I'm looking for an algorithm, and I have no idea where to start!
I'm trying to get from point A to point B in a cartesian graph. Movement is restricted to that of a RC car: backward, forward, forward-left, and forward-right (constant turning radius; car is either turning completely, or it is not turning at all).
How would I construct an algorithm which takes the following:
turningRadius, initialPosition, initialOrientation, finalPosition
And yields an ordered set of steps to get to finalPosition?
Note that I don't care what the final orientation is.
Thanks!
EDIT: Note that this is not in a graph with discreet nodes, but a continuous coordinate system
The way you problem is described, the algorithm is straightforward and requires only two simple steps: 1) move forward while turning (left or right) until the car is pointed directly at B, 2) move straight forward until you hit B. Done.
The only relatively tricky part is the first step. If B lies to the left from the longitudinal axis of the car in its initial position, the natural approach would be to start by turning left. This will work, unless point B lies inside the circular trajectory produced by such a left turn (of radius turningRadius). In the latter case the car will run in circles, but will never be able to aim directly at B. In such cases the proper strategy is actually to start with a right turn and keep turning until you aim the car at B.
So, if you don't have any optimality requirements for your trajectory, the simplest algorithm for the first step would be to unconditionally turn "away" from the point: turn right if B lies to the left of the longitudinal axis of the car, and turn left if B lies to the right. Keep turning until the car is aimed directly at B. This sounds a bit unnatural, but it always works, i.e. you will always be able to eventually aim the car.
If you care for a more optimal (shorter) trajectory, then you need to analyze the location of B with respect to the initial position/orientation of the car ("Is B inside the turning circle or outside?") and choose the direction of the first turn accordingly.
In general this is not an easy problem. It falls under the category of "Planning under differential constrains". The last three chapters of LaValle's book (available online here) deal with this. In particular, look at section 14.4.2., that deals with a "Dubins car", which is like your RC car, except that it doesn't move backwards.
Also search for "Dubins car path planning". You will find a lot of papers.
Have your tried a* (a-star)? it is also nice when you provide it a terrain map. You can assign weights to different portions of terrain which will result in a different path. I believe the algorithm by default does not provide diagonal directions, but you can add that in pretty easily.
Also it does not by default deal with "turning" but a-star will give the full path. What you could do is calculate the turn radius based on 2 points. The current position and the next calculated position, OR the last position and the current position. You can then add or subtract the facing direction with the change in angle. You may need to tweak this some.
Sounds like an interesting and fun project! To get a specific algorithm recommendation, you should probably provide more detail… Like are you expecting to literally run this on some sort of embedded controller attached to an RC car? Or is the algorithm to run on a workstation and control the car remotely? (Or is this purely an abstract exercise and there is no car… awwww.)
My generic recommendation for getting a handle on where to start would be Building Problem Solvers, which is a great intro to the world of "AI" problem solving techniques. It might be a bit dated these days… but wait, what am I saying! Probably not. :-)
[Okay I should explain that last comment: Most "modern" AI techniques that I've seen in practice actually date back to ideas many years old… They've just become practical now thanks to the relentless advance of Moore's Law. So a book written in 1993 is still discussing fairly state-of-the-art techniques, from what I have personally seen. I'd love to be pointed at a counter-example!]
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I'm a relatively inexperienced programmer, and recently I've been getting interested in making a Checkers game app for a school project. I'm not sure where I can start (or if I should even attempt) at creating this. The project I have in mind probably wouldn't involve much more than a simple AI & a multiplayer player mode.
Can anyone give some hints / guidance for me to start learning?
To some extent I agree with some of the comments on the question that suggest 'try something simpler first', but checkers is simple enough that you may be able to get a working program - and you will certainly learn useful things as you go.
My suggestion would be to divide the problem into sections and solve each one in turn. For example:
1) Board representation - perhaps use an 8x8 array to represent the board. You need to be able to fill a square with empty, white piece, black piece, white king, black king. A more efficient solution might be to have a look at 'bit-boards' in which the occupancy of the board is described by a set of 64-bit integers. You probably want to end up with functions that can load or save a board state, print or display the board, and determine what (if anything ) is at some position.
