Simple Simulation of Time Dependent Dynamics - drake

So, I am wanting to simulate the dynamics of a system which varies over time.
Essentially:
xdot = Q/C_a - x/(R_aC_a)
where Q is an impulse train with period T. I estimate the solution by hand with some different techniques. But, I was curious if there was a simple way in drake to account for this time-dependence.

Time dependence is supported in basically every workflow -- even in the SymbolicVectorSystem that I know you have been using, you can define a variable for time and your dynamics method can depend on it.
An impulse train (in time), though, is a particular dependence on time that we need to think through. These are often used as models of sampling/reconstruction (particularly useful in the frequency domain), but not very common in continuous-time simulation, I think? I'm not sure you actually want to have that on your input? If you do, then drake's event systems are probably up to the task, but first I want to check if it's really your intended workflow.

Related

Inquiry of Drake simulator automatic differentiation

I have a question regarding the drake simulator's automatic differentiation abilities. I have a paper coming out soon in a few months and some of the feedback was that I didn't comment enough on automatic differentiation.
I am familiar with automatic differentiation but am unclear how it works with physics simulators exactly.As far as i'm aware, once you have constructed the graph, you can query it several times with a forwards pass and calculate the partial derivatives of outputs with respect to inputs. In my head, querying such a graph should be computationally quick.
In the drake simulator, once I load a scene, lets say a robot arm with a single free body item (like a cube or cylinder), does it create a graph that you can query regardless of the state of the system? Or does the graph need to be reconstructed depending on the system state. For instance would the same graph work in a situation when the arm was in contact with the free body item and also when it is doing free space motion?
There is this paper (https://arxiv.org/pdf/2202.13986.pdf) where they use drake for contact based manipulation tasks in python. Their optimization takes significant time and they claim it is down to drakes automatic differentiation scheme. The only way I can think getting the derivatives over their trajectories takes so long is if at each time step, a new graph needs to be constructed.
Is anyone able to comment on this from the drake team? Or maybe even link me a useful document regarding how drake's automatic differentiation works? I have been unsuccessful in finding this information myself so far.
Drake uses Eigen's AutoDiffScalar instead of double to obtain derivatives from the same code we use for computation. That method does not build a graph at all but rather performs rote propagation of the chain rule though the computation, ending up finally with both the result and partial derivatives of that result with respect to any chosen variables.

Turning some of the states in a Drake system into inputs

Consider an existing Drake System (for example MultibodyPlant). Is there a way to wrap that System inside a Diagram in such a way as to convert some of the states of the internal System to be inputs instead, i.e. set directly from input ports of the outer Diagram?
The motivation would be essentially to make a change in modeling decisions. For example, a quadrotor is sometimes considered to have its angular rates and collective thrust as inputs, instead of the collective thrust and body moments (or similarly, individual rotor commands).
In a more complex system, perhaps I might assume I have instantaneous control over certain velocities (e.g. internal, fully-actuated joints with fast dynamics), but still want to model the entire multibody system's dynamics accounting for the current choice of velocity in terms of Coriolis terms etc.
What I'm getting at is actually very similar to the modeling choice for the elevator in the Flat-Plate Glider Model - but I'd like to avoid manually implementing a LeafSystem because my system has nontrivial multibody dynamics.
My sense is that this may not be possible since I don't know of any way for a Diagram to interfere with the internal dynamics of a System, so "deleting" a state and promoting it to an input seems impossible. But I thought there might be some clever method to do this.
Thanks in advance!
I agree with your analysis. The simplest answer is "no" -- systems that declare state cannot be post-hoc exploded to have that state come from an input port. But for the specific examples that you mention, there are a few possibilities / related ideas.
The first is the notion of a prescribed motion constraint -- e.g. that one can set the positions/velocities of joints in a MultibodyPlant directly. We don't implement that yet, unfortunately, but it is a reasonable request that we've discussed occasionally
(here is one example: https://github.com/RobotLocomotion/drake/issues/14694).
As you say, you could implement a PD controller just outside of the system to achieve the desired effect. The only real difference between this and the way that we would implement the prescribed motion constraint internally, is that we can choose the gains well and inform the solver about that constraint directly.
Another possibility is to implement a force element that works "inside" the plant and accepts an input port. This would allow you to apply forces to implement your modeling ideas even in ways that are not possible through the actuation_input_port (e.g. not achievable by a declared actuator).
The glider example you link is a good one. In that case, I was very worried about having a model that avoided even declaring the velocity of the elevator as state (since our verification methods scale in complexity with the dimension of the state space). For now, that still requires writing a bespoke LeafSystem implementation.

