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Unformatted text preview: ECE 594D Robot Locomotion Winter 2010 Homework 1 (due 1/20) 1.1 2D Robot Platform. In Figure 1, the large rectangle represents a robot platform that can move (friction free) in the plane of the paper. (For example, imagine the platform floats on an air hockey table.) The system has 3 degrees of freedom (DOFs): x , y , and . It also has 3 actuators. Each actuator is rigidly mounted at a particular location and angle on the perimeter of the platform and can provide thrust (+ or - direction) along its axis. x y m, J F a F b F c Figure 1: 2D robot platform. a) Assume the 3 thrust actuators are at the following locations (in meters) and angles: F a : x =- . 75 , y =- . 5 , = 60 F b : x = 0 . 75 , y =- . 5 , = 120 F c : x = 0 , y = 0 . 5 , = 90 We want to determine if this system is fully actuated or underactuated . That is, we aim to find combinations of thrust that decouple the motions, so we can move in each of the 3 DOFs independently. Recall the robot manipulator equation: q = f 1 ( q , q ,t ) + f 2 ( q , q ,t ) u (i) Given the current configuration, what is f 2 ? (i.e., What are the values in this 3x3 matrix?) (ii) What is the rank of f 2 ? Is the system fully- or underactuated? (iii) Is the system controllable? (Does a path exist to get to any desired location and orientation?) Is the controllability matrix described in class a valid way to determine this? Why or whyIs the controllability matrix described in class a valid way to determine this?...
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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