2) Move representation - find a way to calculate legal moves. Which pieces can move and where they can move to. You will need to take into account - moving off the edges of the board, blocked moves, jumps, multiple jumps, kings moving 'backwards' etc. You probably want to end up with functions that can calculate all legal moves for a piece, determine if a suggested move is legal, record a game as a series of moves, maybe interface with the end user so by mousing or entering text commands you can 'play' a game on your board. So even if you only get that far then you have a 'product' you can demonstrate and people can interact with.
3) Computer play - this is the harder part - You will need to learn about minimax, alpha-beta pruning, iterative deepening and all the associated guff that goes into computer game AI - some of it sounds harder than it actually is. You also need to develop a position evaluation algorithm that measures the value of a position so the computer can decide which is the 'best' move to make. This can be as simple as the naive assumption that taking an opponents piece is always better than not taking one, that making a king is better than not making one, or that a move that leaves you with more future moves is better than one that leaves you with less choices for your next move. In practice, even a very simple 'greedy' board evaluation can work quite well if you can look 2-3 moves ahead.
All in all though, it may be simpler to look at something a little less ambitious than checkers - Othello is possibly a good choice and it is not hard to write an Othello player that can thrash a human who hasn't played a lot of the game. 3D tic-tac-toe, or a small dots-and-boxes game might be suitable too. Games like these are simpler as there are no kings or boundaries to complicate things, all (well most) moves are legal and they are sufficiently 'fun' to play to be a worthwhile software demonstration.
First let me state, the task you are talking about is a lot larger then you think it is.
How you should do it is break it down into very small manageable pieces.
The reasons are
Smaller steps are easier to understand
Getting fast feed back will help inspire you to continue and will help you fix things as they go wrong.
As you start think of the smallest step possible of something to do. Here are some ideas of parts to start:
Make a simple title screen- Just the title and to hit a key for it to
go away.
make the UI for an empty checkerboard grid.
I know those sound like not much but those will probably take much ore time than you think.
then add thing like adding the checkers, keeping the the gameboard data etc.,
Don't even think about AI until you have a game that two players can play with no UI.
What you should do is think about: what is the smallest increment I can do and add that, add that and then think about what the next small piece is.
Trust me this is the best way about going about it. If you try to write everything at once it will never happen.
I was wondering if there's an efficient and easy way to determine waves in MQL4, just like zigzag indicator does it.
I was asked to help automate indicator, for that I need to determine 'waves', essentially max and min of a graph over some period of time (which is vague and all relative).
I don't have a clear image of how I want an indicator to work, but it would be something like that:
Find the last wave, i.e. where the direction of price last changed (neglecting the noise), and then for example reflect it with a trend line.
Is it possible to use zigzag structure to find that point, where direction changed. (Possibly not the only one, might need to find more that just the last point, but the preceding one. So i will want to adopt the algorithm)
I know it's a while since you asked this question and you probably already have an answer, but if not...
I dislike Zigzag and have not found a way to do what I want to do with it, so I will the last part of your questions with no, and believe me I tried.
The way I prefer it is to find bars that conform to the classic definition of fractals/swing points (i.e. a high with two lower highs on either side, or a low with two higher lows on either side), then try to make up for the shortcomings. E.g. Often there will be two high fractals/swings/waves in a row without an intermediate low fractal/swing/wave. So I add the best intermediate low point as a wave, or remove one of the highs (E.g. if the first one wasn't as subjectively significant). Some of the swing points that are identified are 'noisy', to use your term, and not ones that a human trader would have picked. So these need to be dealt with and so on. If you go down this route it is a long one, computers make many mistakes identifying appropriate swing points, so unfortunately not what I would call easy, but it is accurate, and how many easy indicators are there that actually make money over the long run?
I'm trying to devise an algorithm for a robot trying to find the flag(positioned at unknown location), which is located in a world containing obstacles. Robot's mission is to capture the flag and bring it to his home base(which represents his starting position). Robot, at each step, sees only a limited neighbourhood (he does not know how the world looks in advance), but he has an unlimited memory to store already visited cells.
