Monthly Archives: June 2021

Another Try at Wall Offset Tracking, Part II

Posted 22 June 2021

In my previous post on this subject, I described my effort to improve Wall-E2’s wall tracking performance by leveraging controlled-rate turns and the dual VL53L0X ToF LIDAR arrays. This post describes an enhancement to that effort, aimed at allowing the robot to start from a non-parallel orientation and still capture and track a desired wall offset.

The previous post showed that when starting from a parallel orientation either inside or outside the desired wall offset, the robot would make a turn toward the offset line, move straight ahead until achieving the desired offset, then turn down-track and start tracking the desired offset. The parallel starting condition was chosen to make things easier, but of course that isn’t realistic – the starting orientation may or may not be known. In previous work I created an entire function ‘RotateToParallelOrientation()’ to handle this situation, but I would rather not have to do that. It occurred to me that I might be able to eliminate this function entirely by utilizing the known characteristics of the triple-VL53L0X array. The linear array exhibits a definite relationship between ‘steering value’, (the difference between the front and rear sensor values, divided by 100) and the off-perpendicular orientation of the array. At perpendicular (parallel orientation of the robot), this value is nominally zero, and exhibits a reasonably linear relationship out to about +/- 40º from perpendicular, as shown in the following plot from this post from a year ago.

Array distances and steering value for 30 cm offset. Note steering value zero is very close to parallel orientation

As can be seen above, the ‘Steering’ value is reasonably linear, with a slope of about -0.0625/deg. So, for instance, the calculated value for an offset of 30cm would be -0.0625*30 = -0.1875, which is very close to the actual plotted value above for 30º

So, it should be possible to calculate the off-perpendicular angle of the robot, just from the measured steering value, and from that knowledge calculate the amount of rotation needed to achieve the desired offset line approach angle.

The desired approach angle was set more or less arbitrarily by

and this assumes an initial parallel orientation (i.e. 0º offset in the above plot). If, for instance, the initial steering value was -0.1875, indicating that the robot was pointing 30º away from parallel, then the code to compute the total cut (assuming we are tracking the wall on the left side of the robot) would look something like this:

So, for example, if the robot’s starting orientation was offset 30º away from the wall, and 20cm inside the desired offset line of 30cm, we would have:

cutAngleDeg = WALL_OFFSET_TGTDIST_CM – (int)(Lidar_LeftCenter / 10.f);

cutAngleDeg = 30 – 10 = 20

adjCutAngleDeg = cutAngleDeg – 30 = -10º, so the robot would actually turn 10º CCW (back toward the wall) before starting to move to capture the desired offset line.

If, on the other hand, the robot was starting from outside the desired offset (say at 60cm), but with the same (away from wall) pointing angle, then the result would be

cutAngleDeg = WALL_OFFSET_TGTDIST_CM – (int)(Lidar_LeftCenter / 10.f);

cutAngleDeg = 30 – 60 = -30

adjCutAngleDeg = cutAngleDeg – 30 = -30 – 30 = -60º, so the robot would actually turn 60º CCW (back toward the wall) before starting to move to capture the desired offset line.

26 June 2021 Update:

I modified my test program to just report the rear, center, and front VL53L0X distances, plus the steering value and the computed off-parallel angle, using the -0.0625 slope value obtained from the above plots. Unfortunately, the results were wildly unrealistic, leading me to believe something was badly wrong somewhere along the line. So, I redid the plots, thinking maybe the left side VL53L0X sensors were different enough to make that much of a difference. When I plotted the steering value vs off-parallel angle for 10, 20, 30 & 40cm wall offsets, I got a significantly different plot, as shown below:

As can be seen in the above plot, the slope of steering values to off-parallel angles is nice and linear, and also quite constant over the range of wall offset distances from 10 to 40 cm; this is quite a bit different than the behavior of the right-side sensor array, but it is what it is. In any case, it appears that the slope is close to 1.4/80 = 0.0175, or almost twice the right-side slope derived from the previous right-side plots.

Using the value of 0.0175 in my GetSteeringAngle() function results, and comparing the calculated off-parallel angle with the actual measured angle, I get the following Excel plot.

As can be seen in the above plot, the agreement between measured and calculated off-parallel angles is quite good, using the average slope value of 0.0175.

