Exactly one polygon is extracted from a binary radar image, the so-called ... may not be modeled with sufficient accuracy, due to high memory consumption ... In [Ger01] different approaches to autonomous river mapping with a fused sensor ... dilated five times and combined with the raw radar image using the AND operator.
Mapping Of Inland Waters Using Radar Matthias Greuter, Michael Blaich, Michael Schuster, Johannes Reuter, Matthias Franz Institute of System Dynamics Konstanz University of Applied Sciences Konstanz Konstanz, Germany
Abstract. This paper presents a mapping approach for inland waters using a noisy radar sensor installed on a boat. The vessel’s position is acquired from GPS, thus this is a pure mapping problem. For the actual mapping the probabilistic open-source mapping framework octomap as presented by [WHB+ 10] is used. Exactly one polygon is extracted from a binary radar image, the so-called Water Enclosing Polygon. This discards inland echos and multi-path measurements. Additionally, an approach to detect bridges and dolphins is presented. The runtime of the mapping algorithm is less then 2.5 seconds. Thus, each new radar scan is integrated into the octomap.
1
Introduction
In the field of water robotics, the type of sensor used for navigation typically differs from the standard indoor or vehicle scenario: the sensors must cover a much larger distance range since the control of water vehicles requires a considerable reaction time. The most common example of such a sensor is the classical radar used on boats. A radar sensor’s range is much larger than the range of a laser range finder while being insensitive to such environmental influences as weather and lighting conditions. In principle, a radar sensor can be used to acquire a dynamic map of the surrounding seascape. Although one could use static maps of the shore instead, these maps may not represent environmental changes. For example an anchoring ship needs to be inserted into the map on one day, while on the next it may have moved on and the map needs to be updated accordingly. This paper presents an algorithm to provide a dynamic map of the environment of a boat using a noisy radar sensor. The position is acquired from GPS, thus this paper describes a pure mapping algorithm, named Free Space Octree Mapping (FSOM). It extracts one polygon out of the radar image. With the probabilistic managing of the extracted polygon in the octomap framework as presented in [WHB+ 10], the shores of Lake Constance are mapped. Furthermore, dolphins are classified and inserted into the created map. Bridges are detected at runtime. The next section presents related work. Section 3 describes the FSOM approach and the detection of bridges and dolphins. Section 4 presents the mapping results. Section 5 concludes.
2
Related Work
The occupancy grid approach offers a strong mathematical framework to update the map accordingly to new sensor information. Probabilistic occupancy grids are a common and well-proven concept used for robot mapping. However, huge environments may not be modeled with sufficient accuracy, due to high memory consumption of the grid. A probabilistic quadtree has been presented in [KGU04] for variable resolution mapping of large environments. With this approach, a certain balance between a high resolution map and low memory consumption is achieved. In [WHB+ 10] one dimension has been added resulting in a probabilistic octree. This framework is called octomap and is used in the FSOM approach. In [Foe99] it has been shown that occupancy grids can be used for incorporating noisy radar readings. There, the radar sensor was stationary. [FBBW01] described a radar sensor model for occupancy grids and the integration of the measurements into a 3D grid. Again, the sensor was stationary, sweeping only on one axis to construct the 3D map. Each grid cell stored a value representing the probability if this cell is occupied or free. This approach is based on a rigorous probabilistic formulation for updating the occupancy grid which is computationally expensive. In [Ger01] different approaches to autonomous river mapping with a fused sensor approach of radar, laser and camera stereo systems were presented. However, only the first radar echo was used, resulting in possible discontinuities of the extracted shore line. Different mapping approaches were discussed, such as occupancy grids or a polygonal extraction approach. The FSOM approach presented in this paper is based on this first radar echo approach, however the shortcoming of discontinuities in the shore line is overcome. The polygonal maps used in the FSOM approach were also described in [Ger01].
