A novel curvature-based method for analyzing the second-order immobility of frictionless grasp

Robotica ◽  
2011 ◽  
Vol 30 (4) ◽  
pp. 613-625 ◽  
Author(s):  
Chen Luo ◽  
LiMin Zhu ◽  
Han Ding
Keyword(s):  
Distance Function ◽  
Taylor Expansion ◽  
Second Order ◽  
Nonlinear Programming Problem ◽  
Signed Distance Function ◽  
Numerical Examples ◽  
Signed Distance ◽  
Differential Motion ◽  
Negative Condition ◽  
Differential Properties

SUMMARYThis paper presents a new method to analyze frictionless grasp immobility based on defined surface-to-surface signed distance function. Distance function's differential properties are analyzed and its second-order Taylor expansion with respect to differential motion is deduced. Based on the non-negative condition of the signed distance function, the first- and second-order free motions are defined and the corresponding conditions for immobility of frictionless grasp are derived. As one benefit of the proposed method, the second-order immobility check can be formulated as a nonlinear programming problem. Numerical examples are used to verify the proposed method.

Registration and integration of multiple depth images using signed distance function

2012 ◽  
Author(s):  
Daniel B. Kubacki ◽  
Huy Q. Bui ◽  
S. Derin Babacan ◽  
Minh N. Do
Keyword(s):  
Distance Function ◽  
Signed Distance Function ◽  
Signed Distance ◽  
Depth Images

A Workspace Limit Approach for Teleoperation Based on Signed Distance Function

2021 ◽  
Vol 6 (3) ◽  
pp. 5589-5596
Author(s):  
Gaofeng Li ◽  
Fernando Caponetto ◽  
Edoardo Del Bianco ◽  
Vasiliki Katsageorgiou ◽  
Ioannis Sarakoglou ◽  
...  
Keyword(s):  
Distance Function ◽  
Signed Distance Function ◽  
Signed Distance

Signed Distance Function based Geofencing for UAV Corridor

2022 ◽  
Author(s):  
Aashay A. Bhise ◽  
Stuti Garg ◽  
Ashwini Ratnoo ◽  
Debasish Ghose
Keyword(s):  
Distance Function ◽  
Signed Distance Function ◽  
Signed Distance

On the Convexity Correction Approximation in Pricing Volatility Swaps and VIX Futures

2018 ◽  
Vol 14 (03) ◽  
pp. 383-401
Author(s):  
Song-Ping Zhu ◽  
Guang-Hua Lian
Keyword(s):  
Theoretical Analysis ◽  
Fourth Order ◽  
Taylor Expansion ◽  
Second Order ◽  
Approximation Technique ◽  
Third Order ◽  
Numerical Examples ◽  
Taylor Expansions ◽  
Vix Futures ◽  
Validity Condition

Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second-order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

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