Finding Effective Force Targets for Two Dimensional Multifinger Frictional Gri

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Finding Effective Force Targets for Two Dimensional Multifinger Frictional Gri
Jacob T Schwartz
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One is to calculate n- 1 max min p, (n)x, « 1 = 1 where we have put p„^i(ji) = -e, and then find the smallest value of ft (or rather the infimum of all values of ji) for which this maximum is nonpositive. This can be done in exactly the same way as in the preceding section, at computational cost 0(n log^/i log log n) (or 0{n log'n)). However, this solution requires application of FIND-ji each time the exter- nal force-and-torque vector e changes, i. E. Once each control cycle, and is therefore ...prohibi- tive (even from a theoretical point of view). Alternative approaches are therefore desirable. These can involve (possibly costly) preprocessing before object manipulation begins, and then use the structures generated by preprocessing to find the optimal ji. And the balancing finger- force targets quickly during each control cycle.
This can be done as follows. Consider the family of convex cones C(jjl) spanned by the vectors p, (ji). These increase steadily with jx, from the minimum cone C(0).


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