3
Free Area OcTree Mapping
Only the area which is safe for navigation is extracted from the radar image. This area is limited by the detected echoes in the radar image, which enclose the current vessel’s position. The border of this area is extracted as a polygon. Everything outside this polygon is assumed to represent land or obstacles. We refer to this polygon as Water Enclosing Polygon (WEP). Extracting the WEP provides a number of advantages: – Free space is clearly separated from the occupied area. – Since the polygon is closed, it can be extracted with a simple line following algorithm. – Inland echoes are dismissed right from the beginning. – Inaccurate measurements are ignored (e. g. behind bridges). In order to extract the WEP, a breadth-first search as presented in [Cor01] is started at the boat’s position in the center of the image. After the breadth-first search, the free area is stored in an image as foreground pixels. This image is then copied to another
Rhine, not extracted as polygon
Dolphins of a public swimming bath
Bridges
(a)
Holes of polygon
(b)
(c)
Fig. 1. Processing of the radar image to obtain the WEP: (a) radar image of the Rhine with the free area pixels around the boat marked in grey; (b) dilated water area; (c) the dilated water area is subtracted from the water area and the polygon is built by following its perimeter. The resulting WEP is shown with a border, the holes are drawn in grey.
image and subjected to a morphological dilation operation. The previous image is then subtracted from the dilated image, resulting in the perimeter of the WEP. The perimeters of obstacles within the water area are also obtained in this step. The perimeters are converted to closed polygons by standard line following. In a last step, the polygon, which encloses all other polygons is determined. This polygon represents the border of the WEP. The other polygons are added to the WEP as holes. The steps taken to extract the WEP are shown in Figure 1. Since bridges cannot be discriminated from other obstacles in the radar image without additional a priori knowledge, we extract only the WEP directly enclosing the boat from every radar image, even if the image contains other polygons representing water. If the WEPs are directly inserted into the octomap, the resulting shore lines are often not continuously connected. Therefore, the WEP is dilated five times and combined with the raw radar image using the AND operator before it is inserted. The resulting WEP has a broader border while the inner border retains exactly the same shape as in the raw radar image.
3.1
Octomap
A WEP is described as a set of points, representing the border. It contains additionally for each hole another set of points, describing its inner borders. To insert such a WEP into the octomap, these points are treated as point cloud, with the vessel’s position within the WEP as sensor origin. Internally, each point in the cloud is traversed and inserted separately. A line is computed from the sensor origin to the inserted point. The probability of being occupied for the line end point is increased accordingly to a sensor model. All nodes on the line are assumed to be free leading to a decreased occupation probability according to the sensor model. The sensor model for the radar is assumed to have a 90% hit rate and a false alarm rate of 30%. These values were determined experimentally.
3.2
Bridge and Dolphin Detection
The mapping procedure becomes problematic when the boat passes under a bridge. Here, the GPS coverage is disturbed, as well as the on-board compass, which may be due to the metallic bridge construction. Furthermore, dolphins appear to grow with increasing distance in the radar image due to the aspect angle and the opening angle of the beam. This results in large elliptic echoes which do not correspond to their true size. In contrast, dolphins are detected very well as circles in close-up range. Dolphins are detected well up to a distance of 40m. These measurements are inserted into a second octomap or layer. Regions of connected foreground pixels appear as blobs in the radar image. Since dolphins are characterized as small, circular blobs, a pattern recognition algorithm is used to identify these objects. In a first step, the algorithm is trained with different sample images, each containing an exemplary dolphin. On these samples, the connected foreground region representing the blob is computed by the run length algorithm of [JKS95]. The shape of the resulting blobs is represented by the tree central moments [FSZE09] computed up the the second order. Finally, to create the dolphin class, the arithmetic mean and variance are computed from all moments. While mapping, the blobs are extracted from the second layer and passed to the recognition routine. There the blobs are analyzed according to the following criteria: – Size: Small blobs are candidates for dolphins, large blobs for bridges. – Path Intersection: If the vessel’s path crossed the blob, the blob is assumed to be a bridge. – Location: If a larger blob contains the origin or the beginning of a new path, it is assumed to be an anchoring place and consequently removed from the list of candidate blobs for bridges. For the dolphin candidates the central moments are computed as shape descriptors from which we calculate the Mahalanobis distance to the mean of the training images of the dolphins. If the Mahalanobis distance is smaller than 11.34 (corresponding to a c 2 value for three degrees of freedom and an error probability of 1%), we classify the blob as dolphin. Since we detect bridges at run-time, we can automatically switch off the insertion of radar images while passing under a bridge which considerably improves mapping quality. In open waters, we cannot detect the shore line in all directions around the vessel due to the limited range of our radar. In these cases, we insert a line of open water into the octomap ending at the maximal range of the sensor. The final polygons extracted from the octomap are obtained with the same algorithm used to extract the WEP from the radar images.
