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Sim3 is just the lie group associated a similarity transform which is the exact same thing as your 3D Affine transform. If you work out the multiplication for your two matrices you would find that they end up with the same result as we are dealing with homogenous coordinates. Therefore the following is true $$x=kx$$ where $k$ is just some constant, and $x$ ...

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I think you'll find section IV. Loop Closure useful here: http://www.roboticsproceedings.org/rss06/p10.pdf

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If you want communicate over internet: I think you should explore websockets for the purpose. Websocket connections allow both clients and server to send data. It's a full duplex communication mode. If you are using python, you can simply use a websocket client package like this one and get the python code to talk to your server (and let server talk to the ...

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If you want to incoorporate our sensors properly you first need to build a sensor model. This model tells you whenever your sensor measured something, what is the probability that this is the real value. You will get a distribution. So when you measure 1m there is a prob. of .5 that thus measurement is true and a prob of .3 that the real distance ist ...

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Cause of the intrinsic noise in sensory data, we have to consider a probabilistic model (mostly Gaussian) for the sensor measurements. As a matter of fact, the description and definition of the mapping problem will be probabilistic. The goal is to compute the most likely map given the sensor data and commands given to the robot: In occupancy grid mapping as ...

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As the wikipedia page of Occupancy grid mapping explains, the result of the mapping process is a binary 1 or 0, occupied or not, the decision itself may be based on noisy data, which involves the probabilistic assessment of prior information to infer the posterior probability of the occupancy.

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