I'm looking for any suggestions about how to do this in an efficient manner. Especially the first part; namely getting to the flag.
A simple Breadth First Search/Depth First Search will work, albeit slowly. Be sure to prevent the bot from checking paths that have the same square multiple times, as this will cause these algorithms to run much longer in standard cases, and indefinitely in the case of the flag being unable to be reached.
A* is the more elegant approach, especially if you know the location of the flag relative to yourself. Wikipedia, as per usual, does a decent job with explaining it. The classic heuristic to use is the manning distance (number of moves assuming no obstacles) to the destination.
These algorithms are useful for the return trip - not so much the "finding the flag" part.
Edit:
These approaches involve creating objects that represents squares on your map, and creating "paths" or series of square to hit (or steps to take). Once you build a framework for representing your square, the problem of what kind of search to use becomes a much less daunting task.
This class will need to be able to get a list of adjacent squares and know if it is traversable.
Considering that you don't have all information, try just treating unexplored tiles as traversable, and recomputing if you find they aren't.
Edit:
As for seaching an unknown area for an unknown object...
You can use something like Pledge's algorithm until you've found the boundaries of your space, recording all information as you go. Then go have a look at all unseen squares using your favorite drift/pathfinding algorithm. If, at any point long the way, you see the flag, stop what you're doing and use your favorite pathfinding algorithm to go home.
Part of it will be pathfinding, for example with the A* algorithm.
Part of it will be exploring. Any cell with an unknown neighbour is worth exploring. The best cells to explore are those closest to the robot and with the largest unexplored neighbourhood.
If the robot sees through walls some exploration candidates might be inaccessible and exploration might be required even if the flag is already visible.
It may be worthwhile to reevaluate the current target every time a new cell is revealed. As long as this is only done when new cells are revealed, progress will always be made.
With a simple DFS search at least you will find the flag:)
Well, there are two parts to this.
1) Searching for the Flag
2) Returning Home
For the searching part, I would circle the home point moving outward every time I made a complete loop. This way, you can search every square and idtentify if it is a clear spot, an obstacle, map boundary or the flag. This way, you can create a map of your environment.
Once the Flag is found, you could either go back the same way, or find a more direct route. If it is more direct route, then you would have to use the map which you have created to find a direct route.
What you want is to find all minimal-spanning-tree in the viewport of the robot and then let the robot game which mst he wants to travel.
If you met an obstacle, you can go around to determine its precise dimensions, and after measuring it return to the previous course.
With no obstacles in the range of sight you can try to just head in the direction of the nearest unchecked area.
It maybe doesn't seem the fastest way but, I think, it is the good point to start.
I think the approach would be to construct the graph as the robot travels. There will be a function that will return to the robot the particular state of a grid. This is needed since the robot will not know in advance the state of the grid.
You can apply heuristics in the search so the probability of reaching the flag is increased.
As many have mentioned, A* is good for global planning if you know where you are and where your goal is. But if you don't have this global knowledge, there is a class of algorithms call "bug" algorithms that you should look into.
As for exploration, if you want to find the flag the fastest, depending on how much of the local neighborhood your bot can see, you should try to not have this neighborhood overlap. For example if your bot can see one cell around it in every direction, you should explore every third column. (columns 1, 4, 7, etc.). But if the bot can only see the cell it is currently occupying, then the most optimal thing you can do is to not go back over what you already visited.
This is a long shot, but I thought I might try before starting the dirty work.
I've got a project to build an application which will, for a defined input stations (vertices) and lines (edges), that is, a real map of some public transportation, schematize a given map into a metro map. I've done some research on the problem and it's an NP-complete problem equivalent to the 3-SAT problem. I also have some theoretic ideas on how to generate such a map, but they aren't detailed enough.
What I'm looking for is any other existing solution of this problem, some sort of pseudo-code, some real code in (almost) any other programming language etc, anything that would reduce the time I need to spend working on the algorithm itself, which will in return give me more time to work on other aspects of the application.
If anyone has ever seen anything that can help me, I'd appreciate it very much.