The above plot shows the raw values that produced the first plot.

So, back to my ‘FourWD_WallTrackTest’ program to develop Wall-E2’s ability to capture and then track a particular desired offset. In my first iteration, I always started with Wall-E2 parallel to the wall, and calculated an intercept angle based on the difference between the robot’s actual and desired offsets from the near wall. This worked very nicely, but didn’t address what happens if the robot doesn’t start in a parallel orientation. However, when I tried to use the data from a previous post, the results were wildly off. Now it is time to try this trick again, using the above data instead. Because the measured steering value/off angle slopes for all selected wall offsets were essentially identical, I can eliminate the intermediate step of calculating the appropriate slope value based on the current wall offset distance.

So, I modified my ‘getSteeringAngle()’ function to drop the ‘ctr_dist_mm’ parameter and to use a constant 0.0175 slope value, as shown below:

With this modification, I was able to get pretty decent results; Wall-E2 successfully captured and tracked the desired offsets from three different ‘inside’ (robot closer to wall than the desired offset) orientations, as shown in the following short videos:

‘Inside’ capture, with initial orientation angle > desired approach angle
‘Inside’ capture with initial orientation angle < desired approach angle
‘Inside’ capture with negative initial orientation angle

04 July 2021 Update:

After succeeding with the ‘inside’ cases, I started working on the ‘outside’ ones. This turned out to be considerably more difficult, as the larger distances from the wall caused considerable variation in the VL53L0X measurements (lower SNR?), which in turn produced more variation in the starting and ‘cut’ angles. However, the result does seem to be reasonably reliable, as shown in the following videos.

‘outside’ capture with initial outward angle
‘outside’ capture with initial inward angle
‘outside’ capture with small outward angle.

05 July Update:

After getting the left-side tracking algorithm working reasonably well, I ported the ‘TrackLeftWallOffset()’ functionality to ‘TrackRightWallOffset()’. After making (and mostly correcting) the usual number of mistakes, I got it going reasonably well, as shown in the following short videos:

Right wall tracking, starting inside desired offset, oriented toward wall
Right wall tracking, starting inside desired offset, oriented away from wall
Right wall tracking, starting outside desired offset, oriented toward wall
Right wall tracking, starting outside desired offset, oriented away from wall

Here is the complete code for my wall capture/track test program:

Here is a link to the above file, plus all required library & ancillary files.

Stay tuned,

Frank

Another Try at Wall Offset Tracking

Posted 22 June 2021

About nine months ago (October 2020) I made a run at getting offset tracking to work (see here and here). This post describes yet another attempt at getting this right, taking advantage of recent work on controlled-rate turns. I constructed a short single-task program to do just the wall tracking task, hopefully simplifying things to the point where I can understand what is happening.

One of the big issues that arose in previous work was the inability to synch my TIMER5 ISR with the PID library’s ‘Compute()’ function. The PID library insists on managing the update timing internally, which meant there was no way to ensure that Compute() would be called every time the ISR ran. I eventually came to the conclusion that I simply could not use the PID library version, and instead wrote my own small function that did the Compute() function, but with the timing value passed in as an argument rather than being managed internally. This forces the PID calculations to actually update in synch with the TIMER5 interrupt. Here’s the new PIDCalcs() function:

As can be seen from the above, this is a very simple routine that just does one thing, and doesn’t incorporate any of the improvements (windup suppression, sample time changes, etc) available in the PID library. The calling function has to manage the persistent parameters, but that’s a small price to pay for clarity and the assurance that the output value will indeed be updated every time the function is called.

With this function in hand, I worked on getting the robot to reliably track a specified offset, but was initially stymied because while I could get it to control the motors so that the robot stayed parallel to the nearest wall, I still couldn’t get it to track a specific offset. I solved this problem by leveraging my new-found ability to make accurate, rate-controlled turns; the robot first turns by an amount proportional to it’s distance from the desired offset, moves straight ahead until the offset is met, and then turns the same number of degrees in the other direction. Assuming the robot started parallel to the wall, this results in it facing the direction of travel, at the desired offset and parallel to the nearest wall. Here is the code for this algorithm.

Here are a couple of videos showing the ability to capture and track a desired offset from either side.

