Structure-Preserving Quantum Circuit Architectures for Robot Kinematics

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.

Robotic arms capable of traversing arbitrary spatial paths, especially in highly obstructed workspaces, are highly desired across several industries. Quaternion-joints have recently empowered a specific class of robotic arms -- cable-driven redundant manipulators -- beyond its prior capabilities. Specifically, quaternion-joints reduce the number of required motors per degree of freedom, paving the way for more compact solutions.An ongoing challenge is that the complexity of the kinematic model of quaternion joints challenges a priori decisions on manipulator configurations and imposes higher computational demands on the control system and its non-linearities amplify all discrepancies between design and physical artifact arising from fabrication imprecision. Here we show a that a 4-segment, 8-joint manipulator can achieve a broader workspace than extant configurations, at lower hardware cost, and that Residual Reinforcement Learning outperforms extant state-of-the-art methods -- specifically, the FABRIK algorithm -- on the control of such manipulator. Our results show that this configuration is more workspace-effective than prior designs, and that Residual Reinforcement Learning outperforms FABRIK by three orders of magnitude on positional and orientational accuracy, effecting precise control of the novel 4-segment, 8-joint manipulator. Additionally, the control implementation is simpler: we describe the complete FABRIK process for control and corresponding learning implementation. Our methodology is applicable to the design of new systems, providing designers with further tools for the development of this class of manipulators and corresponding control systems for novel configurations.

Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce \emph{quantum topological data encoding} (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.