4
Experimental Results
The FSOM approach suffers from the low angular resolution of the radar and aspect angle issues for targets at a far distance. To obtain acceptable mapping results, the radar
range was limited to 200m. More accurate results can be obtained by decreasing the range to 100m. In Figure 2 (a) the mapped entrance of the Lake Constance from the Rhine (black) is compared against a given polygonal map 1 . (yellow). The polygonal map contains the pillars of bridges. The radar detects bridges at runtime, but pillars are neither detected nor inserted into the map. The measured shore lines are within few meters from the polygonal shore lines. In Figure 2 (b) the map is validated near the harbor. The harbor walls provide large echos, which results in a broader wall than the polygonal map provides. However, the harbor entrance and the inside of the harbor are mapped with sufficient accuracy for autonomous navigation. The area where the paddleboat rent is located is not mapped, see (1) in Figure 2 (b). This area is of no navigational interest, since it is very unlikely that the vessel is navigating there.
(1)
(a)
(b)
Fig. 2. A comparison of the radar map (black) with a range of 200m against a polygonal map (yellow) of the Lake Constance. In (a) the entrance to the lake from the Rhine is shown. In (b) the mapped area near the harbor is shown.
Runtime measurements have been done on a MacBook Pro with a 2.53 GHz Intel Core 2 Duo processor, 4GB DDR3 memory and running Mac OS X. The average runtimes are for a cruise on the Lake Constance for a range of 200m 667ms and for 100m 703ms. Since a radar image is provided every 2.5 seconds, the algorithm works fast enough to integrate online each radar scan into the octomap. A map with an area of approx. 1km ⇥ 1km needs less than 1MB disc storage.
5
Conclusion
Runtime measurements show that the radar images can be processed in real-time. Dynamic obstacles are ignored by the mapping process. These dynamic objects have not been measured often enough at the same location so that their likelihood for being an obstacle stays remains small which finally makes these objects vanish from the map 1
Available at http://www.bodensee-navigationskarte.scbh.at/
with increasing measurement time. Even though the provided map from the FSOM algorithm is currently not as accurate as the existing polygonal map of Lake Constance, it provides an area safe for autonomous navigation (with the exception of bridge pillars). In particular, the navigable ship passage as marked by the dolphins was represented accurately in the FSOM map. In future work, the detection of bridge pillars will be investigated further as this is needed to model the drivable connection between two WEPs. A further improvement of mapping accuracy could be achieved by the modeling of the vessel’s inaccurate location. For instance, when inserting a measurement into the octomap, the surrounding nodes can be updated with a gaussian distribution according to the accuracy of the location measurements.
References [Cor01] T.H. Cormen. Introduction to algorithms. The MIT press, 2001. [FBBW01] A. Foessel-Bunting, J. Bares, and WL Whittaker. Three-dimensional map building with mmw radar. In Proceedings of the International Conference on Field and Service Robotics, RCA Halme and E. Prassler, Eds., Helsinki, Finland, 2001. [Foe99] A. Foessel. Scene modeling from motion-free radar sensing. Variations, 3:2, 1999. [FSZE09] J. Flusser, T. Suk, B. Zitov, and Inc Ebrary. Moments and moment invariants in pattern recognition. Wiley Online Library, 2009. [Ger01] Thomas Gern. Automatische Flußkartengenerierung. PhD thesis, University Stuttgart, 2001. [JKS95] R. Jain, R. Kasturi, and B.G. Schunck. Machine vision, volume 5. McGraw-Hill New York, 1995. [KGU04] G.K. Kraetzschmar, G.P. Gassull, and K. Uhl. Probabilistic quadtrees for variableresolution mapping of large environments. In Proceedings of the 5th IFAC/EURON symposium on intelligent autonomous vehicles. Citeseer, 2004. [WHB+ 10] K.M. Wurm, A. Hornung, M. Bennewitz, C. Stachniss, and W. Burgard. Octomap: A probabilistic, flexible, and compact 3d map representation for robotic systems. In Proc. of the ICRA 2010 workshop on best practice in 3D perception and modeling for mobile manipulation, volume 2, 2010.
