Design and analysis of a quadruped wheel-legged robot based on virtual equivalent parallel mechanism theory

Wheel-legged robots represent a promising hybrid solution for locomotion in complex and unstructured environments. However, the strong coupling between terrain-adaptive limb motion and omnidirectional wheel-ground interaction poses challenges for kinematic modeling and configuration design. Based on the Virtual Equivalent Parallel Mechanism (VEPM) theory, this paper establishes a systematic framework for the structural synthesis and locomotion performance optimization of a quadruped wheel-legged robot. First, a number-synthesis method is used to enumerate candidate limb topologies, and a spectral-geometric isomorphism identification method is introduced to remove redundant topological configurations in highly symmetric mechanism graphs. Then, the robot-terrain interaction is formulated as a parallel mechanism with a non-coplanar virtual moving platform, leading to a unified kinematic model. Four global performance indices, namely workspace volume, kinematic dexterity, static rollover stability, and static stiffness, are derived to evaluate the locomotion quality. The optimization results show a significant improvement in the Comprehensive Performance Index (CPI). This study provides a unified theoretical foundation for the design and analysis of the quadruped wheel-legged robot.