In both of the above videos, the desired wall offset is 30 cm.

Stay Tuned,

Frank

Turn Rate PID Tuning, Part IV

Posted 10 June 2021,

In my last post on this issue, I described using a small test program to explore an in-line version of the PID (Proportional-Integral-Differential) algorithm for turn rate control with Wall-E2, my autonomous wall-following robot. This post describes some follow-on work on this same subject.

The fundamental problem with all the available Arduino PID libraries is they all require the user to wait in a loop for the PID::Compute() function to decide when to actually produce a new output value, and since this computation is inside the function, it is difficult or impossible to synchronize any other related timed element with the PID function. In my case where I want to control the turn rate of a robot, the input to the PID engine is, obviously, the turn rate, in degrees/sec. But, calculation of the turn rate is necessarily a timed function, i.e. (curent_heading – last_heading) / elapsed_time, where the ‘elapsed_time’ parameter is usually a constant. But, all the Arduino PID libraries use an internal private class member that defines the measurement period (in milliseconds), and this value isn’t available externally (well, it is, but only because the user can set the sample time – it can’t be read). So, the best one can do with the current libraries is to use the same constant for PID::SetSampleTime() and for any external time-based calculations, and hope there aren’t any synchronization issues. With this setup, it would be quite possible (and inevitable IMHO) for the PID::Compute() function to skip a step, or to be ‘phase-locked’ to producing an output that is one time constant off from the input.

The solution to this problem is to not use a PID library at all, and instead place the PID algorithm in-line with the rest of the code. This ensures that the PID calculation any related time-based calculations are operating on the same schedule. The downside of this arrangement is loss of generality; all the cool enhancements described by Brett Beauregard in his wonderful PID tutorial go away or have to be implemented in-line as well. From Brett’s tutorial, here’s ‘the beginner’s PID algorithm’:

The difficulty with all the current PID libraries is the ‘dt’ parameter in the above expression; the implementation becomes much easier if ‘dt’ is a constant – i.e. the time between calculations is a constant. However, this constraint also requires that the library, not the user program, controls the timing. This just doesn’t work when the ‘Input’ parameter above also requires a constant time interval for calculation. In my case of turn rate control, the turn rate calculation requires knowledge of the time interval between calculations, and the calculation itself should be done immediately after the turn rate is determined, using the same time interval. So, the turn rate is calculated and then PID::Compute() is called, but Compute() may or may not generate a new output value, because it can return without action if it’s internal time duration criteria isn’t met; see the problem? It may, or even might, generate a new output value each time, but there is no way to ensure that it will!

After figuring this out the hard way (by trying and failing to make the library work), I finally decided to forget the library – at least for my turn rate problem, and in-line all the needed code. Once I had it all running, I abstracted just the PID algorithm to its own function so I could use it elsewhere. This function is shown below:

As you can see, the explanatory comments are much bigger than the function itself, which is really just eight lines long. Also, it has a huge number of arguments, five of which are references that are updated by the function. This function wouldn’t win any awards for good design, as it has too many arguments (wide coupling), but it does have high cohesion (does just one thing), and the coupling is at least ‘data’ coupling only.

Once this function was implemented, the calling function (in this case ‘SpinTurn()’ looks like this:

In the above code, the lines dealing with ‘TIMSK5’ are there to disable and then re-enable the TIMER5 interrupt I have set up to update external sensor values every 100 mSec. I’m not really sure that this HAS to be done, but once I learned how to do it I figured it wouldn’t hurt, either ☺

Now that I have this ‘PIDCalcs()’ function working properly, I plan to use it in several other places where I currently use the PID library; it’s just so much simpler now, and because all the relevant parameters are visible to the calling program, debugging is now a piece of cake where before it was just an opaque black box.

12 June 2021 Update:

After chasing down and eliminating a number of bugs and edge-case issues, I think I now have a pretty stable/working version of the ‘SpinTurn’ function, as shown below:

With this code in place, I made some 180º turns at 45 & 90 deg/sec, both on my benchtop and on carpet, as shown in the plots and video below:

Average turn rate = 41.8 deg/sec
Average turn rate = 86 deg/sec
Average turn rate = 44.8 deg/sec
Average turn rate = 90.1 deg/sec

Stay Tuned!

Frank