microReticulumTbeam/exercises/21_six_axis/Discussion.md

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