Michael I. Jordan, Generic constraints on underspecified target trajectories, Proceedings of international conference on neural networks, (1989), 217-225
기존 SLAM에서 쓰이는 레이저 레인지 스캐너 등 range and bearing 센서 대신 공간에 대한 풍부한 정보를 주는 카메라를 쓰면, 1차원 (인식된 물체까지의 거리 정보, depth)을 잃게 되어 bearing-only SLAM이 된다.
EKF requires Gaussian representations for all the involved random variables that form the map (the robot pose and all landmark's positions). Moreover, their variances need to be small to be able to approximate all the non linear functions with their linearized forms.
두 입력 이미지 프레임 사이에 baseline을 구할 수 있을 만큼 충분한 시점 차가 존재해야 랜드마크의 위치를 결정할 수 있으므로, 이를 확보하기 위한 시간이 필요하게 된다.
Danica Kragic1 and Markus Vincze2 1 Centre for Autonomous Systems,
Computational Vision and Active Perception Lab, School of Computer
Science and Communication, KTH, Stockholm, 10044, Sweden, dani@kth.se 2 Vision for Robotics Lab, Automation and Control Institute, Technische Universitat Wien, Vienna, Austria, vincze@acin.tuwien.ac.at
SUGGESTED CITATION: Danica Kragic and Markus Vincze (2010) “Vision for Robotics”,
Foundations and Trends® in Robotics: Vol. 1: No. 1, pp 1–78.
http:/dx.doi.org/10.1561/2300000001
Abstract
Robot vision refers to the capability of a robot to
visually perceive the environment and use this information for
execution of various tasks. Visual feedback has been used extensively
for robot navigation and obstacle avoidance. In the recent years, there
are also examples that include interaction with people and manipulation
of objects. In this paper, we review some of the work that goes beyond
of using artificial landmarks and fiducial markers for the purpose of
implementing visionbased control in robots. We discuss different
application areas, both from the systems perspective and individual
problems such as object tracking and recognition.
1 Introduction 2
1.1 Scope and Outline 4
2 Historical Perspective 7
2.1 Early Start and Industrial Applications 7
2.2 Biological Influences and Affordances 9
2.3 Vision Systems 12
3 What Works 17
3.1 Object Tracking and Pose Estimation 18
3.2 Visual Servoing–Arms and Platforms 27
3.3 Reconstruction, Localization, Navigation, and Visual SLAM 32
3.4 Object Recognition 35
3.5 Action Recognition, Detecting, and Tracking Humans 42
3.6 Search and Attention 44
4 Open Challenges 48
4.1 Shape and Structure for Object Detection 49
4.2 Object Categorization 52
4.3 Semantics and Symbol Grounding: From Robot Task to Grasping and HRI 54
4.4 Competitions and Benchmarking 56
D-SLAM: A Decoupled Solution to Simultaneous Localization and Mapping
Z. Wang, S. Huang and G. Dissanayake
ARC Centre of Excellence for Autonomous Systems (CAS), Faculty of Engineering, University of Technology, Sydney, Australia International Journal of Robotics Research Volume 26 Issue 2 - Publication Date: 1 February 2007 (Special Issue on the Fifth International Conference on Field and Service Robotics, 2005) http://dx.doi.org/10.1177/0278364906075173
On the Structure and Solution of the Simultaneous Localisation and Map Building Problem. Paul Michael Newman.
1999. Ph. D. thesis, Australian Centre for Field Robotics - The University of Sydney
Randall C. Smith and Peter Cheeseman. 1986. On the representation and estimation of spatial uncertainly. Int. J. Rob. Res. 5, 4 (December 1986), 56-68.
