Lab2: IMU

Use the equations from class to convert accelerometer data into pitch and roll.

• Show the output at { -90, 0, 90 } degrees pitch and roll.
• Write a Jupyter function to plot data vs time (ms/us) for future labs.
• Discuss accelerometer accuracy and (optional) two-point calibration.

Using the standard accelerometer-based attitude equations mentioned in the class with radians-to-degrees conversion, pitch and roll were computed from the 3-axis acceleration data in Jupyter. The time traces show clear plateaus near 0° (board flat) and near ±90° (board on an edge), with brief spikes during handling due to transient linear acceleration.

Accelerometer accuracy was evaluated using six static poses (±X, ±Y, ±Z). The mean readings for the gravity-aligned axis were: X+: +995.35 mg, X−: −1000.20 mg, Y+: +991.32 mg, Y−: −1004.00 mg, Z+: +1000.71 mg, Z−: −1018.04 mg. These results confirm the sensor is close to the expected ±1 g level, with the largest endpoint deviation observed on Z− (≈ −1018 mg).

A per-axis two-point calibration (linear scale + offset) was then applied using the measured +1 g and −1 g endpoints. The fitted parameters were: X: k=1.0022, b=−2.42 mg; Y: k=1.0023, b=−6.34 mg; Z: k=0.9907, b=−8.66 mg. After calibration, the gravity-magnitude mean moved closer to the ideal 1000 mg (from 1013.94 mg to 1011.76 mg), while the overall standard deviation changed only slightly (70.58 mg to 70.22 mg), indicating calibration mainly corrects static bias/scale error and the remaining variation is dominated by motion/transition segments.

Code Snippet

Open on GitHub Gist

When the accelerometer is noisy, especially near the RC car. Record data and analyze the frequency spectrum.

# --- Core: estimate sampling rate + compute/plot FFT amplitude spectra (ax/ay/az) ---
t = df["t_ms"].to_numpy(dtype=float) * 1e-3
t -= t[0]
fs = 1.0 / np.median(np.diff(t))

def amp_spectrum(x, fs):
    x = x - np.mean(x)
    n = len(x)
    X = np.fft.rfft(x)
    f = np.fft.rfftfreq(n, d=1/fs)
    A = (2.0 / n) * np.abs(X)
    A[0] *= 0.5
    return f, A

plt.figure(figsize=(10,5))
for k in ["ax_mg","ay_mg","az_mg"]:
    f, A = amp_spectrum(df[k].to_numpy(dtype=float), fs)
    m = (f >= 0.5) & (f <= min(200, fs/2))
    plt.plot(f[m], A[m], label=k)

plt.xlabel("Frequency (Hz)")
plt.ylabel("Amplitude (mg)")
plt.title("Accelerometer Noise Spectrum (FFT)")
plt.grid(True)
plt.legend(loc="best")
plt.show()

Code Snippet (Gist)

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Include a graph of the Fourier Transform of accelerometer data and discuss a reasonable cutoff frequency for filtering.

Implement a simple low-pass filter on accelerometer data and plot original vs filtered signals.

Across all three axes, the low-pass filter reduces high-frequency fluctuations while preserving the slower baseline/step changes of the signal. The filtered traces are visibly smoother than the raw data, and large transient spikes are attenuated but not fully removed (as expected for impulsive events). Overall, the result confirms that the chosen cutoff primarily suppresses vibration/noise components while maintaining the underlying motion trend.

Code Snippet

Open on GitHub Gist

Gyroscope angular rates were integrated over time using the class equations to obtain pitch, roll, and yaw. During data collection, the IMU was rotated slowly through different angles (to create smooth attitude changes) and lightly tapped/knocked (to introduce brief vibration/impulse disturbances).

In Figure 19, the accelerometer-based pitch is stable in quasi-static segments but exhibits spikes during taps/motion. The gyro-integrated pitch responds smoothly to rotation but shows noticeable drift over time. The complementary filter (alpha = 0.02) tracks the accelerometer baseline while suppressing high-frequency accelerometer noise and limiting gyro drift, producing the most stable estimate.

Figure 20 shows the same trend for roll: accelerometer roll contains occasional impulsive outliers, gyro roll is smoother but slowly diverges, and the complementary filter yields a smoother trajectory that remains close to the gravity-referenced roll during slow tilts while rejecting tap-induced noise.

As shown in Figure 21, yaw was computed by integrating the gyro z-rate; unlike pitch/roll, yaw does not have a gravity-based accelerometer reference, so the integrated yaw accumulates bias and drifts over time, especially after disturbances and sustained rotation.

A complementary filter was applied to pitch and roll to combine low-frequency, drift-free information from the accelerometer with high-frequency responsiveness from the gyroscope. With alpha = 0.02, the output stays stable during static periods, responds well to slow angle changes, and is noticeably less sensitive to quick vibrations/taps than raw accelerometer angles while avoiding the long-term drift of pure gyro integration.

Speed up execution of the main loop

• Implemented a non-blocking loop that checks dataReady() each iteration and only logs when new IMU data is available (no waiting).
• Removed debugging delays during recording and minimized serial printing to avoid slowing the loop.
• Sampling speed achieved (Figure 25): N=1700 samples in 5.00 s → fs≈339.8 Hz (median-based estimate).
• The loop can iterate faster than the IMU update rate; extra iterations simply do not append samples unless the IMU indicates new data.

Collect and store time-stamped IMU data using start/stop flags

Data logging was controlled via BLE commands: CLEAR resets buffers, START begins recording, STOP ends recording, and SEND transmits the buffered samples to the computer and saves them as CSV (Figure 24).

Data storage design (arrays, data types, memory)

• Stored each sample with a timestamp and both sensor axes (e.g., t_ms, ax_mg, ay_mg, az_mg, gx, gy, gz), keeping accel and gyro aligned by time.
• Preferred numeric storage on-board (integers/fixed-point) for memory efficiency; timestamps as uint32_t.
• Memory estimate: using uint32_t time (4B) + 6×int16_t axes (12B) ≈ 16 B/sample. For 5 s at ~340 Hz: 1700 samples → ~27 KB, which is practical for the Artemis.

Demonstrate ≥ 5 s capture and BLE transfer

The recorded run satisfies the requirement: duration=5.00 s and the check reports “≥5s: YES” (Figure 25). The dataset was successfully sent over BLE and saved as imu_ble_dump.csv> (Figure 24).

Mounted the RC car battery with correct polarity (red-to-red, black-to-black) and installed AA batteries in the remote controller.

Recorded a driving video and establish a baseline of the car dynamics (forward/backward speed, turning radius, acceleration/braking response).