5.1 KiB
5.1 KiB
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# Exercise 21 — Six-Axis IMU Characterization
## Overview
Exercise 21 establishes a foundational understanding of the six-axis inertial measurement unit (IMU) on the T-Beam Supreme. The IMU (QMI8658) provides:
- **Accelerometer** (X, Y, Z) — measures acceleration, including gravity
- **Gyroscope** (X, Y, Z) — measures angular velocity
This exercise focuses on interpreting **accelerometer data** to determine device orientation relative to gravity.
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## Objective
The goals of this exercise are:
1. Demonstrate that IMU outputs are **frame-dependent but physically consistent**
2. Show that **startup orientation does not define the IMU axes**
3. Compute **roll and pitch** from raw accelerometer data
4. Quantify real-world deviations from ideal values
5. Identify sources of measurement error
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## Test Setup
Two static orientations of the device were evaluated:
### Orientation A — Sideways
Device resting on its side (edge of AlleyCat case)
Measured accelerometer values:
Ax = -0.951 Ay = -0.043 Az = -0.003
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### Orientation B — Upright
Device standing upright (antenna vertical)
Measured accelerometer values:
Ax = 0.028 Ay = 0.987 Az = 0.012
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## Methodology
Roll and pitch were computed using standard inertial navigation formulas:
roll = atan2(Az, Ay) pitch = atan2(-Ax, sqrt(Ay² + Az²))
These equations derive orientation from the **gravity vector projection** onto the sensor axes.
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## Implementation
A Perl script was used to compute roll and pitch:
scripts/imu_roll_pitch_demo.pl
This script:
- Accepts predefined accelerometer values
- Computes roll and pitch in radians and degrees
- Uses Perl’s built-in `atan2()` for accurate quadrant handling
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## Results
### Sideways Orientation
roll = -176.009° pitch = 87.405°
Interpretation:
- Pitch ≈ 90° → confirms device is rotated onto its side
- Roll near ±180° is expected due to sign conventions when vertical
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### Upright Orientation
roll = 0.697° pitch = -1.625°
Interpretation:
- Both values near 0° → device is nearly level
- Small deviations indicate real-world imperfections
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## Key Findings
### 1. IMU Axes Are Fixed
The IMU coordinate system is defined by the sensor hardware and PCB layout:
- It does **not change at startup**
- It is independent of how the device is oriented when powered on
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### 2. Orientation Is Derived from Gravity
The accelerometer measures the gravity vector:
- Different orientations produce different raw values
- The underlying physics is consistent
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### 3. Roll and Pitch Are Orientation-Invariant
While raw values differ between orientations:
- Computed roll/pitch reflect true physical orientation
- Results are consistent regardless of startup pose
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## Sources of Error
The observed deviations (~1–2°) are expected and arise from several factors:
### Surface Imperfection
- Table or support surface not perfectly level
- Enclosure geometry (AlleyCat case) introduces tilt
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### Sensor Bias (Offset)
- Example: Ax ≠ 0 when it should be
- Typical of MEMS sensors
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### Scale Error
Measured magnitude:
|A| ≈ 0.988 g (ideal = 1.000 g)
Indicates slight gain inaccuracy.
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### Axis Misalignment
- Sensor axes are not perfectly orthogonal
- Manufacturing tolerances introduce small angular errors
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### Noise and Quantization
- Finite precision (3 decimal places)
- Minor fluctuations expected
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## Limitations of Exercise 21
This exercise deliberately omits several important elements:
### No Absolute Heading
- Without a magnetometer, yaw (heading) is undefined
- Only roll and pitch can be determined
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### No Sensor Fusion
- Gyroscope data is not integrated
- No filtering (e.g., complementary or Kalman)
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### No Calibration
- Raw sensor values are used directly
- Bias and scale errors are uncorrected
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### Static Analysis Only
- No dynamic motion analysis
- Gyroscope output not utilized
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## Significance
Exercise 21 provides a critical baseline:
- Confirms correct IMU operation
- Establishes device coordinate frame
- Demonstrates physical interpretation of accelerometer data
- Quantifies real-world sensor error
This forms the foundation for:
- Magnetometer integration (Exercise 22)
- Tilt-compensated compass
- Full sensor fusion (AHRS)
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## Conclusion
The IMU behaves as expected:
- Raw outputs vary with orientation
- Derived angles correctly reflect physical pose
- Measured errors are consistent with typical MEMS performance
Most importantly:
> The IMU does not define orientation — it measures vectors.
> Orientation is derived through mathematical interpretation of those vectors.
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## Next Steps
Exercise 22 will extend this work by introducing:
- Magnetometer (QMC6310)
- Absolute heading (yaw)
- Tilt compensation using roll and pitch
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## References
- Perl Script: `scripts/imu_roll_pitch_demo.pl`
- Images:
- `img/upright_DSC_5194.webp`
- `img/sideways_DSC_5195.webp`
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