DOI=10.1177/027836498600500404 http://dx.doi.org/10.1177/027836498600500404
// ground truth of num_landmarks landmarks in the world coordinate
double landmark[num_landmarks];// = { 200, 600, 400 }; // x-position
for( int n = 0; n < num_landmarks; n++ )
{
landmark[n] = width * uniform_random();
}
// set the initial state
double rob_pos = 25.0; // initial robot position
double rob_vel = 10.0; // initial robot velocity
// set the initial covariance of the state
double rob_pos_cov = 0.01; // covariance of noise to robot position
double rob_vel_cov = 0.01; // covariance of noise to robot velocity
double obs_cov = 900; // covarriance of noise to measurement of landmarks
double xGroundTruth, vGroundTruth;
xGroundTruth = rob_pos;
vGroundTruth = rob_vel;
// H matrix
int Hrow = num_landmarks;
int Hcol = num_landmarks + 2;
CvMat* H = cvCreateMat(Hrow, Hcol, CV_64FC1);
cvZero(H); // initialize H matrix
// set H matrix
for (int row = 0; row < Hrow; row++)
{
cvmSet(H, row, 0, -1.0);
cvmSet(H, row, row+2, 1.0);
}
displayMatrix(H, "H matrix");
// Q matrix ; covariance of noise to H ; uncertainty of control
CvMat* Q = cvCreateMat(Hrow, Hrow, CV_64FC1);
cvZero(Q); // initialize Q matrix
// set Q matrix
for (int row = 0; row < Q->rows; row++)
{
cvmSet(Q, row, row, obs_cov);
}
displayMatrix(Q, "Q matrix");
// G matrix // transition
int Grow = num_landmarks + 2;
int Gcol = Grow;
CvMat* G = cvCreateMat(Grow, Gcol, CV_64FC1);
cvZero(G); // initialize G matrix
// set G matrix
cvmSet(G, 0, 0, 1.0); // previous position
cvmSet(G, 0, 1, 1.0); // velocity
for (int row = 1; row < Grow; row++)
{
cvmSet(G, row, row, 1.0); // constance of velocity
}
displayMatrix(G, "G matrix");
// R matrix ; covariance of noise to H ; uncertainty of observation
CvMat* R = cvCreateMat(Grow, Grow, CV_64FC1); // 5x5
cvZero(R); // initialize R matrix
// set R matrix
cvmSet(R, 0, 0, rob_pos_cov);
cvmSet(R, 1, 1, rob_vel_cov);
displayMatrix(R, "R matrix");
CvMat* mu = cvCreateMat(num_dim, 1, CV_64FC1); // state vector to be estimated
CvMat* rob_ground = cvCreateMat(num_dim, 1, CV_64FC1); // state vector to be estimated
CvMat* mu_p = cvCreateMat(num_dim, 1, CV_64FC1); // state to be predicted
CvMat* u = cvCreateMat(1, 1, CV_64FC1); // control vector
cvmSet(u, 0, 0, 1.0); // set u(0,0) to 1.0, the constant velocity here
CvMat* sigma = cvCreateMat(num_dim, num_dim, CV_64FC1); // covariance to be updated
CvMat* sigma_p = cvCreateMat(num_dim, num_dim, CV_64FC1); // covariance to be updated
CvMat* z = cvCreateMat(num_landmarks, 1, CV_64FC1); // measurement vector
CvMat* K = cvCreateMat(num_dim, num_landmarks, CV_64FC1); // K matrix // Kalman gain
// initialize "mu" vector
cvmSet(mu, 0, 0, rob_pos + sqrt(rob_pos_cov)*gaussian_random()); // set mu(0,0) to "rob_pos"
cvmSet(mu, 1, 0, rob_vel + sqrt(rob_vel_cov)*gaussian_random()); // set mu(0,0) to "rob_vel"
for(int n = 0; n < num_landmarks; n++)
{
// cvmSet(mu, n+2, 0, landmark[n] + sqrt(obs_cov)*gaussian_random());
cvmSet(mu, n+2, 0, landmark[n]);
}
displayMatrix(mu, "mu vector");
// initialize "sigma" matrix <-- This is the most critical point in tuning
cvSetIdentity(sigma, cvRealScalar(obs_cov));
displayMatrix(sigma, "sigma matrix");
// set the initial covariance of the state uncertainty
