Module racing_mppi_powertrain 

Reference-free racing MPPI with a motor-lag and battery-sag powertrain.

This deepens crate::racing_mppi_motor one more level: between the commanded rotor thrusts and the rigid-body physics it inserts a powertrain with two unmodeled-by-the-planner effects that every real racing quad has.

1. First-order motor lag. A rotor cannot change thrust instantly; the actual thrust tracks the command through a first-order spin-up lag with time constant motor_tau. Aggressive attitude flicks are therefore smeared in time — the torque the body actually feels lags the command.
2. Battery sag. The available per-rotor thrust ceiling is not constant. It droops instantaneously with electrical load (internal resistance) and permanently as the pack’s state of charge falls over the run. A drone that flies hard early has less authority late in the race.

The powertrain is built by composition: it reuses MotorQuadParams::step verbatim for the translational and rotational physics and only adds the actuator front-end (lagged rotor thrusts plus a battery state). With the PowertrainParams::ideal constructor — zero lag, no discharge, no sag — it reduces exactly to the motor-level model, which is the baseline the benchmark compares against.

• PowertrainState wraps a MotorQuadState with the actual (lagged) rotor thrusts and the battery state of charge.
• PowertrainParams holds the base MotorQuadParams plus the lag, discharge, and sag coefficients, and exposes PowertrainParams::step.
• simulate_powertrain_race drives the powertrain-unaware MotorMppiController (which plans assuming ideal actuators) through the real powertrain and reports PowertrainLapReport, adding battery and ceiling-saturation metrics. The honest result is how much an idealized plan costs when it meets a laggy, sagging powertrain.
• PowertrainMppiController is the powertrain-aware answer: it rolls candidates out through PowertrainParams::step, so it plans within the deliverable authority and conserves charge for later gates. simulate_powertrain_race_aware runs it through the same closed loop.
• ChargeBudget adds an explicit energy term to the aware controller, penalizing below-reserve current draw so it can trade lap progress for charge held back; simulate_powertrain_race_budgeted runs it.
• PowertrainParams::with_recovery adds a relaxation overpotential so the terminal voltage (and thus the thrust ceiling) recovers when the load eases, even as the state of charge only ever falls.

Structs

ChargeBudget

Powertrain-aware MPPI controller.

PowertrainLapReport

Lap-progress, attitude, and powertrain (lag + battery) metrics.

PowertrainMppiController

PowertrainParams

Powertrain parameters layered on top of the base motor model.

PowertrainState

State of the powertrain-level quadrotor.

Functions

simulate_powertrain_race

Drive the powertrain-unaware MPPI controller through the real powertrain.

simulate_powertrain_race_aware

Drive the powertrain-aware MPPI controller through the real powertrain.

simulate_powertrain_race_budgeted

Drive a charge-budgeted powertrain-aware controller through the powertrain.