RTOM3 Ground Testing
Comprehensive testing was conducted during the development of RTOM3. This is a summary of three types of ground testing that might be of interest to RTOM3 users:
1. Static testing to establish the recommended amount of time prior to launch for the RTOM3 to compute an accurate estimate of the gyro offsets.
2. Dynamic roll testing to establish an upper bound on dynamic gyro drift.
3. Simulated flight testing to demonstrate overall accuracy.
Static testing consisted of powering up the device under test, waiting for a specific amount of time, manually simulating a launch and then again waiting for the same amount of time. The RTOM3 was motionless for the entire duration of the test, hence the designation "static testing" for this test. No particular effort was made to level the RTOM3. Six units were tested with time durations of 1, 2, 3, 5 and 10 minutes. Estimates of roll and tilt angles were plotted. Roll angle is the amount of apparent rotation around the Z axis of the RTOM3 (indicated by the UP arrow) from its initial value. Tilt angle is the angle between the Z axis and vertical. A typical plot for a delay of 3 minutes - Figure 1.:
The pre-launch variation of the estimates of tilt and roll angles is produced by the algorithm that is estimating the offsets of the gyros for all three axes. The convergence of the tilt and roll estimates after 3 minutes (180 seconds) indicates the offset estimates are also converging to their true values. The small amount of noise in the tilt estimate prior to the simulated launch at three minutes is due to noise produced by the accelerometers. The noise disappears after the simulated launch because the accelerometers are subsequently ignored. During flight, the RTOM3 uses only the gyros to compute orientation.
Note in Figure 1 that after launch the gyro drift was identically equal to zero for 3 minutes. That is because the estimates of the gyro offsets were identically equal to the true values. This is possible because both the gyro outputs and the estimates of the gyro offsets are 16 bit integers. In other words, the 16 bit integer net rotation rates reported for all three gyros were identically equal to zero.
Testing was performed with pre-launch pauses of 1, 2, 3, 5 and 10 minutes. With a 1 minute pause, the residual gyro offsets were close to their initial values, on the order of 2 degrees per second. With a 2 minute pause, there were small but non-zero residual offsets. As shown above, with a 3 minute pause, the residual offsets were zero. They were also zero with a 5 and 10 minute pause. As can be seen from figure 1, it took the entire 3 minute period for the tilt and roll estimates to converge. Therefore, in order to provide a margin of safety, a pre-launch pause of 5 minutes is recommended. After the 5 minute pause was established, all subsequent testing was done with that value.
Dynamic roll testing
Another set of ground tests was performed to explore gyro drift under dynamic conditions. During one of the tests, an RTOM3 was placed on the platter of a record player and after a 5 minute pre-launch pause, was manually launched. The platter was then manually rotated 20 turns. Plots of tilt and rotation rates are shown in the next three figures:
In Figures 2. and 3., you can see that roll rotations began about 1 minute after simulated launch and proceeded for about 1 minute, followed by a time period of 1 minute with no motion. The total shift in estimated tilt during the one minute of rotations was less than 0.5 degrees. After rotations stopped, the drift rate reverted to the static value of identically zero.
Roll rate during the test is shown above in Figure 3. Peak roll rate was around 200 degrees per second. Roll was applied manually, so the roll rate was quite variable. Marks were placed on both the platter and the record player so that the true roll angle at the end of the test was equal to the true roll angle at the start.
Yaw and pitch rates during the test are shown below in Figure 4. Peak rates are on the order of 1 or 2 degrees per second, which are much larger than the resolution of the gyros, indicating that there was enough rotation rate on all three of the gyro axes to provide a valid test of dynamic gyro drift for all three axes. The source of the yaw and pitch rates was probably a combination of wobble, gyro cross axis coupling and rocking of the platter caused by manual spinning of the platter.
Simulated flight testing
Simulated flight testing was performed to demonstrate overall accuracy under severe flight conditions. An RTOM3 was placed on the platter of a record player. After 5 minutes pre-launch, a launch was triggered manually. The record player was turned on and spun alternately at 33 and 78 RPM while the record player was picked up, tilted and set down, several times over a period of little less than one minute. Plots of tilt and rotation rates are shown in figures 5, 6 and 7. The plots speak to the severity of the simulated flight.
Note that the absence of acceleration during the simulated flight test does not invalidate the results. There are only two potential paths for high-g acceleration to impact the accuracy of the orientation estimation. One is a direct path through the accelerometers. Since the accelerometers are not used by the RTOM3 in orientation estimation after launch, that path is blocked. The other potential path is coupling of acceleration into the gyro sensors. For the gyros used in the RTOM3, there is no coupling of acceleration into the gyros, so that path is not possible either. Therefore, high-g acceleration does not corrupt orientation estimation during accelerated flight and ground testing is adequate to verify the performance of the RTOM3.
Regarding the direct path through the accelerometers, tilt orientation is computed entirely from gyro data after launch. Some algorithms use combinations of accelerometer, magnetometer or GPS data to compensate for the accumulation of error in the estimate of orientation from sources such as gyro drift, numerical round-off and approximations to the nonlinear kinematic equations of rotation. The problem is that these secondary sources themselves introduce errors. For example, during high acceleration, accelerometer data must be compensated for acceleration. The compensation calculations are subject to substantial error in rocket applications.
During 10 years of rocket flight testing and improvements to the algorithms used in RTOM3, effects of gyro drift, numerical round-off and approximations have been reduced to a net dynamic drift rate in orientation estimation of less than 0.5 degrees per minute, or less than 0.0083 degrees per second, obviating the need for secondary sources of orientation information such as accelerometers. The accelerometers in the RTOM3 are used only by the computations prior to launch to determine gyro offsets and to detect the launch.
Note in Figure 5. above that each time the record player was returned to a level position, the indicated tilt was between 1 and 2 degrees. Some of that is due to dynamic drift while some of it is due to the fact that record player could rock a little bit, depending on where it was placed on the table. Also note that there is some wobbling motion evident which is probably produced by a combination of tilt of the record player with respect to vertical, tilt of the RTOM3 with respect to the platter and gyro cross axis coupling.
Figures 5. and 6. taken together can be used to understand the details of the simulated flight. From 20 to 30 seconds, the platter was level and spinning at 33 RPM. From 30 to 40 seconds the platter was coasting and the record player was tilted. The center of gravity of the RTOM3 and battery on the platter were not at the center of the platter, so the platter "flopped around" during the tilt. From 40 to 65 seconds the spinning at 33 RPM was resumed while tilt was varied. Because of the off-center loading on the platter, there was a distinct variation of the spin rate. After 70 seconds, the platter was spun up to 78 RPM, then shut off and allowed to spin down to a rest at the same time that the tilt was varied.
Yaw and pitch rate are shown in Figure 7. above. It is interesting to note the fact that it is the combination of roll, yaw and pitch rate that determine tilt and that even though yaw and pitch rate are small, if they had been zero the tilt would have been zero.
RTOM3 Flight Testing
The core tilt-engine firmware utilized in the RTOM3 has been regularly flight tested over the period of the last 10 years plus in the RTOM2 and some other forms, including several modifications to improve its performance for tilt detection and now motion detection.
Mechanically, the new RTOM3 ignition-disabling hardware has been flight tested to over 40 g of vertical and 27 g of lateral acceleration.