20 – 20 Inexact Motion 1 V3

So, let’s talk about inaccurate robot motion. We’re again given five grid cells and let’s assume a robot executes its action with high probability correctly, say 0.80 over the 0.1 chance, it finds itself short of the intended action and get another 1.1 probability it finds itself overshooting its target. You can define the same for other U values, say U equals one, then with 0.8 chance, it would end up over here, 0.1 it stays in the same element. In 0.1, it hops two elements ahead. Now, this is a model of inaccurate robot motion. This robot attempts to go U grid cells but occasionally falls short of its goal or overshoots and that’s a more common case robots as they move accrue uncertainty and it’s really important to model this because this is the primary reason why localization is hard because robots are not very accurate. We now are going to look into this first, for the mathematical side. I will be giving you a prior distribution and we’re going to be using the value U equals two and for the motion model that shifts the robots exactly two steps, we believe there’s a 0.8 chance if we assign a 0.1 to the cases where the robot over undershoots by exactly one. That’s kind of written by this formula over here where the two gets a 0.8 probability, the one and three end up with 0.1 probability. What I ask you now for the initial distribution that I’m writing up here, can you give me the distribution after the motion.

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