A QUBO Formulation Framework for Kinematic Structure-Based Robot Design Optimization: A Robotic Hand Case Study

TL;DR

This paper introduces a quadratic unconstrained binary optimization framework for robot design, demonstrated on a robotic hand, enabling classical and quantum annealing methods to optimize kinematic structures.

Contribution

It presents a novel unified quadratic formulation for robot design optimization that integrates classical evaluation and quantum annealing compatibility.

Findings

Feasible robotic hand designs satisfying constraints were identified.

Quantum annealing applied successfully to the design problem.

Objective-value range narrows with increased reads, indicating solution stability.

Abstract

This paper presents a quadratic unconstrained binary optimization-based formulation framework for robot design optimization using kinematic structure-level evaluation metrics. In the proposed framework, classical computation is used to evaluate design-dependent metrics while the resulting combinatorial selection problem is formulated in a structure compatible with quantum annealing-based optimization. A robotic hand is adopted as a representative case study, as its performance is determined by both the individual kinematic characteristics of each finger and interaction terms. The proposed formulation incorporates individual design rewards, overlap workspace interactions, one-hot constraint, and structural dependency penalties into a unified quadratic model. A 27-variable robotic hand design problem is constructed, and simulated annealing is used as a classical baseline to verify the feasibility of the formulation. Quantum annealing is further performed to examine the applicability of the proposed formulation to annealing-based hardware execution. The results show that feasible design combinations satisfying both one-hot selection and pairwise constraints can be obtained, with the observed objective-value range becoming narrower as the number of reads increases. In addition, the formulation process is discussed for other robotic systems. The proposed framework provides a generalized approach for transforming kinematic structure-based robot design problems into combinatorial optimization problems.