How do i represent the chromosome using Genetic Algorithm?

My task is to calculate clashes between alert time schedule and the user calendar schedule to generate the clashes less alert time schedule.
How should i represent the chromosome according to this problem?
How should i represent the time slots? (Binary or Number)
Thank You
(Please Consider i'm a beginner to the genetic algorithm studies)
Questions would be: What have you tried so far? How good are your results so far? Also your Problem is
stated quite unspecific. Thus here is what I can give:
The Chromosome should probably be the starttime of the alerts in your schedule (if I understood your Problem correctly).
As important is to think of the ways you want to evaluate and calculate the Fitness of your individuals (here clashes (e.g. amount or time overlap between appointments), but it is obvious that you might find better heuristics to receive better solutions / faster convergence)
Binary or continuous number might both work: I am usually going for numbers whenever there is no strong reason to not do so (since it is easier to Interpret, debug, etc.). Binary comes with some nice opportunities with respect to Mutation and Recombination.
I strongly recommend playing around and reading about those Things. This might look like a lot of extra work to implement, but you should rather come to see them as hyperparameters which Need to be tuned in order to receive the best Outcome.

Image analysis technique to determine approximate change in view over a short period of time?

I am working on an open source package for robot owners. I want to do a decent job of detecting when the robot is having movement problems. One of the problems the robot commonly has is that the back wheel gets "tucked underneath" in a bad way and makes it turn very slowly when on carpet. I believe that with a combination of accelerometer value inspection and (I hope) a relatively simple yet robust vision analysis technique, I will be able to tell when the robot is having this specific problem.
What I need is to be able to analyze two images, separated by about 1/2 second in time, and get a numerical value that tells about how close they are, but in a way that has some intelligence about the objects in the screen instead of just a simple color/hue/etc. analysis. I've heard of an algorithm called optical flow that is used in object and scene tracking, but I'm hoping I don't need something heavyweight.
Is there an machine vision algorithm/function that can analyze two JPEG's and tell if they belong to the same scene and viewpoint, yet can also deliver a numerical monotonically increasing value that tells me rough how different they are? If I could get that numerical value and compare it to the number of milliseconds past, while examining the current accelerometer activity, I believe I can detect when the robot is having the "slow turn of death" problem.
If so, please tell me the basic technique involved, and if you know of machine vision library that implements it, which one it is.
but in a way that has some intelligence about the objects in the screen instead of just a simple color/hue/etc. analysis
What you are suggesting is a complex problem by itself, so forget about 'lightweight' solutions. Probably you are going to need something like optical flow.
Other options I would recommend you looking into are:
Vanishing points detection and variation from image to image. This quite fits into your problem domain Wikipedia
Disparity map: related to optical flow. Used for stereographic vision, but I think you can use it for the kind of application you are looking for. Take a look at this

How to train an artificial neural network to play Diablo 2 using visual input?

