The hierarchical atlas

Abstract

With the CPU times of 4.7 ms and 175.8 ms, we have P = [00:0080 0:0023 0 0:0030 0 0:0449 0:0220 0 0:0359] T z max (0P ) = 0:5159 < 1:Hence, the grasp is force closure. V. CONCLUSION AND FUTURE WORKA shortcut is found to simplify Liu's ray-shooting based algorithm for force-closure test [4]. The optimal objective value of the LP problem (2) with respect to t = 0P is the ratio of d2 to d1 ; that is, z max (0P ) = d 2 =d 1 . If z max (0P ) < 1, then the grasp is force closure; otherwise, it is not. Consequently, we can skip the steps of computing Q, d1 , and d2 . Having the geometric insight into the maximum z max (0P ), we can apply it to optimal grasp planning as a force-closure index. As this work goes beyond the topic of the paper, it is decent to leave it for the future. ACKNOWLEDGMENTThe authors wish to thank the editors and the reviewers for fair ratings of this paper and helpful suggestions for revision. REFERENCES[1] J. K. Salisbury and B. Roth, "Kinematic and force analysis of articulated hands," ASME Abstract-This paper presents a new map specifically designed for robots operating in large environments and possibly in higher dimensions. We call this map the hierarchical atlas because it is a multilevel and multiresolution representation. For this paper, the hierarchical atlas has two levels: at the highest level there is a topological map that organizes the free space into submaps at the lower level. The lower-level submaps are simply a collection of features. The hierarchical atlas allows us to perform calculations and run estimation techniques, such as Kalman filtering, in local areas without having to correlate and associate data for the entire map. This provides a means to explore and map large environments in the presence of uncertainty with a process named hierarchical simultaneous localization and mapping. As well as organizing information of the free space, the map also induces well-defined sensor-based control laws and a provably complete policy to explore unknown regions. The resulting map is also useful for other tasks such as navigation, obstacle avoidance, and global localization. Experimental results are presented showing successful map building and subsequent use of the map in large-scale spaces.Index Terms-Concurrent mapping and localization, generalized Voronoi diagram, Kalman filtering, mobile robots, simultaneous localization and mapping (SLAM), topological maps.

A unified Bayesian framework for global localization and SLAM in hybrid metric/topological maps

“…Existing solutions typically rely on one of three map representations: obstacle-based grid maps or particle maps (Burgard et al 1996(Burgard et al , 1998Fox et al 1999b;Grisetti et al 2005;Eliazar and Parr 2003), featurebased metric maps (Smith et al 1990;Dissanayake et al 2001;Montiel et al 2006;Civera et al 2007;Tully et al 2008Tully et al , 2010Montemerlo et al 2002Montemerlo et al , 2003, and topological maps (Choset and Burdick 1995;Nourbakhsh et al 1995;Simmons and Koenig 1995;Cassandra et al 1996;Choset and Nagatani 2001;Dudek et al 1996;Tomatis et al 2002;Ranganathan et al 2006;De et al 2008;Kuipers and Byun 1991;Tully et al 2007;Lisien et al 2005;Blanco et al 2008Blanco et al , 2007Angeli et al 2008;Kouzoubov and Austin 2004). Arguably, the most efficient of the three is topological mapping, as it concisely represents an environment as a graph, whose vertices are interesting "places" and whose edges represent the paths between them (Kuipers and Byun 1991).…”

A Scalable Hybrid Multi-robot SLAM Method for Highly Detailed Maps

“…Given the individual strengths and shortcomings, researchers have tried to combine multiple representations in hybrid approaches [3][4][5][6][7]. These are potentially as scalable as topological approaches, and at the same time provide the same geometric detail as grid maps.…”

Voronoi-based space partitioning for coordinated multi-robot exploration

“…The aforementioned inefficiency and lack of flexibility of occupancy grids have motivated the use of alternative world representations based on polygonal models (e.g., [8], [10], [13]). In that case, the exploration algorithm is modified to deal with points and regions instead of cells, in some cases by modelling the free space as a graph of basic convex regions (e.g., trapezoids and triangles in [8], [10]), and in other cases by defining graphs of curves (roadmaps) contained in the empty space (e.g., [2], [13]).…”

“…In that case, the exploration algorithm is modified to deal with points and regions instead of cells, in some cases by modelling the free space as a graph of basic convex regions (e.g., trapezoids and triangles in [8], [10]), and in other cases by defining graphs of curves (roadmaps) contained in the empty space (e.g., [2], [13]). …”