Combinatorial Optimization of Robotic Hand Kinematic Structures Using a Potential-Dexterity-Based QUBO Formulation

Abstract

Robotic hand kinematic design involves combinatorial selection among multiple finger structures whose performance depends on both individual kinematic characteristics and inter-finger interactions. This study presents a potential-dexterity-based quadratic unconstrained binary optimization (QUBO) formulation for combinatorial optimization of robotic hand kinematic structures. Potential dexterity-related metrics were evaluated through kinematic analysis and encoded into a 27-variable QUBO problem incorporating individual finger performance, thumb-to-finger workspace-overlap interactions, one-hot selection constraints, and pairwise structural compatibility. Exhaustive evaluation of the design space established a reference optimum and enabled direct validation of the formulated objective. Discretization sensitivity analysis showed that the selected design remained unchanged across the tested joint-space sampling intervals and at a finer workspace voxel resolution, while sensitivity was observed under coarse voxelization. Simulated annealing consistently recovered the reference optimum at higher sampling counts, and direct execution on D-Wave quantum annealing hardware also recovered the reference optimum under all tested sampling conditions. These results demonstrate that the proposed formulation provides a common QUBO representation for constrained robotic hand kinematic structure selection and enables evaluation using exhaustive, classical annealing, and quantum annealing approaches.

arXiv commentThis manuscript has been submitted for possible publication. 15 pages, 5 figures