I'm currently trying to get an ANN to play a video game and and I was hoping to get some help from the wonderful community here.
I've settled on Diablo 2. Game play is thus in real-time and from an isometric viewpoint, with the player controlling a single avatar whom the camera is centered on.
To make things concrete, the task is to get your character x experience points without having its health drop to 0, where experience point are gained through killing monsters. Here is an example of the gameplay:
Now, since I want the net to operate based solely on the information it gets from the pixels on the screen, it must learn a very rich representation in order to play efficiently, since this would presumably require it to know (implicitly at least) how divide the game world up into objects and how to interact with them.
And all of this information must be taught to the net somehow. I can't for the life of me think of how to train this thing. My only idea is have a separate program visually extract something innately good/bad in the game (e.g. health, gold, experience) from the screen, and then use that stat in a reinforcement learning procedure. I think that will be part of the answer, but I don't think it'll be enough; there are just too many levels of abstraction from raw visual input to goal-oriented behavior for such limited feedback to train a net within my lifetime.
So, my question: what other ways can you think of to train a net to do at least some part of this task? preferably without making thousands of labeled examples.
Just for a little more direction: I'm looking for some other sources of reinforcement learning and/or any unsupervised methods for extracting useful information in this setting. Or a supervised algorithm if you can think of a way of getting labeled data out of a game world without having to manually label it.
UPDATE(04/27/12):
Strangely, I'm still working on this and seem to be making progress. The biggest secret to getting a ANN controller to work is to use the most advanced ANN architectures appropriate to the task. Hence I've been using a deep belief net composed of factored conditional restricted Boltzmann machines that I've trained in an unsupervised manner (on video of me playing the game) before fine tuning with temporal difference back-propagation (i.e. reinforcement learning with standard feed-forward ANNs).
Still looking for more valuable input though, especially on the problem of action selection in real-time and how to encode color images for ANN processing :-)
UPDATE(10/21/15):
Just remembered I asked this question back-in-the-day, and thought I should mention that this is no longer a crazy idea. Since my last update, DeepMind published their nature paper on getting neural networks to play Atari games from visual inputs. Indeed, the only thing preventing me from using their architecture to play, a limited subset, of Diablo 2 is the lack of access to the underlying game engine. Rendering to the screen and then redirecting it to the network is just far too slow to train in a reasonable amount of time. Thus we probably won't see this sort of bot playing Diablo 2 anytime soon, but only because it'll be playing something either open-source or with API access to the rendering target. (Quake perhaps?)
I can see that you are worried about how to train the ANN, but this project hides a complexity that you might not be aware of. Object/character recognition on computer games through image processing it's a highly challenging task (not say crazy for FPS and RPG games). I don't doubt of your skills and I'm also not saying it can't be done, but you can easily spend 10x more time working on recognizing stuff than implementing the ANN itself (assuming you already have experience with digital image processing techniques).
I think your idea is very interesting and also very ambitious. At this point you might want to reconsider it. I sense that this project is something you are planning for the university, so if the focus of the work is really ANN you should probably pick another game, something more simple.
I remember that someone else came looking for tips on a different but somehow similar project not too long ago. It's worth checking it out.
On the other hand, there might be better/easier approaches for identifying objects in-game if you're accepting suggestions. But first, let's call this project for what you want it to be: a smart-bot.
One method for implementing bots accesses the memory of the game client to find relevant information, such as the location of the character on the screen and it's health. Reading computer memory is trivial, but figuring out exactly where in memory to look for is not. Memory scanners like Cheat Engine can be very helpful for this.
Another method, which works under the game, involves manipulating rendering information. All objects of the game must be rendered to the screen. This means that the locations of all 3D objects will eventually be sent to the video card for processing. Be ready for some serious debugging.
In this answer I briefly described 2 methods to accomplish what you want through image processing. If you are interested in them you can find more about them on Exploiting Online Games (chapter 6), an excellent book on the subject.
UPDATE 2018-07-26: That's it! We are now approaching the point where this kind of game will be solvable! Using OpenAI and based on the game DotA 2, a team could make an AI that can beat semi-professional gamers in a 5v5 game. If you know DotA 2, you know this game is quite similar to Diablo-like games in terms of mechanics, but one could argue that it is even more complicated because of the team play.
As expected, this was achieved thanks to the latest advances in reinforcement learning with deep learning, and using open game frameworks like OpenAI which eases the development of an AI since you get a neat API and also because you can accelerate the game (the AI played the equivalent of 180 years of gameplay against itself everyday!).
On the 5th of August 2018 (in 10 days!), it is planned to pit this AI against top DotA 2 gamers. If this works out, expect a big revolution, maybe not as mediatized as the solving of the Go game, but it will nonetheless be a huge milestone for games AI!
UPDATE 2017-01: The field is moving very fast since AlphaGo's success, and there are new frameworks to facilitate the development of machine learning algorithms on games almost every months. Here is a list of the latest ones I've found:
