# 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. --- ## 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 --- ## 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 ``` --- ### Orientation B — Upright Device standing upright (antenna vertical) Measured accelerometer values: ``` Ax = 0.028 Ay = 0.987 Az = 0.012 ``` --- ## 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. --- ## 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 --- ## 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 --- ### Upright Orientation ``` roll = 0.697° pitch = -1.625° ``` Interpretation: - Both values near 0° → device is nearly level - Small deviations indicate real-world imperfections --- ## 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 --- ### 2. Orientation Is Derived from Gravity The accelerometer measures the gravity vector: - Different orientations produce different raw values - The underlying physics is consistent --- ### 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 --- ### 4. Coordinate Mapping From the observed accelerometer data: - Upright orientation: +Y_sensor ≈ UP - Sideways orientation: -X_sensor ≈ UP (after 90° rotation) We define a **device coordinate system** aligned with the AlleyCat enclosure: - Z_device = UP (antenna direction) - Y_device = FORWARD (normal to display, pointing outward) - X_device = RIGHT (along the long axis of the display) Mapping from sensor frame to device frame: Z_device = +Y_sensor The remaining axes are determined by physical orientation and require sign validation: X_device ≈ +Z_sensor Y_device ≈ ±X_sensor Final sign conventions should be verified empirically by observing motion: - Rotate device forward/back → affects Y_device - Rotate device left/right → affects X_device This mapping separates: - Sensor frame (hardware-defined) - Device frame (application-defined) and provides a consistent basis for roll, pitch, and future magnetometer integration. ## 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 --- ### Sensor Bias (Offset) - Example: Ax ≠ 0 when it should be - Typical of MEMS sensors --- ### Scale Error Measured magnitude: ``` |A| ≈ 0.988 g (ideal = 1.000 g) ``` Indicates slight gain inaccuracy. --- ### Axis Misalignment - Sensor axes are not perfectly orthogonal - Manufacturing tolerances introduce small angular errors --- ### Noise and Quantization - Finite precision (3 decimal places) - Minor fluctuations expected --- ## 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 --- ### No Sensor Fusion - Gyroscope data is not integrated - No filtering (e.g., complementary or Kalman) --- ### No Calibration - Raw sensor values are used directly - Bias and scale errors are uncorrected --- ### Static Analysis Only - No dynamic motion analysis - Gyroscope output not utilized --- ## 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) --- ## 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. --- ## Next Steps Exercise 22 will extend this work by introducing: - Magnetometer (QMC6310) - Absolute heading (yaw) - Tilt compensation using roll and pitch --- ## References - Perl Script: `scripts/imu_roll_pitch_demo.pl` - Images: - `img/upright_DSC_5194.webp` - `img/sideways_DSC_5195.webp`