UAV Payloads #01
Gimbal Stability Is Not the Angle on the Datasheet
The gimbal catalog says "stabilization accuracy ±0.01°". It sounds very precise, until you convert it into pixels on the image.
0.01° is 175 µrad. With a 25 mm lens on a visible camera with 2.4 µm pixels, one pixel corresponds to 96 µrad. ±0.01° means the image wobbles within a range of ±1.82 pixels, 3.64 pixels peak to peak.
That number is not necessarily unacceptable in itself. The point is: the datasheet speaks in angles, your problem is in pixels, and the two are separated by a lens focal length. Fit a longer lens and the same gimbal performs worse straight away, while the number on the datasheet does not change by a single digit.
1. First, convert angle to pixels
The conversion is simple: divide the angle by the instantaneous field of view (pixel pitch ÷ focal length). Taking the two configurations we use most as examples: EO is 2.4 µm pixels with a 25 mm lens (96 µrad/pixel), and IR is 12 µm pixels with a 25 mm lens (480 µrad/pixel):
| Stability spec | Angle | EO 25 mm (96 µrad/px) | IR 25 mm (480 µrad/px) |
|---|---|---|---|
| ±0.1° | 1745 µrad | 18.2 px | 3.64 px |
| ±0.05° | 873 µrad | 9.09 px | 1.82 px |
| ±0.02° | 349 µrad | 3.64 px | 0.73 px |
| ±0.01° | 175 µrad | 1.82 px | 0.36 px |
| ±0.005° | 87 µrad | 0.91 px | 0.18 px |
A common acceptance threshold is to keep the jitter amplitude (± value) within one pixel. According to Table 1, the EO column passes only at ±0.005° (0.91 pixel), twice as strict as the catalog's ±0.01°. So specifications cannot be copied; they have to be worked back from your own lens.
2. Pointing error and jitter are two different problems
"The gimbal is inaccurate" actually mixes up two things, with completely different solutions:
- Pointing error: the gimbal thinks it is pointing due east at a 30-degree depression angle, but it is actually at 30.8 degrees. The image may be steady and sharp, but the target coordinates you calculate are wrong. This is a calibration and attitude measurement problem.
- Jitter: the line of sight wobbles at high frequency over a small range. The average target coordinates may be right, but the image blurs and the tracker cannot hold a lock. This is a mechanism and control loop problem.
They are also accepted differently. Pointing error is tested by flying over ground targets of known coordinates and comparing the reported values; jitter has to be measured with the motors running, and it must be recorded for long enough and analyzed in the frequency domain. An ordinary video that "feels steady" proves nothing: a 30 fps video can only show wobble below 15 Hz, and higher-frequency jitter aliases into false low frequencies or simply blurs within the integration time. To see a 200 Hz component, the frame rate must be above 400 fps (500 fps or more in practice), or record the gyro data on the gimbal directly.
This article covers jitter only. The error budget for pointing error and target geolocation is broken down in full in section 5 of the payload page, and the conclusion may be surprising: in that example, removing the gimbal encoder error altogether leaves the ground error almost unchanged, staying at 4.47 m with magnetometer heading and dropping only from 1.43 m to 1.41 m with dual-antenna heading.
3. Counterweighting: five millimeters off center costs two pixels
The first source of jitter is airframe motion transmitting torque into the gimbal. The disturbance torque about a gimbal axis (the bearings cannot resist it; only the motor can counter it) is:
T = m × a × δ
where m is the payload mass, a the airframe acceleration, and δ the offset of the center of gravity from the axis. If the center of gravity lies exactly on the axis, δ = 0, and no matter how the airframe accelerates no torque is produced, which is why a gimbal must always be balanced after installation.
