hw1a - ECE 594D Robot Locomotion Winter 2010 Homework 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

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.

Page1 / 3

hw1a - ECE 594D Robot Locomotion Winter 2010 Homework 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online