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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 report on a new active, miniature bone-attached, robotic system including its design, high level and low level control, is given together with a description of the system implementation and first experimental use. The system is capable of preparing the bone cavity for an implant during joint arthroplasty procedures. Without loss of generality, the report describes the implementation of the system for a Patellofemoral Joint Replacement procedure. The system is image-free and all planning is performed intra-operatively in the robot coordinate system, eliminating the need for external tracking systems in the operating room. Experiments were conducted using the first robot prototype and the results supported the feasibility of the concept. The methodology which is presented can be modified to other orthopaedic procedures and could improve the results in terms of accuracy and operational time. Moreover, it enables minimally invasive procedures and use of the next generation of more anatomically shaped implants.

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