The sensors for the ground truth system on NavLab11 are mounted on a tubular aluminum rack attached to the brush guard, which is in turn bolted to the front bumper. We observed visible low frequency vibration of sensors attached to the rack, and were concerned that this might affect performance. In order to evaluate this concern, we attached two three-axis accelerometers to the rack, collected data and analyzed it offline.
The conclusion is that a resonance of the sensor mount is contributing a significant amount of vibration, but this does not seem to be a problem for the Bosch SRSS due to the limited angular resolution of the sensors and relatively desirable attachment of the sensors to the rack (rigid and centrally located.)
We attached two three axis MEMS accelerometer modules (Crossbow CXL25LP3) to the sensor rack, left and right of center. This placement allowed us to evaluate the roll motion of the rack, which seemed to be the greatest concern. These sensors have a response from DC to 100Hz and a full-scale range of 25G. The data was acquired at about 100,000 samples/sec, then decimated to 200 samples/sec. To eliminate the sensor offset, the data was then high-pass filtered using a FIR filter with a sharp 0.5 Hz cutoff.
To find the rotational motion of the rack we computed the angular acceleration from the difference of the acceleration of the left and right sensors.
Frequency Domain Results:
We qualitatively evaluated the vibration using spectrograms, which display the three dimensions of frequency, intensity and time as Y, color and X.
This figure shows the roll acceleration during low-speed driving over a rough, pot-holed road. The acceleration shows strong peaking around 13 Hz, with a lesser peak around 1.5Hz. We believe that the 13Hz peak is the rack resonance and the 1.5Hz peak is gross motion of the vehicle resulting from the suspension dynamics. The variable frequency narrow-band features between 30Hz and 50Hz are probably engine vibration.
If we integrate the acceleration twice, we obtain the angular motion. We did this in the time domain because we also directly visualized the time-domain motion. To minimize the effect of accelerometer offsets, we repeated the 0.5Hz high-pass filter after each integration.
This spectrogram shows the motion spectrum vs. time. As is to be expected, the low-frequency component is greatly emphasized relative to the higher frequencies. The 1.5Hz peak is now much more prominent than the 13Hz peak. Larger motions are present at lower frequencies, however (as we will see), at lower frequencies the vehicle state estimate provides considerable help in compensating for this motion.
The variability of the 13Hz motion is somewhat clearer in this spectrogram. There is relatively little motion at 50 seconds, but a great deal at 20 and 56 seconds. As we go over bumps this excites the vibration of the rack.
Time Domain Analysis:
Since we a large part of our concern was for worst-case motion rather than average motion, we also analyzed 2d time vs. intensity plots. This also enables a quantitative comparison of the rack motion vs. the state estimate roll motion (from the Crossbow IMU.)
This figure shows the roll motion in the 0.5..100Hz band as reported by the IMU and accelerometers (only available from 0..75 sec.) At this scale, we mainly see the spiky behavior of the motion (due to going over bumps.)
This figure shows the roll motion at its peak amplitude, about 2.5 degrees peak-to-peak. The bulk of the motion is at the low-frequency 1.5Hz peak, though some 13Hz motion is also visible in the accelerometer data. One thing we notice is that our measurement approach is fairly well validated by the IMU data.
We don’t know whether the LF amplitude mismatch is due to relative LF motion of the rack and body, or whether it is due to an error in the roll-from-acceleration approach. Even if this is a real relative motion of the IMU and sensor rack, the effect of LF vibration on sensor pointing can be largely corrected using the IMU data.
When blurring (rather than gross pointing error) is the concern, angular velocity is more relevant than p-p motion. The peak angular velocity observed in the 0.5-100Hz band was 20 degrees/sec, and is a consequence of the 13Hz resonance. At this rate, a 0.2 degree resolution camera (fairly wide angle) would be blurred by one pixel when the exposure exceeds 1/100 second. Exposure time is unlikely to be this long during daytime operation.
This graph shows the roll motion at the time peak velocity was measured. We can see that the relatively smaller low-frequency velocity component in the previous figure creates a low-frequency motion with an amplitude larger than the high frequency motion (that generated the peak velocity.)
The IMU data is recorded at 20 samples/sec, and has a nominal 10Hz bandwidth, so we would not expect to see the high frequency component in the IMU data. In fact, the since the IMU is not mounted on the sensor rack, and the HF vibration is believed to be due to the rack, the HF vibration is not present at the IMU anyway.
So pointing error due to the HF motion of the sensor rack can’t be corrected because the IMU doesn’t see it. Fortunately, the HF amplitude is almost an order of magnitude smaller than the LF peak motion previously noted, about 0.3 degrees peak-to-peak.
In this graph, we see a time where sustained 13Hz motion is present, and is not so dominated by the LF motion. This the effect of driving over a rough surface without large bumps. This kind of motion can cause blurring in cameras or other sensors with fairly high angular resolution.
The NavLab11 sensor rack does seem to be contributing considerable motion at around
13 Hz, but the amplitude appears to be small enough that it should not significantly affect the performance of the Bosch SRSS sensors (wide angle cameras and SICK scanner.) In particular, the SICK is the primary measurement sensor, and has only 1 degree resolution. Furthermore, this resolution is along the yaw axis, whereas the worst vibration is in roll.
The presence of the 13Hz vibration however remains a cause for concern in future work with NavLab 11 because:
Sensors with high angular resolution or slow measurement times may see blur due to the HF vibration.
Pointing error due to the HF vibration cannot be compensated for using the IMU data (unlike the 1.5 Hz vibration.)
Individual sensor mounts attached to the rack may amplify this vibration if not carefully designed. This is a particular concern with sensors mounted near the outside of the sensor rack, since the linear motion due to the roll is amplified there.
For this reason, with future sensors, we should:
Consider mounting the sensors elsewhere if they are susceptible to 13Hz vibration. Roof rack mounting avoids this particular problem, though the current roof rack is also rather lacking in stiffness. Other means of attaching directly to the body are also desirable, since they both avoid the rack vibration and maximize the coupling with the IMU.
Mount sensors on the rack near the center so that they are subject to less up-and-down and back-to-front motion as a consequence of the rack rotation.
Construct sensor sub-mounts so that they are highly rigid, well damped, or preferably both. This minimizes the risk that the 13Hz vibration will be amplified by a resonance of the sub-mount.
HF vibration could also be minimized by using shock-mounts giving the sensor a resonant frequency well below 13Hz, however this degrades coupling with the IMU by introducing LF vibration. The resonance should also be well above 1.5 Hz to avoid being excited by the suspension resonance.