double rob_px_cov = 0.01; // covariance of noise to robot's x-position
double rob_py_cov = 0.01; // covariance of noise to robot's y-position
double rob_vx_cov = 0.01; // covariance of noise to robot's x-velocity
double rob_vy_cov = 0.01; // covariance of noise to robot's y-velocity
// set the initial covariance of the measurement noise
double obs_x_cov = 900; // covarriance of noise to x-measurement of landmarks
double obs_y_cov = 900; // covarriance of noise to y-measurement of landmarks
// ground truth of state
double xGroundTruth = rob_x;
double yGroundTruth = rob_y;
double vxGroundTruth = rob_vx;
double vyGroundTruth = rob_vy;
// ground truth of num_landmarks landmarks in the world coordinate
double landmark[2*num_landmarks];
for( int n = 0; n < num_landmarks; n++ )
{
landmark[2*n] = width * uniform_random();
landmark[2*n+1] = height * uniform_random();
}
// H matrix, measurement matrix
CvMat* H = cvCreateMat(2*num_landmarks, num_dim, CV_64FC1);
cvZero(H); // initialize H matrix
// set H matrix
for (int r = 0; r < num_landmarks; r++)
{
cvmSet(H, 2*r, 0, -1.0); // robot's x-position
cvmSet(H, 2*r, 2*r+4, 1.0); // landmark's x-position
cvmSet(H, 2*r+1, 1, -1.0); // robot's y-position
cvmSet(H, 2*r+1, 2*r+5, 1.0); // landmarks's y-position
}
displayMatrix(H, "H matrix");
// Q matrix ; covariance of noise to H; uncertainty of control
CvMat* Q = cvCreateMat(2*num_landmarks, 2*num_landmarks, CV_64FC1);
cvZero(Q); // initialize Q matrix
// set Q matrix
for (int row = 0; row < Q->rows; row++)
{
cvmSet(Q, row, row, obs_x_cov);
}
displayMatrix(Q, "Q matrix");
// G matrix // transition
CvMat* G = cvCreateMat(num_dim, num_dim, CV_64FC1);
cvZero(G); // initialize G matrix
// set G matrix
cvmSet(G, 0, 0, 1.0); // previous x-position
cvmSet(G, 0, 2, 1.0); // x-velocity
cvmSet(G, 1, 1, 1.0); // previous y-position
cvmSet(G, 1, 3, 1.0); // y-velocity
for (int row = 2; row < G->rows; row++)
{
cvmSet(G, row, row, 1.0); // constance of velocity
}
displayMatrix(G, "G matrix");
// R matrix ; covariance of noise to G; uncertainty of observation
CvMat* R = cvCreateMat(num_dim, num_dim, CV_64FC1);
cvZero(R); // initialize R matrix
// set R matrix
cvmSet(R, 0, 0, rob_px_cov);
cvmSet(R, 1, 1, rob_py_cov);
cvmSet(R, 2, 2, rob_vx_cov);
cvmSet(R, 3, 3, rob_vy_cov);
displayMatrix(R, "R matrix");
CvMat* rob_ground = cvCreateMat(num_dim, 1, CV_64FC1); // ground truth of state
CvMat* mu = cvCreateMat(num_dim, 1, CV_64FC1); // state vector to be estimated
CvMat* mu_p = cvCreateMat(num_dim, 1, CV_64FC1); // state vector to be predicted
CvMat* sigma = cvCreateMat(num_dim, num_dim, CV_64FC1); // covariance to be updated
CvMat* sigma_p = cvCreateMat(num_dim, num_dim, CV_64FC1); // covariance to be updated
CvMat* z = cvCreateMat(2*num_landmarks, 1, CV_64FC1); // measurement vector
CvMat* K = cvCreateMat(num_dim, 2*num_landmarks, CV_64FC1); // K matrix // Kalman gain
// initialize "mu" vector
cvmSet(mu, 0, 0, rob_x); // set mu(0,0) to "rob_x"
cvmSet(mu, 1, 0, rob_y); // set mu(1,0) to "rob_y"
cvmSet(mu, 2, 0, rob_vx); // set mu(2,0) to "rob_vx"
cvmSet(mu, 3, 0, rob_vy); // set mu(3,0) to "rob_vy"
for (int n = 0; n < 2*num_landmarks; n++)
{
cvmSet(mu, n+4, 0, landmark[n]); // set mu(4,0) to "landmark[0]", ...
