Robogames 2013 has come and gone, with all manner of amazing robot mahem unleashed. Unfortunately, Savage Solder didn’t have the best performance in Robomagellan, hitting a trash can on its first run, and a newly added picnic table on its second. Our motor controller popped after that run, so we didn’t get a third attempt. Hopefully I will post a more detailed post-mortem later, but for now, I’ve uploaded the video of our best competition performance this year.
The final pieces of the cone detection and tracking system for Savage Solder are the tools we used to derive all the constants necessary for each of the algorithms. In part 1 (cone detector) and part 2 (cone tracker) I described how we first pick out possible range and bearings to cones in an image, and then take those range and bearings and turn them into a local Cartesian coordinate through the tracking process. As mentioned there, each of those stages has many tunable knobs.For the first stage, the following are the key parameters:
Additionally, the cone tracker has its own set of parameters:
What we did in 2012, during the preparation for our first RoboMagellan, was take a lot of pictures of cones during our practice runs. Savage Solder normally is configured to save an image twice a second all the time it is running. These image datasets formed the basis of our ability to tune parameters and develop algorithms that would be robust in a wide range of conditions.
The basic idea we worked off was to create a metric for how good the system is, and then evaluate the metric over a set of data using our current algorithms and constants. You can then easily tweak the constants and algorithms as much as you want without running the car one bit and have good confidence that the results will be applicable to actual live runs.
Annotation Pipeline
Most of the metrics we wanted involved knowing where the cones actually were in the images. If we could just robustly identify cones in images programmatically, we wouldn’t really be worrying about this to begin with. So instead, we created a set of tools that let us rapidly mark, or annotate, images to indicate where the absolute ground truth of cones could be found. This is just a simple custom OpenCV program with some keyboard shortcuts that let us classify the cones in about 3000 images in a couple of hours. We selected images from varying times of day, angles, and lighting conditions, so that we would have a robust training set.
OpenCV Application for Annotation
Then, with a little wrapper script, we ran our cone detection algorithm over each of the frames. As mentioned in the on the cone detector, it outputs one or more range/bearing pairs to each of the prospective cones in the image. The quality metric then scores the cone detector based on accuracy of bearing and range to real cones, missed detections, and false detections. It also keeps histograms of each detection category by range. In the end, for a given set of cone detector parameters, we end up with a table that looks like the one below.
| Range | Detection Rate | False Positive Rate |
|---|---|---|
| 3m | 91% | 2% |
| 5m | 95% | 7% |
| 7.5m | 93% | 21% |
| 10m | 89% | 34% |
| 15m | 72% | 26% |
| 20m | 37% | 23% |
After each run over all the images, we would try changing the parameters to the cone detector, then seeing what the resultant table would like. Ideally, you have a much higher detection rate than false positive rate over the ranges you care about. The table above is actually the final one we were able to achieve for 2012, which allowed us to reliably sense cones at 15 meters of range using just our 640x480 stock webcam.
We got our final day of testing in at Danehy park in preparation for Robogames 2013 this weekend. Everything worked as well as we expected, the only things that would have caused problems on race day were trying to fit through areas too narrow for the basic GPS we were getting at the time. All in all, our speed, cornering, and tracking performance are much improved over 2012.
Along with many others, we’re hoping to enter our car into the Sparkfun AVC 2013 this year! In support of our effort, I put together some datasets and 3D assets that might be useful to other participating teams, especially if they do any work in simulation.
First, I used the most recent measurements from April 9th on the AVC website to create a kml file showing where each of the obstacles is, along with the course boundaries. I’ve included a snapshot from Google Earth below to show what it contains.
Sparkfun AVC 2013 Course Layout
Next, I extracted some freely available USGS ortho imagery and created a cropped version covering just the course. I essentially used the techniques described in my post on LIDAR imagery, except that the ortho imagery came from the USGS National Map Viewer. I created both a geotiff that has georeferencing information, and an opaque .png which is projected identically, but has no embedded information. On that last image, I did a little gimp hackery to edit out cars which would be in the path of the actual course.
I also made a set of somewhat (OK very) crude blender models of each of the different obstacles present on the course to approximately correct dimensions. This includes the barrels, the hoop, and the ramp.
 avc2013-barrel.blend |
 avc2013-hoop.blend |
 avc2013-ramp.blend |
|---|
Finally, just for fun, I recorded a screencast of one of the first drivethroughs of Savage Solder on the simulated Sparkfun AVC Course. This was with just the bare minimum of changes from what we’ll use at RoboMagellan in Robogames in two weeks, so for now it was navigating purely by GPS and IMU. It drives through the hoop about one time in three, which is enough to catch a good video! As in my previous simulation videos, the yellow line is where the absolute surveyed GPS path is. The green line is where the car thinks the GPS path is at any moment, which will differ due to GPS error and heading error.
