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PJ Reiniger
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Peter Johnson
Peter Johnson
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tools/sysid/docs/data-collection.md
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tools/sysid/docs/data-collection.md
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# Data Collection
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This document details how data must be sent over NetworkTables for accurate data collection. Note that the data format has changed from what the old [frc-characterization](https://github.com/wpilibsuite/frc-characterization) tool used to generate.
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## NetworkTables Data Entries
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Here is a list of the NT entries that are used to send and collect data between sysid and the robot program:
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| NT Entry | Type | Description |
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| --------------------------------------| -------- | -------------------------------------------------------------------------------------------------------------------------------------------------- |
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| `/SmartDashboard/SysIdTelemetry` | `string` | Used to send telemetry from the robot program. This data is sent after the test completes once the robot enters the disabled state. |
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| `/SmartDashboard/SysIdVoltageCommand` | `double` | Used to either send the ramp rate (V/s) for the quasistatic test or the voltage (V) for the dynamic test. |
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| `/SmartDashboard/SysIdTestType` | `string` | Used to send the test type ("Quasistatic" or "Dynamic") which helps determine how the `VoltageCommand` entry will be used. |
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| `/SmartDashboard/SysIdRotate` | `bool` | Used to receive the rotation bool from the Logger. If this is set to true, the drivetrain will rotate. It is only applicable for drivetrain tests. |
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## Telemetry Format
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There are two formats used to send telemetry from the robot program. One format is for non-drivetrain mechanisms, whereas the other is for all drivetrain tests (linear and angular). All timestamps must be in seconds.
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### Non-Drivetrain Mechanisms
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`timestamp, voltage, position, velocity`
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Example JSON:
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```json
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{
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"fast-backward": [
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[
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timestamp 1,
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voltage 1,
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position 1,
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velocity 1
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],
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[
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timestamp 2,
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voltage 2,
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position 2,
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velocity 2
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]
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],
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"fast-forward": [
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[
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timestamp 1,
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voltage 1,
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position 1,
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velocity 1
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],
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[
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timestamp 2,
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voltage 2,
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position 2,
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velocity 2
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]
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],
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"slow-backward": [
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[
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timestamp 1,
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voltage 1,
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position 1,
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velocity 1
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],
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[
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timestamp 2,
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voltage 2,
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position 2,
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velocity 2
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]
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],
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"slow-forward": [
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[
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timestamp 1,
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voltage 1,
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position 1,
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velocity 1
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],
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[
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timestamp 2,
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voltage 2,
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position 2,
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velocity 2
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]
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],
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"sysid": true,
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"test": "Simple",
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"units": "Rotations",
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"unitsPerRotation": 1.0
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}
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```
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Supported test types for the "test" field in this data format include "Arm",
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"Elevator", and "Simple". Supported unit types include "Meters", "Feet",
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"Inches", "Radians", "Rotations", and "Degrees".
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### Drivetrain
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`timestamp, l voltage, r voltage, l position, r position, l velocity, r velocity, angle, angular rate`
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Note that all positions and velocities should be in rotations of the output and rotations/sec of the output respectively. If there is a gearing between the encoder and the output, that should be taken into account.
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Example JSON:
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```json
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{
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"fast-backward": [
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[
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timestamp 1,
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l voltage 1,
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r voltage 1,
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l position 1,
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r position 1,
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l velocity 1,
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r velocity 1,
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angle 1,
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angular rate 1
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],
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[
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timestamp 2,
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l voltage 2,
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r voltage 2,
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l position 2,
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r position 2,
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l velocity 2,
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r velocity 2,
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angle 2,
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angular rate 2
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]
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],
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"fast-forward": [
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[
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timestamp 1,
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l voltage 1,
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r voltage 1,
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l position 1,
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r position 1,
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l velocity 1,
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r velocity 1,
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angle 1,
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angular rate 1
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],
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[
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timestamp 2,
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l voltage 2,
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r voltage 2,
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l position 2,
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r position 2,
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l velocity 2,
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r velocity 2,
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angle 2,
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angular rate 2
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]
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],
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"slow-backward": [
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[
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timestamp 1,
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l voltage 1,
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r voltage 1,
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l position 1,
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r position 1,
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l velocity 1,
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r velocity 1,
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angle 1,
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angular rate 1
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],
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[
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timestamp 2,
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l voltage 2,
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r voltage 2,
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l position 2,
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r position 2,
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l velocity 2,
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r velocity 2,
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angle 2,
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angular rate 2
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]
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],
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"slow-forward": [
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[
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timestamp 1,
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l voltage 1,
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r voltage 1,
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l position 1,
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r position 1,
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l velocity 1,
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r velocity 1,
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angle 1,
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angular rate 1
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],
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[
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timestamp 2,
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l voltage 2,
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r voltage 2,
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l position 2,
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r position 2,
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l velocity 2,
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r velocity 2,
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angle 2,
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angular rate 2
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]
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],
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"sysid": true,
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"test": "Drivetrain",
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"units": "Rotations",
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"unitsPerRotation": 1.0
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}
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```
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Supported test types for the "test" field in this data format include
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"Drivetrain" and "Drivetrain (Angular)". Supported unit types include "Meters",
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"Feet", "Inches", "Radians", "Rotations", and "Degrees".
