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Unformatted text preview: Massachusetts Institute of Technology Department of Mechanical Engineering 2.12 Introduction to Robotics Problem Set No.8 Out: November 21, 2005 Due: November 30, 2005 Problem 1 Shown below is a vehicle similar to the 2.12 mobile robot having a pair of powered wheels and a frictionless caster. The radius of the wheels is r=3 cm , while the distance between the two wheels is 2 b=20 cm . The angular velocity of the right wheel is , and that of the left wheel is r ω l ω . Each powered wheel is equipped with a shaft encoder to measure the angular velocity. Answer the following questions. r ω l ω ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ Y X ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ) ( ) ( f f t Y t X ) ( f t ϕ ϕ X Y 2 b r Figure 1 Vehicle trajectory Time sec Angular Velocities rad/sec 10 8 6 4 2 0 3 5 8 t f = 10 r ω l ω Figure 2 Time profiles of the wheel velocities a). At time t = 0, the vehicle was at position cm Y cm X 20 , 20 = = with reference to the inertial reference frame O-XY and at orientation = ϕ measured from oved. The time profiles of the wheel angular velocit gure 2. Compute the posit the positive X axis. See Figure 1. Then the vehicle m ies during the movement were recorded, as shown in Fi ion and orientation of the vehicle at time based on the time s shown in Figure 2. Assume no slip....
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.12 taught by Professor Harryasada during the Fall '05 term at MIT.
- Fall '05
- Mechanical Engineering