Let us work the numbers through. Take a 0.35 kg payload, a lateral airframe acceleration of 3 m/s² (a typical magnitude for a multirotor stopping abruptly or correcting for a gust), a payload moment of inertia about the axis of 3.5 × 10⁻⁴ kg·m², and a control loop response delay of 5 ms:
| CG offset δ | Disturbance torque T | Angular acceleration α | Angle accumulated in 5 ms | EO pixels |
|---|---|---|---|---|
| 0.5 mm | 0.525 mN·m | 1.5 rad/s² | 18.8 µrad | 0.20 px |
| 5 mm | 5.25 mN·m | 15 rad/s² | 188 µrad | 1.95 px |
Ten times the balancing accuracy buys ten times less jitter. And getting the center of gravity within 0.5 mm depends on leaving room for the counterweight positions and adjustment travel at the design stage, not on improvising during assembly. Change a lens, add a filter, reroute a cable, and the center of gravity moves, so counterweighting is not a one-off assembly step but one that has to be redone after every change.
4. Vibration isolation: a natural frequency in the wrong place amplifies instead
The second source of jitter is the propellers. 6000 rpm is a 100 Hz fundamental, plus harmonics from the number of blades. An isolation mount is a spring-mass system, and its transmissibility depends on the ratio r of excitation frequency to natural frequency:
T = √(1 + (2ζr)²) ÷ √((1 − r²)² + (2ζr)²)
The key point: isolation only begins when r > √2; whenever r < √2, vibration is amplified. Mount a 0.6 kg gimbal assembly on isolators with a 25 Hz natural frequency (damping ratio 0.2), and the 100 Hz propeller frequency falls at r = 4, with transmissibility 0.125 and 87 % reduction. But during takeoff, as rotor speed climbs from zero, it inevitably sweeps through the resonance at r = 1, and at that moment vibration is amplified 2.7 times. The full transmissibility curve is in section 3 of the payload page.
For a 25 Hz natural frequency, the total stiffness is k = m(2πf)² = 14.8 N/mm, or 3.7 N/mm per mount when shared across four. A quick cross-check: at this stiffness, the static deflection of the gimbal assembly (0.6 kg) is 0.40 mm. If the measured deflection is clearly more than twice this value, the isolators are most likely too soft, and the natural frequency is lower than you think (rubber and silicone damping elements usually have a higher dynamic stiffness than static stiffness, with dynamic-to-static ratios commonly between 1.2 and 2, so a deflection slightly above 0.40 mm is not necessarily a problem; to be sure, measure the actual resonant frequency by tap or sweep testing). Lower is better for isolation, but the gimbal will swing like a pendulum and the travel limits may not be enough. This is the quickest check you can do on site; a pair of calipers is all it takes.
5. Resonance: the mechanism's first mode must be well away from the control bandwidth
The third source is the gimbal itself. The control loop wants a high bandwidth to suppress disturbances, but the mechanism's first structural resonance is the ceiling: once the loop bandwidth gets close to it, the controller's corrections excite the resonance, and the system turns from "suppressing jitter" into "creating jitter". The practical rule of thumb is to put the first mode at least 5 to 10 times above the control bandwidth.
This is most likely to go wrong during lightweighting: thin the arms to save weight, the stiffness drops, the first mode drops with it, and control parameters that were tuned before start to oscillate. So gimbal lightweighting cannot look only at weight; it has to look at the stiffness-to-mass ratio. Removing the same 50 g at the end of a cantilever or near the axis has very different effects on inertia and modes.
6. How to write acceptance conditions
A phrase like "stabilization accuracy ±0.01°" cannot be tested, because it does not say under what conditions or by what method it is measured. An acceptance condition that can be tested looks like this:
- Conditions: the payload is the actual deliverable (including lens and cables), the motors run over the mission speed range, and the airframe is fixed to a vibration table or actually hovering.
- Measurement: record a fixed target 50 m away continuously for 60 seconds at 500 fps or more, and extract the line-of-sight angle time series by image cross-correlation; or record the gyro data on the gimbal simultaneously.
- Criterion: RMS line-of-sight angle ≤ ___ µrad (worked back from your focal length and pixel pitch; do not write an angle directly), and no single peak in the 1 Hz to 200 Hz spectrum exceeds ___ times the RMS.
- Environment: test once at each end of the temperature range, since the fit clearances of aluminum parts and bearings change with temperature.
The spectral condition in the third item is the one most easily left out, yet it is the most direct way to tell "a little shaky overall" from "resonating at one frequency", and the two are handled completely differently: the first by adjusting control parameters, the second by changing the mechanism.
