Bilateral teleoperation of dual-arm mobile manipulators presents considerable challenges. These include increased kinematic redundancy, coordination complexity, and sensitivity to time-varying communication delays. Most existing approaches control each arm independently using leader position-based mappings; however, the teleoperation of mobile dual-arm systems mechanically coupled through an articulated torso remains largely unexplored. Unlike previous studies that primarily emphasize controller tuning, this work emphasizes the critical role of command mapping design in achieving effective teleoperation. Specifically, it analyzes a coupled rate/nonlinear-position mapping strategy that enables coordinated motion in a torso-equipped dual-arm mobile manipulator operated through a dual-leader haptic interface. The proposed framework extends existing single-arm teleoperation schemes by introducing a coupled reference generation mechanism, where the reference for the secondary arm depends on both the position of the secondary leader and the rate-position-type reference of the primary arm. A two-stage stability analysis, based on the Lyapunov-Krasovskii criterion and numerical simulations, is conducted to determine the parameter conditions required to ensure bounded coordination errors in the presence of time-varying communication delays. Preliminary human-in-the-loop tests in dual-arm pick-and-place tasks support the theoretical findings and demonstrate a clear dependence of motion stability on the structure of the command mapping. The results provide foundational insights into the joint optimization of control and mapping strategies and offer practical guidelines for advancing teleoperation in complex, real-world scenarios.
