Kinematics, Kinematics Chains CS 685
Previously
Representation of rigid body motion Two different interpretations - as transformations between different coordinate frames - as operators acting on a rigid body Representation in terms of homogeneous coordi
Probabilistic Robotics
Overview of probability, Representing uncertainty Propagation of uncertainty, Bayes Rule Localization and Mapping
Slides from Autonomous Robots (Siegwart and Nourbaksh), Chapter 5 Probabilistic Robotics (S. Thurn et al. )
Probabili
Potential Field Methods
Idea robot is a particle Environment is represented as a potential field (locally) Advantage capability to generate on-line collision avoidance Compute force acting on a robot incremental path planning
Example: Robot can translate
Autonomous Mobile Robots, Chapter 4
Range Sensing strategies
Active range sensors Ultrasound Laser range sensor
R. Siegwart, I. Nourbakhsh
Autonomous Mobile Robots, Chapter 4
4.1.6
Range Sensors (time of flight) (1)
Large range distance measurement -> ca
10/15/09
ICRA 2003 Tutorial
1
Image
Brightness values
I(x,y)
1
10/15/09
Local, meaningful, detectable parts of the image. Edge detection Line detection Corner detection Motivation Information content high Invariant to change of view point, illumination Re
Motion Planning
Jana Kosecka Department of Computer Science
Probabilistic motion planning
Slides thanks to http:/cs.cmu.edu/~motionplanning, Jyh-Ming Lien
Hard Motion Planning
Configuration Space methods complex even for low dimensional configuration sp
Motion Planning
Jana Kosecka Department of Computer Science
Discrete planning, graph search, shortest path, A* methods Road map methods Configuration space
Slides thanks to http:/cs.cmu.edu/~motionplanning, Jyh-Ming Lien
State space
Set of all possible
Problem Classes
Probabilistic Robotics
Planning and Control: Markov Decision Processes
1
SA-1
Deterministic vs. stochastic actions Full vs. partial observability Today how to make decisions under uncertainty
2
Uncertainty and decisions
Previously how to
CS685 - Homework 2, due Oct 14th, Jana Koeck sa 1. Consider a dierential drive model of the mobile robot with a conguration space [x, y, ]T , where we can control linear and angular velocity of the robot v and . The kinematic model describing the motion o
Markov Kalman Filter Localization
Markov localization
localization starting from any unknown position recovers from ambiguous situation. However, to update the probability of all positions within the whole state space at any time requires a discrete rep
Matrices
! Linear Algebra Review Rigid Body Motion in 2D Rigid Body Motion in 3D
Cn!m = An!m + Bn!m
cij = aij + bij
Jana Kosecka, CS 685
&2 5# &6 2# &8 7 # $3 1! + $1 5! = $4 6! % "% "% "
Why do we need Linear Algebra?
! We will associate coordinates to !
Markov Kalman Filter Localization
Markov localization
Kalman filter localization
tracks the robot and is inherently very precise and efficient. However, if the uncertainty of the robot becomes to large (e.g. collision with an object) the Kalman filter
Robot Control Basics CS 685
Mobile robot kinematics
Differential drive mobile robot Two wheels, with diameter r , point P centered Between two wheels is the origin of the robot frame Each wheel is a distance l from the center
1
Some terminology
Effector
Robotic Behaviors
Potential field techniques - trajectory generation - closed feedback-loop control Design of variety of behaviors - motivated by potential field based approach steering behaviors Closed feedback loop systems - no memory - behaviors no rep
Advanced Features
Jana Kosecka
Slides from: S. Thurn, D. Lowe, Forsyth and Ponce
Advanced Features: Topics
Template matching SIFT features Haar features
CS223b
2
1
Features for Object Detection/Recognition
Want to find in here
3
Template Convolution
Pick
CS 685 notes, J. Koeck sa
1
Trajectory Generation
The material for these notes has been adopted from: John J. Craig: Robotics: Mechanics and Control. This example assumes that we have a starting position and goal pose of the end effector and we are asked
Recommended Text
Intelligent Robotic Systems CS 685 Jana Kosecka, 4444 Research II [email protected] , 3-1876 ! ! ! ! ! [1] S. LaValle: Planning Algorithms, Cambridge Press, http:/planning.cs.uiuc.edu/ [2] S. Thrun, W. Burghart, D. Fox: Probabilistic Roboti
Lecture Notes 1. An Invitation to 3-D Vision: From Images to Models (in preparation) Y. Ma, J. Koeck, S. Soatto and S. Sastry. c Yi Ma et. al. sa
Representation of a three dimensional moving scene
The study of geometric relationships between a three dimen
Basic Linear Algebra
Linear algebra deals with matrixes: two-dimensional arrays of values. Heres a matrix: 15 7 9 3 11 Often matrices are used to describe in a simpler way a series of linear equations. In the example above the matrix might be thought of a
Vision Based Localization Global Localization and Relative Pose Estimation Based on Scale Invariant Keypoints
Given a image(s) acquired by moving camera determine the robots location and pose ?
Jana Kosecka Department of Computer Science Computer Vision a
The SLAM Problem
Probabilistic Robotics
SLAM
A robot is exploring an unknown, static environment. Given:
The robots controls Observations of nearby features
Estimate:
Map of features Path of the robot
2
Structure of the Landmarkbased SLAM-Problem
SLAM A
CS685 - Homework 1 Due date: September 23
Be as concise as possible. 1. (5) Consider rigid body transformations in the plane. Draw a right triangle dened by three points A = (2, 1), B = (4, 1), C = (4, 6). Consider a rotation matrix T1 = cos sin sin cos