docs(how-to-guides): add page about start delays

docs/how-to-guides/others/reducing-start-delays.md

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+# Reducing start delays on real vehicles
+
+In simulation, the ego vehicle reacts nearly instantly to the control commands generated by Autoware.
+However, with a real vehicle, some delays occur that may make ego feel less responsive.
+
+This page presents start delays experienced when using Autoware on a real vehicle.
+We define the start delay as the time between
+(a) when Autoware decides to make the ego vehicle start and
+(b) when the vehicle actually starts moving.
+More precisely:
+
+- (a) is the time when the speed or acceleration command output by Autoware switches to a non-zero value.
+- (b) is the time when the measured velocity of the ego vehicle switches to a positive value.
+
+## Start delay with manual driving
+
+First, let us look at the start delay when a human is driving.
+
+The following figure shows the start delay when a human driver switches the gear
+from _parked_ to _drive_ and instantly releases the brake to push the throttle pedal and make the velocity of the vehicle increase.
+
+![Manual driving delays](./images/start-delays/manual_driving.png)
+
+There are multiple things to note from this figure.
+
+- Brake (red): despite the driver instantly releasing the brake pedal,
+  we see that the measured brake takes around `150ms` to go from `100%` to `0%`.
+- Gear (orange): the driver switches gear _before_ releasing the brake pedal, but the gear is measured to switch _after_
+  the brake is released.
+- Throttle (green) and velocity (blue): the driver pushes the throttle pedal and the vehicle is measured to start moving around `500ms` later.
+
+## Filter delay
+
+To guarantee passenger comfort,
+some Autoware modules implement filters on the jerk of the vehicle, preventing sudden changes in acceleration.
+
+For example,
+the [`vehicle_cmd_gate`](https://autowarefoundation.github.io/autoware.universe/main/control/vehicle_cmd_gate/)
+filters the acceleration command generated by the controller
+and [was previously introducing significant delays](https://github.com/autowarefoundation/autoware.universe/pull/3385)
+when transitioning between a stop command where the acceleration is negative,
+and a move command where the acceleration is positive.
+Because of the jerk filter, the transition between negative and positive was not instantaneous and would take several hundreds of milliseconds.
+
+## Gear delay
+
+In many vehicles, it is necessary to change gear before first starting to move the vehicle.
+When performed autonomously, this gear change can take some significant time.
+Moreover, as seen from the data recorded with manual driving, the measured gear value may be delayed.
+
+In Autoware, the controller sends a stopping control command until the gear is changed to the _drive_ state.
+This means that delays in the gear change and its reported value can greatly impact the start delay.
+Note that this is only an issue when the vehicle is initially in the _parked_ gear.
+
+The only way to reduce this delay is by tuning the vehicle to increase the gear change speed
+or to reduce the delay in the gear change report.
+
+## Brake delay
+
+In vehicles with a brake pedal,
+the braking system will often be made of several moving parts which cannot move instantly.
+Thus, when Autoware sends brake commands to a vehicle,
+some delays should be expected in the actual brake applied to the wheels.
+
+This lingering brake may prevent or delay the initial motion of the ego vehicle.
+
+This delay can be reduced by tuning the vehicle.
+
+## Throttle response
+
+For vehicles with throttle control,
+one of the main cause of start delays is due to the
+[throttle response](https://en.wikipedia.org/wiki/Throttle_response) of the vehicle.
+When pushing the throttle pedal, the wheels of the vehicle do not instantly start rotating.
+This is partly due to the inertia of the vehicle,
+but also to the motor which may take a significant time to start applying
+some torque to the wheels.
+
+It may be possible to tune some vehicle side parameters to reduce this delay,
+but it is often done at the cost of reduced energy efficiency.
+
+On the Autoware side, the only way to decrease this delay is to increase the initial throttle
+but this can cause uncomfortably high initial accelerations.
+
+## Initial acceleration and throttle
+
+As we just discussed, for vehicles with throttle control, an increased initial throttle value can reduce the start delay.
+
+Since Autoware outputs an acceleration value, the conversion module
+[`raw_vehicle_cmd_converter`](https://autowarefoundation.github.io/autoware.universe/main/vehicle/raw_vehicle_cmd_converter/)
+is used to map the acceleration value from Autoware to a throttle value to be sent to the vehicle.
+Such mapping is usually calibrated automatically using the
+[`accel_brake_map_calibrator`](https://autowarefoundation.github.io/autoware.universe/main/vehicle/accel_brake_map_calibrator/accel_brake_map_calibrator/) module,
+but it may produce a low initial throttle which leads to high start delays.
+
+In order to increase the initial throttle, there are two options:
+increase the initial acceleration output by Autoware,
+or modify the acceleration to throttle mapping.
+
+The initial acceleration output by Autoware can be tuned in the
+[`motion_velocity_smoother`](https://autowarefoundation.github.io/autoware.universe/main/planning/motion_velocity_smoother/)
+with parameters `engage_velocity` and `engage_acceleration`.
+However, the [`vehicle_cmd_gate`](https://autowarefoundation.github.io/autoware.universe/main/control/vehicle_cmd_gate/)
+applies a filter on the control command to prevent too sudden changes in jerk and acceleration,
+limiting the maximum allowed acceleration while the ego vehicle is stopped.
+
+Alternatively, the mapping of acceleration can be tuned to increase the throttle corresponding to the initial acceleration.
+If we look at an example
+[acceleration map](https://github.com/tier4/autoware_individual_params/blob/main/individual_params/config/default/pacmod/accel_map.csv),
+it does the following conversion:
+when the ego velocity is `0` (first column), acceleration values between `0.631` (first row) and `0.836` (second row)
+are converted to a throttle between `0%` and `10%`.
+This means that any initial acceleration bellow `0.631m/s²` will not produce any throttle.
+Keep in mind that after tuning the acceleration map,
+it may be necessary to also update the
+[`brake map`](https://github.com/tier4/autoware_individual_params/blob/main/individual_params/config/default/pacmod/brake_map.csv).
+
+| default | _0_     | 1.39  | 2.78  | 4.17  | 5.56   | 6.94   | 8.33   | 9.72   | 11.11  | 12.5   | 13.89  |
+| ------- | ------- | ----- | ----- | ----- | ------ | ------ | ------ | ------ | ------ | ------ | ------ |
+| 0       | _0.631_ | 0.11  | -0.04 | -0.04 | -0.041 | -0.096 | -0.137 | -0.178 | -0.234 | -0.322 | -0.456 |
+| 0.1     | _0.836_ | 0.57  | 0.379 | 0.17  | 0.08   | 0.07   | 0.068  | 0.027  | -0.03  | -0.117 | -0.251 |
+| 0.2     | _1.129_ | 0.863 | 0.672 | 0.542 | 0.4    | 0.38   | 0.361  | 0.32   | 0.263  | 0.176  | 0.042  |
+| 0.3     | _1.559_ | 1.293 | 1.102 | 0.972 | 0.887  | 0.832  | 0.791  | 0.75   | 0.694  | 0.606  | 0.472  |
+| 0.4     | _2.176_ | 1.909 | 1.718 | 1.588 | 1.503  | 1.448  | 1.408  | 1.367  | 1.31   | 1.222  | 1.089  |
+| 0.5     | _3.027_ | 2.76  | 2.57  | 2.439 | 2.354  | 2.299  | 2.259  | 2.218  | 2.161  | 2.074  | 1.94   |