Last time I covered the techniques we use on Savage Solder to pick out orange traffic cones from webcam images in the “Cone Detector”. This time, I’ll look at the next stage in that pipeline, turning the range and bearing reported by the cone tracker into Cartesian coordinate estimates of where any given cone is.
As mentioned last time, our “Cone Tracker” takes as input the range and bearing, (along with their uncertainties), from the cone detector. It also receives the current navigation state of the car. This includes things like the current estimate of geodetic position (latitude and longitude), current map position, (UTM easting and northing), and an unreferenced local coordinate system (x, y). For each of these, it reports the vehicle’s speed and heading.
I won’t go into the details of each of these coordinate systems here, but since the cone tracker actually only uses the local one, I can discuss it a bit. The local coordinate system on Savage Solder starts out at x,y=(0m,0m) with a heading of 0 degrees at the beginning of every run. As time progresses, the heading and position are updated primarily based on our onboard dead reckoning sensors. The local coordinate system is smooth, and never jumps for GPS updates. As a consequence, it isn’t really useful to compare positions in it from more than a minute or two apart, nor is it useful to do GPS based navigation. Fortunately, for cone tracking, from the time to when we see the cone to when we touch it is usually only a couple of seconds total over which time the local solution is very accurate.
Now, let’s cover some broad details of the implementation. The guts of our cone tracker consists of a bank of identical Kalman Filters. Each Kalman filter estimates the position of one particular cone and the error in that estimate. This lets the car keep around several possible cones that could be in sight at one time while still distinguishing them. By storing the cones in a local coordinate system, it allows for easy driving towards, or alongside, the cone and accurate speed control leading up to it. The position uncertainty could be used to control behavior, but we don’t bother in our current implementation.
Cone Tracker Internals
Additionally, the tracker has to handle seeing new cones for the first time, and discarding cones that maybe were false detections in the cone detector. It does this by assigning each cone a “likelihood”, which is just a probability that the cone is a true detection. When data arrives that match the cone well, its likelihood is increased. When the available data doesn’t match the cone very well, or no cone is observed at all when one is expected, the likelihood is decreased.
If a range and bearing arrive which corresponds to no known cones, a new one is created with a relatively low likelihood. Then once it has reached a certain threshold, it is reported to the outside world as a valid target. Conversely, when an existing cone’s likelihood reaches a level which is too low, it is removed entirely on the thesis that it was actually a false detection to begin with.
More specifically, the likelihood update is handled using Bayes theorem. We have an empirically derived table showing, for our detector, the odds that a cone will be detected or a false one will be seen at various ranges. These are used to fill in the various probabilities in the equations.
A “measurement” in this problem is simply the range and bearing that the cone detector reports. To incorporate a new measurement, the tracker looks through all the cones currently in its filter bank. For each, it computes a measure of the likelihood that the given cone could produce the current measurement. This is done using what’s called the Mahalanobis distance. The Mahalanobis distance is just a measure of how far away you are from an uncertain target in a multi-dimensional space.
If the best matching cone has a Mahalanobis distance small enough to count as valid, then the standard Kalman filter update equation is applied to that cone. If no cones match, then we create a new one as described above.
Cone Tracker Flowchart
One final detail, is that in addition to estimating the position of each cone, the tracker also estimates its “scale” as seen by the cone detector. The image based detector we use has the property that the range values are likely to have a fixed scale error for a number of reasons. One, the cones could actually be bigger or smaller than the regulation sized ones. Second, lighting conditions can sometimes cause a fraction of the cone to be not detected, which will result in the cone being seen as smaller than it actually is.
Since the range values are not correct, the position will be similarly off. This error isn’t as bad as it seems, since we (and most every RoboMagellan entrant), approach the cone in a straight line. Thus the position errors will always be directly towards or away from the robot, and as long as you keep moving, you’ll hit it eventually.
Savage Solder has two reasons to care. First, is that we decelerate from a high speed to an appropriate “bumping” speed with just a half meter to spare. Thus, if the cone is estimated as too close, we run the risk of colliding with it at an unsafe speed and damaging our front end. Secondly, we have a mode where the car can just “clip” the cone by driving alongside it and tapping it with a protruding stick. This allows us to avoid stopping entirely when the geometry allows it. However, if the position estimate is incorrect here, we might miss the cone entirely.
To summarize, the cone tracker handles each new range and bearing with the following steps:
One of the challenges with this approach is that there are a lot of constants to tune. I’ll cover the details in a later post, but for most of them we tried to find some way to empirically measure reasonable values for our application. Another problem was debugging. printf doesn’t cut it when you have this much geometry. For that, we created a number of custom debugging and visualization tools which help show what is going on in the system, some of which I’ll cover later too.
