I have timed sensor data for a car - such as Yaw Rate, Absolute Steering Angle etc - and would like to detect if the car is making a turn, left or right.
Currently, I'm thinking about using angular displacement and velocity, but I'm not sure if there's an existing robust algorithm that I could use.
I have also come across this post that hints about a method that could be used, but I'm not sure if this is exactly the one I need.
Algorithm to detect left or right turn from x,y co-ordinates
Sorry, for not giving much, but I'm actually trying to get some literature that I could review and some vocabulary that could help me find better solutions related to my problem. Thanks.
I have a set of (slightly noisy) GPS coordinates that I want to turn into a path. How do I go about this?
I find it similar to this question, except my points are ordered. Also, the path does not need to go through the points, but just follow their general direction.
It seems that Bezier curves might be the answer, but is there a way to use Bezier curves on hundreds of points?
Q&A:
How are your points ordered They are ordered by time and attached to a travelling car. There might be data that specify that the the car is travelling backwards, but I can remove that data by requiring that all points move in a "forward" direction. So then I should have just a list of points that all go forwards in space and don't intersect with themselves.
What if we connect all the lines with straight lines It won't look pretty. I'd like for the lines to be continuous and curvy.
What about using a spline between all the points This too will make too much noise. The path will be very "jumpy". It would be better if we didn't care about going through points, but just near them.
It is a bit of heavy machinery, but you can model your GPS observations as points following a Gaussian process with Gaussian noise, where the main Gaussian process model specifies that the underlying unknown true x and y coordinates of two measurements close in time should be close, and the noise allows the observed x and y GPS measurement values to deviate a bit from the true x and y values predicted by the Gaussian process model. You can read the book "Gaussian Processes for Machine Learning" available online if you're interested. I think it's a really elegant, flexible and powerful solution, but it would take way too much space to explain it in enough detail here so you really do need to read about it from the book.
Once you've learned the most likely Gaussian process model solution, you can make predictions of x and y locations for any time point, and it will be a smooth curve, which you can then plot. It won't pass through the observed GPS locations exactly.
What will be the best way (or) Is there a Google's way already to Calculate the simple Straight Line Distance between Two Points, based on Lat/Lng or even on Postal/Zip Code is possible?
I found the answer by myself, from somewhere else.
Yes, there is a native solution from Google already, at:
https://developers.google.com/maps/documentation/javascript/reference?hl=en-US#spherical
All I need to do is to call the method:
'google.maps.geometry.spherical.computeDistanceBetween (latLngA, latLngB);'
(Ofcourse I also need to include the additional/required '.js')
"Best" is a pretty vague criterion. If you're able to assume the earth is a perfect sphere, then you want the simple formula for great circle distance. See for example the Wikipedia article. With this assumption your distance can be off by something less than half a percent.
The actual shape of the earth is actually a slightly oblate spheroid. The surface distance on this shape is more complicated to compute. See Ed Williams' work in javascript. Maybe he will let you use his code. If not he gives relevant references.
A free solution is at http://ezcmd.com/apps/app_ezip_locator#ezip_locator_api
Can help you find distance between two lat,long coordinates in miles or Km.
Or, you could try http://ezcmd.com/apps/app_geo_postal_codes#geo_postal_codes_api
The "best" way depends on several things. Can you provide a little more background as to how accurate and/or what's the desired application? The google.maps.DirectionsService class will allow you to calculate the driving distance client side with javascript, but if you want an accurate straight line distance you could use postgresql + postgis server side. Calculating accurate distances with lat/lng can get tricky with the different projections of the earth depending on the range of points and distances involved.
I am hacking a vacuum cleaner robot to control it with a microcontroller (Arduino). I want to make it more efficient when cleaning a room. For now, it just go straight and turn when it hits something.
But I have trouble finding the best algorithm or method to use to know its position in the room. I am looking for an idea that stays cheap (less than $100) and not to complex (one that don't require a PhD thesis in computer vision). I can add some discrete markers in the room if necessary.
Right now, my robot has:
One webcam
Three proximity sensors (around 1 meter range)
Compass (no used for now)
Wi-Fi
Its speed can vary if the battery is full or nearly empty
A netbook Eee PC is embedded on the robot
Do you have any idea for doing this? Does any standard method exist for these kind of problems?
Note: if this question belongs on another website, please move it, I couldn't find a better place than Stack Overflow.
The problem of figuring out a robot's position in its environment is called localization. Computer science researchers have been trying to solve this problem for many years, with limited success. One problem is that you need reasonably good sensory input to figure out where you are, and sensory input from webcams (i.e. computer vision) is far from a solved problem.
If that didn't scare you off: one of the approaches to localization that I find easiest to understand is particle filtering. The idea goes something like this:
You keep track of a bunch of particles, each of which represents one possible location in the environment.
Each particle also has an associated probability that tells you how confident you are that the particle really represents your true location in the environment.
When you start off, all of these particles might be distributed uniformly throughout your environment and be given equal probabilities. Here the robot is gray and the particles are green.
When your robot moves, you move each particle. You might also degrade each particle's probability to represent the uncertainty in how the motors actually move the robot.
When your robot observes something (e.g. a landmark seen with the webcam, a wifi signal, etc.) you can increase the probability of particles that agree with that observation.
You might also want to periodically replace the lowest-probability particles with new particles based on observations.
To decide where the robot actually is, you can either use the particle with the highest probability, the highest-probability cluster, the weighted average of all particles, etc.
If you search around a bit, you'll find plenty of examples: e.g. a video of a robot using particle filtering to determine its location in a small room.
Particle filtering is nice because it's pretty easy to understand. That makes implementing and tweaking it a little less difficult. There are other similar techniques (like Kalman filters) that are arguably more theoretically sound but can be harder to get your head around.
