Structure-Control Co-Design via Dimensionality Reduction: A Waist-Towed Wheel-Legged Collaborative Carrier for Complex Terrains

In unstructured environments, human-robot collaborative carriers face coupled challenges in physical interaction, terrain adaptability, and energy efficiency. This paper presents a waist-towed wheel-legged collaborative carrier integrating a front active compliant wheeled leg with rear wheeled propulsion. A partitioned floating-base dynamics analysis shows that the structural geometry and impedance-control gains jointly affect the local pHRI-port response and ground-contact compliance. To quantify this effect, a range-normalized structure-control coupling index is introduced. Based on this coupling analysis, a dimensionality-reduction-driven structure-control co-design framework is developed. Global sensitivity analysis identifies a compact core subspace, while the remaining low-sensitivity dimensions are anchored at a feasible multi-objective knee point. NSGA-II is then applied to simultaneously optimize the retained structural and control variables. Over a 44 m composite unstructured terrain, the selected 3D co-design solution reduces total energy consumption by 36.7% under the nominal 2.0 m/s, 10 kg condition relative to the 8D full-space baseline, while maintaining comparable towing-channel force fluctuation. Additional no-load and 40 kg heavy-load cases are used as validation stress tests; under the tested 40 kg boundary condition, the co-optimized configuration maintains the payload-height band whereas the full-space baseline experiences severe payload-height loss. These results indicate that filtering weakly sensitive dimensions and simultaneously optimizing the dominant core variables can improve energy economy and robustness while maintaining comparable towing-channel force behavior in the reported simulations.