ECE 594D
Robot Locomotion
Homework 2
Winter 2010
(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 post-collision angular velocity
after a gi
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ECE 594D: Homework 1
ECE 594D
Robot Locomotion
Winter 2010
Reading: Lectures 2-3, RW Notes. See also RW m-les.
Homework 2
(due 1/27)
Due Oct. 11, 2013 at 5pm (in dropbox outside 3120 HFH)
2.1 Rimless Wheel (RW) return map. In this problem, you are as
Lecture 7 Intro to Dynamic Programming 59-. M
N a)
This lecture gives more examples of (and intuition for) / (owml
Pontryagins Maximum Princi le (PMP) and resulting bang- 69
bang (min-time) and other optimal control problems, and it gfx
introduces anothe
Lecture 11 Pdrridl Feedback Lineorizotion
This lecture introduces Partial Feedback Linearization (PFL): a
method to control underactuated systems by directly setting
accelerations of m of n joints, using m actuators, wherefy
Given appropriate coupling bet
Lecture 9 PRMS cmd RRTs W \om :v. a?
This lecture describes some motion planning algorithms W a
commonly used in robotics. In particular, for a robot with x
many degrees of freedom (DOFs), finding continuous motions
that are both kinematically feasible an
1/9
Midterm Exam
ECE 594D
Nov. 12, 2013 .
Sohriav,
Name
Grade
No CALCULATORS, and only a ONEwSIDED 8.5x11 inch sheet of notes allowed
There is extra blank paper at the end of the exam, for additional calculations.
ROBOT LOCOMOTION UCSB, 2013 2/9
Problem 1
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AbstractTn travel on rough terrain. a legged system must
adjust the length of its steps so that the leer land on the
available lootholrls. This paper e
Leclure ig Grodienr Descent Methods
This lecture introduces methods for finding locally optimal
parameters/solutions for motion planning, control problems,
or other functions, more generally. we will focus on how to
minimize a cost (or maximize a reward)
Lecture 12 Closs Projects
This lecture finishes the presentation from Lecture 1 and also
lists some possible topics for the Final Project.
- Midterm Exam is NEXT CLASS (New. 12).
- Remaining classes will discuss zero moment point (ZMP)
methods for walking
Lecture 8 Dynomio Programming
This lecture describes some algorithms that use dynamic
programming (DP) to derive either an optimal control policy
or an approximation to the optimal policy.
- Iziscrete-Tirnewwjzmd/xinhatie-Lfor DP
Value Iteration (vs Poli
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ECE 594D: Homework 2
Reading: Lectures 4-7. See also CG m-le: StepCG.m.
Due Oct. 30, 2013 at 5pm (in dropbox outside 3120 HFH)
Problem 1
Rimless Wheel, revisited.
(Impact Equations.)
Diagrams above illustrate parts a), b), and c), respectively.
a) Mu
ECE 594D Game Theory and Multiagent Systems
Homework #1 Solutions
1. Tragedy of the Commons: The social planners optimization equates to
N
max N e1 10
N
which is maximized at N = 10. Therefore, the optimization leads to 1 goat/family which
produces 10 buc
ECE 594D Game Theory and Multiagent Systems
Homework #2 Solutions
1. Craps: To evaluate the probability of winning on the pass line in craps we have the following:
pwin = Pr (7, 11) + Pr (win|4) + . + Pr (win|10)
where Pr (win|10) indicates the probabilit
ECE 594D Game Theory and Multiagent Systems
Homework #6
1. Consider an anonymous routing/congestion game that is parameterized as follows:
A finite set of resources R.
A congestion function for each resource r of the form cr : cfw_0, 1, 2, . R. The cost
ECE 594D Game Theory and Multiagent Systems
Homework #4
1. Consider the following Prisoners Dilemma game where 1 < x < y
C
D
C
x, x
y, 0
D
0, y
1, 1
(a) Find the condition on the discount factor under which the strategy pair in which each
player uses the
ECEN 594D Game Theory and Multiagent Systems
Homework #3
1. Recall BoS, Stag hunt, and Typewriter games from HW#2. Compute all of the NE for
these games (including mixed strategy NE). Note that at the mixed strategy equilibrium, both
players are indiffere
ECEN 594D Game Theory and Multiagent Systems
Homework #5
1. Consider the following cost sharing problem:
Player set: N = cfw_1, 2, 3
Opportunity costs: c : 2N R
c(cfw_1) = 9,
c(cfw_2) = 8,
c(cfw_3) = 9
c(cfw_1, 2) = 14, c(cfw_1, 3) = 15, c(cfw_2, 3) = 1
ECE 594D Game Theory and Multiagent Systems
Homework #1
Text problems:
1. Tragedy of the Commons: Suppose 10 families share a plot of land. A goat that
grazes on fraction a [0, 1] of land produces
1
b = e1 10a
2.
bucket of milk. A social planner would li
182
Chapter 14. Repeated Games: The Prisoners Dilemma
P0 : C
- P1 : C
(, D )
- D: D
all
outcomes
Figure 182.1 The strategy in Exercise 428.1a.
428.1 Strategies in an infinitely repeated Prisoners Dilemma
a. The strategy is shown in Figure 182.1.
b. The st
ECE 594D Game Theory and Multiagent Systems
Homework #3 Solutions
1. Recall BoS, Stag hunt, and Typewriter games from HW#2. Compute all of the NE for these games
(including mixed strategy NE). Note that at the mixed strategy equilibrium, both players are
ECE 594D Game Theory and Multiagent Systems
Homework #2
1. The Pass Line: The pass line in craps is one of the most popular bets in vegas. Craps is a
dice game that utilizes two die. Here are the rules:
The first roll is called the come out roll. Two die
ECE 594D
Robot Locomotion
Homework 3
Winter 2010
(due 5pm 2/5, in HFH 5115)
3.1 Non-collocated Partial Feedback Linearization (PFL) control for the acrobot. In class, we
looked at MATLAB simulation results for collocated PFL control of the acrobot (Figure
_._
T0 Beggiuresgéq %
Lecture 5 Impocr Ean\(& Intro to Opt. Control)
This lecture discusses impact equations, to calculate discrete
jumps in velocities (hybrid dynamics of walking-type systems)
and informally introduces some concepts in optimal control.