OpenAI's Universe: a platform to play virtually any game using machine learning. The API is in Python, and it runs the games behind a VNC remote desktop environment, so it can capture the images of any game! You can probably use Universe to play Diablo II through a machine learning algorithm!
OpenAI's Gym: Similar to Universe but targeting reinforcement learning algorithms specifically (so it's kind of a generalization of the framework used by AlphaGo but to a lot more games). There is a course on Udemy covering the application of machine learning to games like breakout or Doom using OpenAI Gym.
TorchCraft: a bridge between Torch (machine learning framework) and StarCraft: Brood War.
pyGTA5: a project to build self-driving cars in GTA5 using only screen captures (with lots of videos online).
Very exciting times!
IMPORTANT UPDATE (2016-06): As noted by OP, this problem of training artificial networks to play games using only visual inputs is now being tackled by several serious institutions, with quite promising results, such as DeepMind Deep-Qlearning-Network (DQN).
And now, if you want to get to take on the next level challenge, you can use one of the various AI vision game development platforms such as ViZDoom, a highly optimized platform (7000 fps) to train networks to play Doom using only visual inputs:
ViZDoom allows developing AI bots that play Doom using only the visual information (the screen buffer). It is primarily intended for research in machine visual learning, and deep reinforcement learning, in particular.
ViZDoom is based on ZDoom to provide the game mechanics.
And the results are quite amazing, see the videos on their webpage and the nice tutorial (in Python) here!
There is also a similar project for Quake 3 Arena, called Quagents, which also provides easy API access to underlying game data, but you can scrap it and just use screenshots and the API only to control your agent.
Why is such a platform useful if we only use screenshots? Even if you don't access underlying game data, such a platform provide:
high performance implementation of games (you can generate more data/plays/learning generations with less time so that your learning algorithms can converge faster!).
a simple and responsive API to control your agents (ie, if you try to use human inputs to control a game, some of your commands may be lost, so you'd also deal with unreliability of your outputs...).
easy setup of custom scenarios.
customizable rendering (can be useful to "simplify" the images you get to ease processing)
synchronized ("turn-by-turn") play (so you don't need your algorithm to work in realtime at first, that's a huge complexity reduction).
additional convenience features such as crossplatform compatibility, retrocompatibility (you don't risk your bot not working with the game anymore when there is a new game update), etc.
To summarize, the great thing about these platforms is that they alleviate much of the previous technical issues you had to deal with (how to manipulate game inputs, how to setup scenarios, etc.) so that you just have to deal with the learning algorithm itself.
So now, get to work and make us the best AI visual bot ever ;)
Old post describing the technical issues of developping an AI relying only on visual inputs:
Contrary to some of my colleagues above, I do not think this problem is intractable. But it surely is a hella hard one!
The first problem as pointed out above is that of the representation of the state of the game: you can't represent the full state with just a single image, you need to maintain some kind of memorization (health but also objects equipped and items available to use, quests and goals, etc.). To fetch such informations you have two ways: either by directly accessing the game data, which is the most reliable and easy; or either you can create an abstract representation of these informations by implementing some simple procedures (open inventory, take a screenshot, extract the data). Of course, extracting data from a screenshot will either have you to put in some supervised procedure (that you define completely) or unsupervised (via a machine learning algorithm, but then it'll scale up a lot the complexity...). For unsupervised machine learning, you will need to use a quite recent kind of algorithms called structural learning algorithms (which learn the structure of data rather than how to classify them or predict a value). One such algorithm is the Recursive Neural Network (not to confuse with Recurrent Neural Network) by Richard Socher: http://techtalks.tv/talks/54422/
Then, another problem is that even when you have fetched all the data you need, the game is only partially observable. Thus you need to inject an abstract model of the world and feed it with processed information from the game, for example the location of your avatar, but also the location of quest items, goals and enemies outside the screen. You may maybe look into Mixture Particle Filters by Vermaak 2003 for this.
Also, you need to have an autonomous agent, with goals dynamically generated. A well-known architecture you can try is BDI agent, but you will probably have to tweak it for this architecture to work in your practical case. As an alternative, there is also the Recursive Petri Net, which you can probably combine with all kinds of variations of the petri nets to achieve what you want since it is a very well studied and flexible framework, with great formalization and proofs procedures.
And at last, even if you do all the above, you will need to find a way to emulate the game in accelerated speed (using a video may be nice, but the problem is that your algorithm will only spectate without control, and being able to try for itself is very important for learning). Indeed, it is well-known that current state-of-the-art algorithm takes a lot more time to learn the same thing a human can learn (even more so with reinforcement learning), thus if can't speed up the process (ie, if you can't speed up the game time), your algorithm won't even converge in a single lifetime...
To conclude, what you want to achieve here is at the limit (and maybe a bit beyond) of current state-of-the-art algorithms. I think it may be possible, but even if it is, you are going to spend a hella lot of time, because this is not a theoretical problem but a practical problem you are approaching here, and thus you need to implement and combine a lot of different AI approaches in order to solve it.
Several decades of research with a whole team working on it would may not suffice, so if you are alone and working on it in part-time (as you probably have a job for a living) you may spend a whole lifetime without reaching anywhere near a working solution.