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120
tools/sysid/docs/ols-derivations.md
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120
tools/sysid/docs/ols-derivations.md
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# OLS derivations
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## Simple/drivetrain
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Here's the ODE for a drivetrain.
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```
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x)
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```
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### OLS setup
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Let `α = -Kv/Ka`, `β = 1/Ka`, and `γ = -Ks/Ka`.
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```
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dx/dt = αx + βu + γ sgn(x)
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```
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### Feedforward gains
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Divide the OLS terms by each other to obtain `Ks`, `Kv`, and `Ka`.
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```
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Ks = -γ/β
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Kv = -α/β
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Ka = 1/β
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```
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## Elevator
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Here's the ODE for an elevator.
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```
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x) - Kg/Ka
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```
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### OLS setup
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Let `α = -Kv/Ka`, `β = 1/Ka`, `γ = -Ks/Ka`, and `δ = -Kg/Ka`.
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```
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dx/dt = αx + βu + γ sgn(x) + δ
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```
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### Feedforward gains
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Divide the OLS terms by each other to obtain `Ks`, `Kv`, `Ka`, and `Kg`.
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```
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Ks = -γ/β
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Kv = -α/β
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Ka = 1/β
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Kg = −δ/β
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```
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## Arm
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Here's the ODE for an arm:
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```
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x) - Kg/Ka cos(angle)
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```
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If the arm encoder doesn't read zero degrees when the arm is horizontal, the fit
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for `Kg` will be wrong. An angle offset should be added to the model like so.
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```
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x) - Kg/Ka cos(angle + offset)
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```
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Use a trig identity to split the cosine into two terms.
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```
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x) - Kg/Ka (cos(angle) cos(offset) - sin(angle) sin(offset))
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x) - Kg/Ka cos(angle) cos(offset) + Kg/Ka sin(angle) sin(offset)
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```
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Reorder multiplicands so the offset trig is absorbed by the OLS terms.
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```
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dx/dt = -Kv/Ka x + 1/Ka u - Ks/Ka sgn(x) - Kg/Ka cos(offset) cos(angle) + Kg/Ka sin(offset) sin(angle)
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```
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### OLS setup
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Let `α = -Kv/Ka`, `β = 1/Ka`, `γ = -Ks/Ka`, `δ = -Kg/Ka cos(offset)`, and `ε = Kg/Ka sin(offset)`.
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```
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dx/dt = αx + βu + γ sgn(x) + δ cos(angle) + ε sin(angle)
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```
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### Feedforward gains: Ks, Kv, Ka
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Divide the OLS terms by each other to obtain `Ks`, `Kv`, and `Ka`.
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```
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Ks = -γ/β
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Kv = -α/β
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Ka = 1/β
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```
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### Feedforward gains: Kg
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Take the sum of squares of the OLS terms containing the angle offset. The angle
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offset trig functions will form a trig identity that cancels out. Then, just
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solve for `Kg`.
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```
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δ²+ε² = (-Kg/Ka cos(offset))² + (Kg/Ka sin(offset))²
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δ²+ε² = (-Kg/Ka)² cos²(offset) + (Kg/Ka)² sin²(offset)
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δ²+ε² = (Kg/Ka)² cos²(offset) + (Kg/Ka)² sin²(offset)
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δ²+ε² = (Kg/Ka)² (cos²(offset) + sin²(offset))
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δ²+ε² = (Kg/Ka)² (1)
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δ²+ε² = (Kg/Ka)²
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√(δ²+ε²) = Kg/Ka
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hypot(δ, ε) = Kg/Ka
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hypot(δ, ε) = Kg β
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Kg = hypot(δ, ε)/β
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```
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### Feedforward gains: offset
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Divide ε by δ, combine the trig functions into `tan(offset)`, then use `atan2()`
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to preserve the angle quadrant. Maintaining the proper negative signs in the
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numerator and denominator are important for obtaining the correct result.
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```
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δ = -Kg/Ka cos(offset)
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ε = Kg/Ka sin(offset)
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sin(offset)/-cos(offset) = ε/δ
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sin(offset)/cos(offset) = ε/-δ
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tan(offset) = ε/-δ
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offset = atan2(ε, -δ)
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```
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