6.832 - Underactuated Robotics
Practice Problems, Spring 2009
Problem 1 (Numerical Optimal Control Algorithms) An ice skater is skating
around a pond that has several weak spots in the ice. The equations of motion are:
v =u1 ,
=u2 .
(1)
(2)
where
x = v c
6.832 Underactuated Robotics
Spring 2009
Problem Set 1 Solutions
by Rick Cory and John Roberts
1
Denition of Underactuated
a) Without loss of generality, assume there is no damping in the system and the mass and inertia are equal to one.
The manipulator
6.832 Midterm
Name:
April 22, 2009
Please do not open the test packet until you are asked to do so.
You will be given 90 minutes to complete the exam.
Please write your name on this page, and on any additional pages that are in
danger of getting separ
6.832 - Underactuated Robotics
Solution to Problem 2, Spring 2009
Problem 2
a) Traveling from x to x + dx consists of both the translation in x and an accompanying
translation in z by dz =
dz
dx dx
= udx. Therefore, the total distance is:
ds = dx2 + dz 2
6.832 - Underactuated Robotics
Problem Set 3, Spring 09
This problem set is due by 11:59pm on Tuesday, March 31.
Problem 1 (Optimal Swing-up for the Simple Pendulum) Consider the dynamics
of the simple pendulum given by: ml2 q + bq + mgl sin(q ) = u, whe
6.832 - Underactuated Robotics
Final Project Proposal, Spring 09
This problem set is due by 11:59pm on Tuesday, May 5.
Problem 1 (The Weight-Perturbation Algorithm) In this problem you will investi
gate one of the REINFORCE type algorithms, namely the Wei
6.832 - Underactuated Robotics
Final Project Proposal, Spring 09
This problem set is due by 11:59pm on Thursday, April 16.
Problem 1 (The Spring Loaded Inverted Pendulum) Download the le slip.m
from the course website. This le contains the basic matlab c