So my most important advice here would be that you lower down your expectations, and try to reduce the complexity of your problem by using all the information you can, and avoid as much as possible relying on screenshots (ie, try to hook directly into the game, look for DLL injection), and simplify some problems by implementing supervised procedures, do not let your algorithm learn everything (ie, drop image processing for now as much as possible and rely on internal game informations, later on if your algorithm works well, you can replace some parts of your AI program with image processing, thus gruadually attaining your full goal, for example if you can get something to work quite well, you can try to complexify your problem and replace supervised procedures and memory game data by unsupervised machine learning algorithms on screenshots).
Good luck, and if it works, make sure to publish an article, you can surely get renowned for solving such a hard practical problem!
The problem you are pursuing is intractable in the way you have defined it. It is usually a mistake to think that a neural network would "magically" learn a rich reprsentation of a problem. A good fact to keep in mind when deciding whether ANN is the right tool for a task is that it is an interpolation method. Think, whether you can frame your problem as finding an approximation of a function, where you have many points from this function and lots of time for designing the network and training it.
The problem you propose does not pass this test. Game control is not a function of the image on the screen. There is a lot of information the player has to keep in memory. For a simple example, it is often true that every time you enter a shop in a game, the screen looks the same. However, what you buy depends on the circumstances. No matter how complicated the network, if the screen pixels are its input, it would always perform the same action upon entering the store.
Besides, there is the problem of scale. The task you propose is simply too complicated to learn in any reasonable amount of time. You should see aigamedev.com for how game AI works. Artitificial Neural Networks have been used successfully in some games, but in very limited manner. Game AI is difficult and often expensive to develop. If there was a general approach of constructing functional neural networks, the industry would have most likely seized on it. I recommend that you begin with much, much simpler examples, like tic-tac-toe.
Seems like the heart of this project is exploring what is possible with an ANN, so I would suggest picking a game where you don't have to deal with image processing (which from other's answers on here, seems like a really difficult task in a real-time game). You could use the Starcraft API to build your bot, they give you access to all relevant game state.
http://code.google.com/p/bwapi/
As a first step you might look at the difference of consecutive frames. You have to distinguish between background and actual monster sprites. I guess the world may also contain animations. In order to find those I would have the character move around and collect everything that moves with the world into a big background image/animation.
You could detect and and identify enemies with correlation (using FFT). However if the animations repeat pixel-exact it will be faster to just look at a few pixel values. Your main task will be to write a robust system that will identify when a new object appears on the screen and will gradually all the frames of the sprite frame to a database. Probably you have to build models for weapon effects as well. Those can should be subtracted so that they don't clutter your opponent database.
Well assuming at any time you could generate a set of 'outcomes' (might involve probabilities) from a set of all possible 'moves', and that there is some notion of consistency in the game (eg you can play level X over and over again), you could start with N neural networks with random weights, and have each of them play the game in the following way:
1) For every possible 'move', generate a list of possible 'outcomes' (with associated probabilities)
2) For each outcome, use your neural network to determine an associated 'worth' (score) of the 'outcome' (eg a number between -1 and 1, 1 being the best possible outcome, -1 being the worst)
3) Choose the 'move' leading to the highest prob * score
4) If the move led to a 'win' or 'lose', stop, otherwise go back to step 1.
After a certain amount of time (or a 'win'/'lose'), evaluate how close the neural network was to the 'goal' (this will probably involve some domain knowledge). Then throw out the 50% (or some other percentage) of NNs that were farthest away from the goal, do crossover/mutation of the top 50%, and run the new set of NNs again. Continue running until a satisfactory NN comes out.
I think your best bet would be a complex architecture involving a few/may networks: i.e. one recognizing and responding to items, one for the shop, one for combat (maybe here you would need one for enemy recognition, one for attacks), etc.
Then try to think of the simplest possible Diablo II gameplay, probably a Barbarian. Then keep it simple at first, like Act I, first area only.
Then I guess valuable 'goals' would be disappearance of enemy objects, and diminution of health bar (scored inversely).
Once you have these separate, 'simpler' tasks taken care of, you can use a 'master' ANN to decide which sub-ANN to activate.
As for training, I see only three options: you could use the evolutionary method described above, but then you need to manually select the 'winners', unless you code a whole separate program for that. You could have the networks 'watch' someone play. Here they will learn to emulate a player or group of player's style. The network tries to predict the player's next action, gets reinforced for a correct guess, etc. If you actually get the ANN you want this could be done with video gameplay, no need for actual live gameplay. Finally you could let the network play the game, having enemy deaths, level ups, regained health, etc. as positive reinforcement and player deaths, lost health, etc. as negative reinforcement. But seeing how even a simple network requires thousands of concrete training steps to learn even simple tasks, you would need a lot of patience for this one.
All in all your project is very ambitious. But I for one think it could 'in theory be done', given enough time.
Hope it helps and good luck!

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