The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
A fast and robust GJK implementation for collision detection of convex objects
Journal of Graphics Tools
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Convex Optimization
Dynamic Force Distribution in Multifingered Grasping by Decomposition and Positive Combination
IEEE Transactions on Robotics
Fast Computation of Optimal Contact Forces
IEEE Transactions on Robotics
Distance Between a Point and a Convex Cone in -Dimensional Space: Computation and Applications
IEEE Transactions on Robotics
A general dynamic force distribution algorithm for multifingeredgrasping
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A Fast Procedure for Optimizing Dynamic Force Distribution in Multifingered Grasping
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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One of the fundamental problems in grasping and manipulation of an object by a multi-fingered robotic hand is the computation of contact forces to equilibrate the dynamic external wrench on the grasped object. This paper proposes a two-phase algorithm to calculate the contact forces in order to achieve maximum grasp stability, assuming there is no any slippage in the process of grasping. In the off-line phase, a nonsingular simplex set is obtained by the zone triangulation of the contact primitive wrench set in the wrench space, and the neighbors of the resultant simplexes are recorded by a neighbor-searching procedure. In the on-line phase, a specific simplex in which the required resultant wrench is located can find out rapidly since all neighbors of each simplex have been recorded before. The optimal contact forces can be obtained by the combination of the primitive forces corresponding to the vertices of this simplex. A numerical example shows the proposed algorithm takes a thousandth of the computation time exhausted by the sequential quadratic programming (SQP) or the straightforward bisection method with only a slight lost of optimality, and obtains better solution compared to the decomposition and positive combination (DPC) algorithm at the similar computation speed.