Speed and torque optimization of a two-module vibration-driven system with unbalanced rotors

Selecting resonance parameters alone does not establish an efficient operating regime for a vibration-driven robot. This numerical study formulates the joint optimization of mean transport speed and combined root-mean-square drive torque for two sliding modules with unbalanced rotors. A hybrid dry-friction model includes normal-load modulation and inverse rotor torques. Analytical contact-capacity and torque bounds constrain six dimensionless design variables. A reproducible search is checked using an independent event-driven solver. For an illustrative 0.55 kg system, a 9 mN m torque-budget design increases mean speed from 0.0641 to 0.1336 m/s while reducing RMS torque by 14.3 %. The highest-speed design found reaches 0.4078 m/s at 30.95 mN m. The results distinguish contact admissibility, resonance tuning and drive loading; all reported gains concern the stated numerical model and parameter bounds.