J-uncertainty

# J-uncertainty - (It is not the world that is imperfect it...

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1 1 Introducing Uncertainty (It is not the world that is imperfect, it is our knowledge of it) R&N: Chap. 3, Sect 3.6 + Chap. 13 2 ± So far, we have assumed that: World states are perfectly observable, the current state is exactly known Action representations are perfect, states are exactly predicted ± We will now investigate how an agent can cope with imperfect information ± We will also study how limited resources (mainly time) affect reasoning ± Occasionally, we will consider cases where the world is dynamic 3 Introductory Example Goal A robot with imperfect sensing must reach a goal location among moving obstacles (dynamic world) 4 air bearing gas tank air thrusters Robot created at Stanford’s ARL Lab to study issues in robot control and planning in no-gravity space environment 5 Model, Sensing, and Control ± The robot and the obstacles are represented as disks moving in the plane ± The position and velocity of each disc are measured by an overhead camera every 1/30 sec x y robot obstacles 6 Model, Sensing, and Control ± The robot and the obstacles are represented as disks moving in the plane ± The position and velocity of each disc are measured by an overhead camera within 1/30 sec ± The robot controls the magnitude f and the orientation α of the total pushing force exerted by the thrusters x y α f robot obstacles α M q=(x,y) s=(q,q') u=(f, ) 1 x"= fcos m 1 y"= fsin m ff

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2 7 Motion Planning The robot plans its trajectories in configuration × time space using a probabilistic roadmap (PRM) method t x y Obstacle map to cylinders in configuration × time space 8 But executing this trajectory is likely to fail . .. 1) The measured velocities of the obstacles are inaccurate 2) Tiny particles of dust on the table affect trajectories and contribute further to deviation Obstacles are likely to deviate from their expected trajectories 3) Planning takes time, and during this time, obstacles keep moving The computed robot trajectory is not properly synchronized with those of the obstacles Î The robot may hit an obstacle before reaching its goal [Robot control is not perfect but “good” enough for the task] 9 But executing this trajectory is likely to fail . .. 1) The measured velocities of the obstacles are inaccurate 2) Tiny particles of dust on the table affect trajectories and contribute further to deviation Obstacles are likely to deviate from their expected trajectories 3) Planning takes time, and during this time, obstacles are moving The computed robot trajectory is not properly synchronized with those of the obstacles Planning must take both uncertainty in world state and time constraints into account 10 Dealing with Uncertainty ± The robot can handle uncertainty in an obstacle position by representing the set of all positions of the obstacle that the robot think possible at each time (belief state) ± For example, this set can be a disc whose radius grows linearly with time t = 0 t = T t = 2T Initial set of possible positions Set of possible
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J-uncertainty - (It is not the world that is imperfect it...

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