If you google for "metro map layout problem" and "metro map line crossing" you'll find a lot of references, since it has been researched very actively in the past 10 years.
The problem seems no trivial at all, and translating the "artistic" features to mathematical constraints is seemingly one of the most difficult tasks.
Anyway here are three publications that I found interesting to start with (among many, many others):
Metro Map Layout Using Multicriteria Optimization
Line Crossing Minimization on Metro Maps
The Metro Map Layout Problem
HTH!
Research that's similar to your topic: http://graphics.stanford.edu/papers/routemaps/
This is just some suggestion with handwaving - take with a pinch of salt.
My notion of a "metro" map is one where lines tend to one of the eight cardinal directions and stations are regularly spaced.
I'm assuming you're trying to convert a set of real coordinates into "metro" coordinates.
I would start with your main route (e.g., a city loop), then incrementally add other routes in order of importance.
For each route you want to find the nearest approximation that uses the fewest number of straight lines travelling in the eight cardinal directions. You might do this by starting with the bounding box for the real coordinates, splitting that into a grid, then finding a "metro" route from grid square to grid square, then successively refining that route to reduce the number of bends without distorting the map too much and without introducing crossings with other routes if at all possible.
Having done that, scale each line so that consecutive stations are the same distance apart on the "metro" view.
My guess is you'll still want to support manual tweaking of the result.
Good luck!
Feels like a planning problem.
Looks like your hard constraints are:
Every station must be on a point. A points are on a grid with a distance of X between points (I'd make this static on 2cm)
There should not be 2 stations on the same spot
There should be enough room to draw the station label. Note that the label can be assigned different directions from the point to which the station is assigned.
There should be enough room to draw the subway lines.
Looks like your soft constraints are:
For each station, minimize the actually geographical location distance to the point assigned to the station.
Then throw something like Drools Planner on it, here's an example of hard and soft constraints for nurse rostering.
I have a bit of a difficult algorithm question, I can't find any suitable algorithm from a lot of searching, so I am hoping that someone here on stackoverflow might know the answer.
I have a set of x,y coordinates for a vehicle as it moves through a 2D space, the coordinates are recorded at "decision points" in the time period (i.e. they have stopped and made a determination of where to move next).
What I want to do is find a mechanism for comparing these trails efficiently (i.e. not going through each point individually). Compounding this is that I am interested in the "pattern" of their movement, not necessarily the individual points they went to. This means that the "path" is considered the same if you reflect it around an axis, or if you rotate it by 90,180 or 270 degrees.
Basically I am trying to distil some sort of "behaviour" to the way they move through the space, then examine the different "behaviours" for classification purposes.
Cheers,
Aidan
This may be way more complicated than you're looking for, but it sounds like what the guys did at astrometry.net may be similar to what you're looking for. Essentially, you can upload a picture of some stars, and it will figure out the position in the sky it belongs, along with rotation, you may be able to use similar pattern matching in what you're looking for.
They have a great pdf explaining how it works here, and apparently you can email them and they'll send you the source code (details are in the pdf).
Edit: apparently you can download the code directly here.
Hope it helps.
there are several approaches you could make:
Using vector paths and translation matricies together with two algorithms, The A* (a star) algorithm ( to locate best routes from what are called greedy functions ), and the "nearest neighbour" algorithm --- these are both commonly used for comparing path efficiencies for routes.
you may not know it but the issue you have is known as the "travelling salesman" problem and has many many approaches.
so look up
traveling salesman problem
A*
Nearest neighbour
also look at
Random walk algorithm - for the most basic approach
for a learned behaviour approach try neural networks "ANN" or genetic algorithms
the mathematics for this type of problem are covered under what is called "graph theory"
It seems that basically what is needed is some metric to compare two(N in general) paths and choose the best one?
If that's the case then I'd suggest plain statistics. I'd start with heading(orientation) histogram, relative(relative to previous heading) heading histogram and so on. Other thing comes to mind - distance/orientation between points covariance. Or just simply make up some kind of "statistics"(number of turns, etc.) and compare those paths using that.