Energy dissipation and operating time analysis of a vibro-impact capsule robot powered by lithium battery under PWM control

This paper investigates energy dissipation and operating time of a vibro‑impact capsule robot powered by a compact LIR1040 lithium battery under pulse‑width modulation (PWM) excitation. An improved mathematical model incorporating coil inductance and a nonlinear excitation force is developed and validated against experiments. Numerical simulations and laboratory tests quantify losses from viscous damping, Coulomb friction, and impact events, and show their dependence on excitation frequency and duty cycle. Analysis of hysteresis loops of impact force versus relative displacement and relative velocity clarifies how collision dynamics convert mechanical energy into irreversible loss. Higher frequencies generally favor forward locomotion with reduced impact losses, while lower frequencies produce larger instantaneous displacements and faster energy dissipation. Comparison of theoretical operating time based on battery capacity with operating time accounting for voltage decay reveals that voltage drop substantially shortens effective operation. Practical PWM tuning guidelines are provided to balance locomotion efficiency and battery endurance for biomedical and industrial applications.