sym- point of view bolic problem solvers may yield suboptimal paths The metric maps considered here are two-dimensional, dis- Table 1: Comparison of grid-based and topological approaches to crete occupancy grids, as originally proposed in (Elfes 1987; map building. Moravec 1988) and since implemented successfully in vari- ous systems. Each grid-cell (z, y) in the map has an occu- do not require the exact determination of the geometric po- pancy value attached, which measures the subjective belief sition of the robot, they often recover better from drift and whether or not the center of the robot can be moved to the slippage-phenomena that must constantly be monitored and center of that cell (i.e., the occupancy map models the con- compensated in grid-based approaches. To summarize, both $guration space of the robot, see e.g., (Latombe 1991)). paradigms have orthogonal strengths and weaknesses, which This section describes the four major components of our ap- are summarized in Table 1. proach to building grid-based maps (see also (Thrun 1993)): This paper advocates to integrate both paradigms, to gain (1) sensor interpretation, (2) integration, (3) position esti- the best of both worlds. The approach presented here com- mation, and (4) exploration. Examples of metric maps are bines both grid-based (metric) and topological representa- shown in various places in this paper. tions. To construct a grid-based model of the environment, sensor values are interpreted by an artificial neural network Sensor Interpretation and mapped into probabilities for occupancy. Multiple in- terpretations are integrated over time using Bayes’ rule. On To build metric maps, sensor reading must be “translated” top of the grid representation, more compact topological into occupancy values OCC~:,~for each grid cell (z, y) . The maps are generated by splitting the metric map into coher- idea here is to train an artificial neural network using Back- ent regions, separated through critical lines. Critical lines Propagation to map sonar measurements to occupancy val- correspond to narrow passages such as doorways. By parti- ues. The input to the network consists of the four sensor tioning the metric map into a small number of regions, the readings closest to (x:, y), along with two values that encode number of topological entities is several orders of magnitude (z, y) in polar coordinates relative to the robot (angle to the smaller than the number of cells in the grid representation. first of the four sensors, and distance). The output target Therefore, the integration of both representations has unique for the network is 1, if (z, y) is occupied, and 0 otherwise. advantages that cannot be found for either approach in iso- Training examples can be obtained by operating a robot in a lation: the grid-based representation, which is considerably known environment and recording its sensor readings; notice easy to construct and maintain in environments of moderate that each sonar scan can be used to construct many training complexity (e.g., 20 by 30 meters), models the world consis- examples for different x-y coordinates. In our implemen- tently and disambiguates different positions. The topological tation, training examples are generated with a mobile robot