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Unformatted text preview: ECE 594D Robot Locomotion Winter 2010 Homework 2 (due 1/27) 2.1 Rimless Wheel (RW) return map. In this problem, you are asked to annonate Figure 1, in which the solid (blue) lines show the return map relating the postcollision angular velocity after a given step, Ω + n , to the velocity after the next step, Ω + n +1 . (Note that Coleman02 [1] plots return maps on “ Z ”; Figure 1 maps Ω itself.) Hint: Grab a ruler! Also, download the “RW cheatsheet” from the homework website. (Assume a unit length leg ( L = 1 [m]), point mass ( J = 0 ), and 8 spokes ( 2 α = 2 π/ 8 ).)87654321 1 2 3 487654321 1 2 3 4 Ω n + (rad/s) Ω n+1 + (rad/s) Figure 1: Rimless Wheel return map. (Last revised January 23, 2010) 1 Homework 2 ECE 594D Robot Locomotion Winter 2010 2.1 Rimless Wheel (RW) return map. (continued...) a) From Figure 1, what (approximately) is the value of the rolling fixed point, Ω + * ? b) Given your estimate of Ω + * (from part a), estimate the angle of the ground, γ . c) What is the slope of the return map near Ω + * ? d) Given: “ Ω + n = Ω + * + . 01 ”, estimate Ω + n +1 . Hint: Use part c. e) Graphically find the basins of attraction for the standing and rolling fixed points, using a “stair step” approach. Shade in the portions corresponding to the “rolling” fixed point. Hint: down load the mfiles called “RW_return.m” and “RW_stairstep.m” from the homework webpage. Run RW_return to create a return map. Then run RW_stairstep to graphically click on the fig ure to create stair steps to the appropriate fixed point for this initial condition. You can continue to run RW_stairstep again and again, to overlay many stair step traces. Note that the return map shown will (intentionally) be for a different value of ground slope,...
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This note was uploaded on 12/29/2011 for the course ECE 594d taught by Professor Teel,a during the Fall '08 term at UCSB.
 Fall '08
 Teel,A

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