Multi-Legged Robot BAM Servo Actuator & Battery Voltage Sag Calculator

Stance support is approximated by $N_{stance}=\max(1,N_{legs}d)$. Weight per stance leg times horizontal reach and the dynamic factor gives joint torque demand. Total torque is multiplied by 1.45 for the user's assumed multi-joint load; the empirical voltage-drop gain gives a bus voltage limited to at least 75% of nominal. The output-shaft DC motor approximation gives $\tau=\max[0,(k_t/R)(d_{PWM}V_{eff}-k_e\dot q)]$. Subtract the specified Coulomb/Stribeck term and 4% of electromechanical torque; compare with required torque.

The coefficients 1.45, 0.75, 0.035 N·m, 0.025 N·m, 0.15 rad/s and 4%, plus the default actuator and battery parameters, are supplied by the user and have not been validated against hardware. The voltage-drop gain is an empirical V/(N·m) parameter, not internal resistance in ohms. Mean stance legs may be fractional; contact timing, uneven foot loading, multi-joint kinematics, regenerative current and motor/controller current limits are omitted. The motor constants must refer to the same output shaft and consistent current/voltage convention. The provided friction expression is an even-in-speed torque magnitude, not a signed friction-force law. The torque margin is not a thermal safety factor; no winding temperature or sustained stall heating is calculated.

Preliminary steady operating-point screening within the input ranges only. The 75% voltage floor is a stipulated cap on computed sag, not evidence the battery can sustain that voltage. A SAFE label indicates only the specified instantaneous torque ratio, not push-recovery performance or structural safety.