In the area of mobile robotics, optimal robot positions are required for effi- cient exploration of unknown environments. In order to apply information gain driven exploration, metric grid maps are used. Several mapping methods that integrate range data into a voxelmap have been presented (Thrun et al., 2005). In contrast to a stationary robot, a mobile robot needs to build a map of its environment and localize itself within the map by active perception before a next-best robot position can be planned. This problem is known as simul- taneous localization and mapping (SLAM) and has been addressed by many
2.4. MAPPING AND EXPLORATION 25 researchers (González-Baños and Latombe, 2002; Durrant-Whyte and Bailey, 2006; Nüchter and Hertzberg, 2008). The two key solutions to solve the SLAM problem make use of the extended Kalman filter (Dissanayake et al., 2001) and the Rao-Blackwellized particle filters (Montemerlo et al., 2002).
However, SLAM does not consider the problem of where the robot should go next. This problem is similar to the NBV problem (see previous section), but aims at exploration of unknown environments and not modeling of unknown objects. In (González-Baños and Latombe, 2002), safe-regions for a mobile robot are defined within the current map. A next robot position is iteratively selected within the safe region, which maximizes the information gain consid- ering an overlap with the global map. The frontier-based approach presented by Yamauchi (1997), is a well-known concept which explores the environment by planning robot positions on the frontier between free and unknown space. This is similar to the occlusion edge principle (Maver and Bajcsy, 1993) for object modeling. The frontier-based approach has been extended by several researchers (González-Baños and Latombe, 2002; Freda and Oriolo, 2008) and used in a variety of applications such as in (Blodow et al., 2011) for planning positions of a mobile robot in order to explore a complete room. In the work of Oriolo et al. (2004), the Sensor-based Random Tree (SRT) method, a sensor- based version of the rapidly-exploring random tree (RRT) method (Kuffner and LaValle, 2000) used for path planning, is introduced. SRT represents a roadmap of explored areas with local safe regions associated to each node, providing an estimate of the surrounding free space for each configuration. However, the SRT method only works for disc shaped robots. The next robot positions are itera- tively chosen by sampling random directions from the current configuration and selecting a new configuration which is at least a certain distance away and is still within the safe region. Here, only a 2D map is obtained and the problem of localization is not considered. In (Low and Lastra, 2006), 3D models of larger environments are obtained using a mobile platform with a 360 degree scanner. The authors introduce a hierarchical NBV algorithm by grouping neighboring views into view volumes and neighboring surface points into surfaces patches. Then they evaluate the view metric for the groups and perform a subdivision (if required) which finally leads into an NBV. Although here a 3D map of the en- vironment is obtained, it is assumed that the robot always moves on one level. Therefore, the viewpoint space is only a 3DOF problem in contrast to NBV planning for object modeling. Therefore, these approaches do not seem to work in feasible time if a 6DOF problem is given.
(a) Table scene (b) Outdoor map
Figure 2.4: Probabilistic 3D representations are used in a variety of applications such as exploration of table scenes with industrial robots (left) or mapping of larger outdoor environments with mobile robots (right). Image credits: a) (Suppa, 2008) b) (Hornung et al., 2013)
or manipulate objects on a table. Therefore, for complex robotic tasks, local- ization within a 3D map of the environment is required, which is referred to by 6D SLAM (Nüchter, 2009). Thus, efficient 3D representations and meth- ods to update the model by sensing have been developed in the field of SLAM and exploration. An efficient approach to 3D mapping, the OctoMap, has been proposed by Wurm et al. (2010) and advanced by Hornung et al. (2013), who also give a more detailed overview of the literature. The map is a volumetric model based on octrees and uses probabilistic occupancy estimation. For details on octree data structures see (Samet, 1990). A very similar mapping approach has been proposed earlier in the context of work cell exploration with an in- dustrial robot (Suppa, 2008). In contrast to OctoMap, distant-dependent noise is considered during ray tracing. In the work of Suppa, different probabilistic update strategies for beam-based mapping relying on depth measurements are compared. The necessity to consider sensor uncertainty is demonstrated and a probabilistic approach which interprets the sensor data is utilized. Well-known 2D-mapping techniques as in (Thrun et al., 2005) are introduced to 3D. Suppa gives a detailed survey of update-strategies and their application in the con- text of autonomous robot work cell exploration. Furthermore, a preliminary approach how to integrate NBV planning for exploration and 3D modeling is shown. Suppa proposes to use a Bayesian update rule for voxels. The work of Potthast and Sukhatme (2011) shows that a Bayesian space update proved to be faster than using a simple approach for exploration of cluttered scenes. The authors utilized a humanoid robot and an eye-in-hand camera in their evalua- tion.
Probabilistic 3D volumetric models are applied in various fields such as local- ization, mapping, 3D modeling and exploration. For instance, the models are used for exploration of a table scenes with an industrial robots (see Fig. 2.4(a)) or mapping of larger outdoor environments with mobile robots (see Fig. 2.4(b)).