A QR Code poster in each room would not only make an interesting Modern art piece, but would be relatively easy to spot with the camera!
If you can place some markers in the room, using the camera could be an option. If 2 known markers have an angular displacement (left to right) then the camera and the markers lie on a circle whose radius is related to the measured angle between the markers. I don't recall the formula right off, but the arc segment (on that circle) between the markers will be twice the angle you see. If you have the markers at known height and the camera is at a fixed angle of inclination, you can compute the distance to the markers. Either of these methods alone can nail down your position given enough markers. Using both will help do it with fewer markers.
Unfortunately, those methods are imperfect due to measurement errors. You get around this by using a Kalman estimator to incorporate multiple noisy measurements to arrive at a good position estimate - you can then feed in some dead reckoning information (which is also imperfect) to refine it further. This part is goes pretty deep into math, but I'd say it's a requirement to do a great job at what you're attempting. You can do OK without it, but if you want an optimal solution (in terms of best position estimate for given input) there is no better way. If you actually want a career in autonomous robotics, this will play large in your future. (
Once you can determine your position you can cover the room in any pattern you'd like. Keep using the bump sensor to help construct a map of obstacles and then you'll need to devise a way to scan incorporating the obstacles.
Not sure if you've got the math background yet, but here is the book:
http://books.google.com/books/about/Applied_optimal_estimation.html?id=KlFrn8lpPP0C
This doesn't replace the accepted answer (which is great, thanks!) but I might recommend getting a Kinect and use that instead of your webcam, either through Microsoft's recently released official drivers or using the hacked drivers if your EeePC doesn't have Windows 7 (presumably it does not).
That way the positioning will be improved by the 3D vision. Observing landmarks will now tell you how far away the landmark is, and not just where in the visual field that landmark is located.
Regardless, the accepted answer doesn't really address how to pick out landmarks in the visual field, and simply assumes that you can. While the Kinect drivers may already have feature detection included (I'm not sure) you can also use OpenCV for detecting features in the image.
One solution would be to use a strategy similar to "flood fill" (wikipedia). To get the controller to accurately perform sweeps, it needs a sense of distance. You can calibrate your bot using the proximity sensors: e.g. run motor for 1 sec = xx change in proximity. With that info, you can move your bot for an exact distance, and continue sweeping the room using flood fill.
Assuming you are not looking for a generalised solution, you may actually know the room's shape, size, potential obstacle locations, etc. When the bot exists the factory there is no info about its future operating environment, which kind of forces it to be inefficient from the outset.
If that's you case, you can hardcode that info, and then use basic measurements (ie. rotary encoders on wheels + compass) to precisely figure out its location in the room/house. No need for wifi triangulation or crazy sensor setups in my opinion. At least for a start.
Ever considered GPS? Every position on earth has a unique GPS coordinates - with resolution of 1 to 3 metres, and doing differential GPS you can go down to sub-10 cm range - more info here:
http://en.wikipedia.org/wiki/Global_Positioning_System
And Arduino does have lots of options of GPS-modules:
http://www.arduino.cc/playground/Tutorials/GPS
After you have collected all the key coordinates points of the house, you can then write the routine for the arduino to move the robot from point to point (as collected above) - assuming it will do all those obstacles avoidance stuff.
More information can be found here:
http://www.google.com/search?q=GPS+localization+robots&num=100
And inside the list I found this - specifically for your case: Arduino + GPS + localization:
http://www.youtube.com/watch?v=u7evnfTAVyM
I was thinking about this problem too. But I don't understand why you can't just triangulate? Have two or three beacons (e.g. IR LEDs of different frequencies) and a IR rotating sensor 'eye' on a servo. You could then get an almost constant fix on your position. I expect the accuracy would be in low cm range and it would be cheap. You can then map anything you bump into easily.
Maybe you could also use any interruption in the beacon beams to plot objects that are quite far from the robot too.
You have a camera you said ? Did you consider looking at the ceiling ? There is little chance that two rooms have identical dimensions, so you can identify in which room you are, position in the room can be computed from angular distance to the borders of the ceiling and direction can probably be extracted by the position of doors.
This will require some image processing but the vacuum cleaner moving slowly to be efficiently cleaning will have enough time to compute.
Good luck !
Use Ultra Sonic Sensor HC-SR04 or similar.
As above told sense the walls distance from robot with sensors and room part with QR code.
When your are near to a wall turn 90 degree and move as width of your robot and again turn 90deg( i.e. 90 deg left turn) and again move your robot I think it will help :)
As some of you may know, there is an encoding algorithm in Google maps API which optimizes polyline drawings in different zoom levels. It removes-adds the coordinates of a path according to the current zoom level and decreases-increases the drawing computation time. Specifically, I mean the algorithm in the GPolyline.fromEncoded method.
In a different platform other than javascript I need an algorithm like that. Of course I don't think using a google style professional code. Is there another algorithm like that of which I can see the code and re-implement it according to the suitable platform? Or what are your suggestions to accomplish the optimization of path drawings in different zoom levels?
What about the following.
Pick a constant DetailRadius depending on the zoom level.
Pick a start point on the polygon.
Test if the next point of the polygon is inside or outside a circle with a radius of DetailRadius around the current point, that is if the distance between the current and the next point is smalleer or larger then DetailRadius.
If the next point is outside the radius, move from the current to this point.
If the next point is inside the radius, delete it and continue at 3. with the new next point.
One could also think about removing all points in the circle, not only neighoubrs of the current point. This will lead to further detail reduction, but it is computationaly more expensive and might lead to more geometric distortion because it will "push away points from the current point".