However, I will state that using e.g. Lyapunov functions to prove the stability of the system requires a model of the system. And even if you need a guarantee for your system, that guarantee is only as good as the fidelity of your model. For an inexpensive RC car, with slippage and saturation, without torque control or inertial sensing, you're going to have a hard time doing something that sounds as principled as what you suggest.
In any case I think I understand your comment, that in addition to the control problem, there's a perception problem.
I think Rockets are straightforward too just a bottle with expanding gasse through a series of nozzles, pointed at different angles at correct time but since I know I am not a rocket scientist I dont go around claiming moon-landing was not a "great intellectual" effort.
A tree falls in an intersection because some carpenter ants chewed through trunk. Cars swerve to miss the tree and collide in an inelastic ball of nonlinearity, showering debris everywhere. You approach this at 65 mph and have 23 ft to decide what to do. Fear not, you have a list, a perfect list with coordinates, velocities, and material properties of every solid body in the area. Furthermore, without great intellectual effort, you can solve the millions of coupled differential equations that govern the dynamics of the entire system in near real time. Oh, and your list also has a measure of importance of each bit of mass, whether it is human, animal, or inert. And your list also accounts for the degrees of freedom introduced by every other car approaching the intersection, also using their own respective lists and perfect knowledge of the world to miss each other?
This is an unbelievably wrong comment. All the Lyapunov and traditional Process control theory in the world won't help you solve autonomous driving. Also regarding "Guarantees and Safety" they don't magically appear out of thin air when you use traditional process control especially in noisy domains like autonomous driving. This comment is equivalent of "I can write code to solve Atari Pong in any programming language deterministicly so any post showing Deep Reinforcement Learning is stupid"...
Guarantees of safety (more accurately stability) is the entire point of lyaponov analysis, and it's used on noisy systems all of the time (https://www.mathematik.hu-berlin.de/~imkeller/research/paper...). Can you point to a specific noisy system that control theory is ill suited for?
The whole Lyapunov and control theory assumes perfect knowledge of sensors. Even though the signal itself might be error prone you have a signal. In case of autonomous driving even in simple cases as those described in the blogposts knowing the exact position of the markers and then using them to tune the contoller is not as easy as you might think.
The end-to-end system shown here solves three problems it processes the images to derive the signal, it then represents it optimally to the controller and then tunes the controller using provided training labels.
But classical control theory hasn't been able to extract, from camera pixels, the open path in a road with cars, bicycles, and pedestrians. Camera inputs are million-dimensional, and there aren't accurate theoretical models for them.
But in this case though, any kind of state space control also requires rather precise knowledge of the physical laws that govern the dynamics of the vehicles. When such information is not available, can neural nets do a decent job at mimicking an analytical control algorithm? I think that's an interesting problem worth exploring.
It uses a Raspberry Pi and ~50 lines of code. So I don't think anyone should expect it to do something that's impossible with other approaches.
Is it really trivial? Honest question... Which control algorithms are you speaking of?
Computing how much of an adjustment is required is where the PID part comes in. The controller uses the Derivative (rate of change) of the error as well the the Integral of the error to improve its estimate. These two values can intuitively be thought of as the predicted error and history of the error, respectively.
The handful of parameters you need to adjust in a PID controller parameterizes a very small class of controllers. For a given control problem, the controller you want might fall outside that class. People try to expand the class of "PID" controllers in all sorts of ways (e.g. anti-windup), but from where I stand it's just hacks on top of hacks.
It makes sense to consider a much wider class of controllers, with many more parameters, to possibly achieve better performance, or at least to avoid having an expert tune some gains in place of collecting bucket-loads of data.
The delay in your steering response (how fast you can measure the error and turn the wheel) is large enough here that if you aren't actively taking the non-linearities of the problem into account you will oscillate off the road. The other way to fix this is to aim for a point far ahead of you such that your steering response time is significantly less than your "following distance", but that results in cutting corners.
Thanks also for the link to wikiwand!
Yeah, Wikiwand is amazing. Be sure to grab the browser plugin: it automatically redirects any Wikipedia links to Wikiwand.
While this example is simplified - and I wouldn't recommend it for a real-world full-size vehicle trial - it does implement everything (scaled down) described in NVidia's paper:
https://images.nvidia.com/content/tegra/automotive/images/20...
In short, the project uses OpenCV for the vision aspect, a small CNN for the model, uses "behavioral cloning" (where the driver drives the vehicle, taking images of the "road" and other sensor data like steering - as features and labels respectively - then trains on that data), and augmentation of the data to add more training examples, plus training data for "off course" correction examples...
If you read the NVidia paper, you'll find that's virtually all the same things they did, too! Now - they gathered a butt-ton (that's a technical measurement) more data, and their CNN was bigger and more complex (and probably couldn't be trained in reasonable time without a GPU), plus they used multiple cameras (to simulate the "off-lane" modes), and they gathered other label data (not just steering, but throttle, braking, and other bits)...but ultimately, the author of the smaller system captured everything.
Furthermore, NVidia's system was used on a real-world car, and performed quite well; there are videos out there of it in action.
This is virtually the same kind of example system that the "behavioral cloning" lab of Udacity's Self-Driving Car Engineer Nanodegree is using. We're free to select what and how to implement things, of course, but I am pretty certain we all understand that this form of system works fairly well in a real-world situation, and so most of us are going down the same route (ie, behavioral cloning, cnn, opencv, etc). Our "car" though is a simulation vehicle on a track, built using Unity3D.
> Of course, the CV part -- "seeing" the lines -- requires some form of ML to work in the real world.
Actually, it doesn't. The first lab we did in the Udacity course used OpenCV and Numpy exclusively to "find and highlight lane-lines" (key part was to convert the image from BGR to HSV, and mask using the hue). No ML was required.
That said - I wouldn't trust it for real-world vehicle driving use - but it possibly could be used as part of a system; however, as NVidia has shown, a CNN works much better, without needing to do any pre-processing with OpenCV to extract features of the image - the CNN learns to do this on its own.