}
displayMatrix(mu, "mu vector");
/* // initialize "sigma" matrix
cvmSet(sigma, 0, 0, rob_px_cov);
cvmSet(sigma, 1, 1, rob_py_cov);
cvmSet(sigma, 2, 2, rob_vx_cov);
cvmSet(sigma, 3, 3, rob_vy_cov);
for (int r = 4; r < sigma->rows; r=r*2)
{
cvmSet(sigma, r, r, obs_x_cov);
cvmSet(sigma, r+1, r+1, obs_y_cov);
}
*/ // initialize "sigma" matrix <-- This is the most critical point in tuning
cvSetIdentity(sigma, cvRealScalar(obs_x_cov));
displayMatrix(sigma, "sigma matrix");
// matrices to be used in calculation
CvMat* Hx = cvCreateMat(H->rows, mu->cols, CV_64FC1);
CvMat* Gt = cvCreateMat(G->cols, G->rows, CV_64FC1);
cvTranspose(G, Gt); // transpose(G) -> Gt
CvMat* sigmaGt = cvCreateMat(sigma->rows, G->rows, CV_64FC1);
CvMat* GsigmaGt = cvCreateMat(G->rows, G->rows, CV_64FC1); // 10x10
// observation relative to robot's position
for( int n = 0; n < 2*num_landmarks; n++ )
{
cvmSet(obs, n, 0, cvmGet(mu,0,0) + cvmGet(z,n,0));
}
// update the state with Kalman gain (ref. L5, EKF algorithm, 42p)
cvMatMul(H, mu, Hmu); // H * mu -> Hmu
cvSub(z, Hmu, miss); // z - Hmu -> miss
cvMatMul(K, miss, adjust); // K * miss -> adjust
cvAdd(mu_p, adjust, mu); // mu_p + adjust -> mu
displayMatrix(mu, "mu vector");
Robot mechanism Byung-Ju Yi (Hanyang University, Korea)
한양대 휴먼로보틱스 연구실 이병주 교수님 bj@hanyang.ac.kr - Classification of robotic mechanism and Design consideration of robotic mechanism
- Design Issue and application examples of master slave robotic system
- Trend of robotic mechanism research
Actuator and Practical PID Control Youngjin Choi (Hanyang University, Korea)
한양대 휴먼로이드 연구실 최영진 교수님 cyj@hanyang.ac.kr - Operation Principle of DC/RC/Stepping Motors & Its Practice
- PID Control and Tuning
- Stability of PID Control and Application Examples
Coordination of Robots and Humans Kazuhiro Kosuge (Tohoku University, Japan)
일본 도호쿠 대학 시스템 로보틱스 연구실 고스게 카즈히로 교수님 - Robotics as systems integration
- Multiple Robots Coordination
- Human Robot Coordination and Interaction
Robot Control Rolf Johansson (Lund University, Sweden)
스웨덴 룬드 대학 로보틱스 연구실 Rolf.Johansson@control.lth.se - Robot motion and force control
- Stability of motion
- Robot obstacle avoidance
Lecture from Industry or Government
(S. -R. Oh, KIST)
Special Talk from Government
(Y. J. Weon, MKE)
Mobile Robot Navigation Jae-Bok Song (Korea University, Korea)
고려대 지능로봇 연구실 송재복 교수님 jbsong@korea.ac.kr - Mapping
- Localization
- SLAM
3D Perception for Robot Vision In Kyu Park (Inha University, Korea) 인하대 영상미디어 연구실 박인규 교수님 pik@inha.ac.kr - Camera Model and Calibration
- Shape from Stereo Views
- Shape from Multiple Views
Lecture from Industry or Government
(H. S. Kim, KITECH)
Software Framework for LEGO NXT Sanghoon Lee (Hanyang University, Korea)
한양대 로봇 연구실 이상훈 교수님 - Development Environments for LEGO NXT
- Programming Issues for LEGO NXT under RPF of OPRoS
- Programming Issues for LEGO NXT under Roboid Framework
Lecture from Industry or Government
(Robomation/Mobiletalk/Robotis)
Robot Intelligence : From Reactive AI to Semantic AI Il Hong Suh (Hanyang University, Korea)
한양대 로봇 지능/통신 연구실 서일홍 교수님 - Issues in Robot Intelligence
- Behavior Control: From Reactivity to Proactivity
- Use of Semantics for Robot Intelligence
AI-Robotics
Henrik I. Christensen (Georgia Tech., USA)
- Semantic Mapping - Physical Interaction with Robots
- Efficient object recognition for robots
Lecture from Industry or Government
(M. S. Kim, Director of CIR, 21C Frontier Program)
HRI Dongsoo Kwon (KAIST, Korea)
- Introduction to human-robot interaction
- Perception technologies of HRI
- Cognitive and emotional interaction
Robot Swarm for Environmental Monitoring Nak Young Chong (JAIST, Japan)
- Self-organizing Mobile Robot Swarms: Models
- Self-organizing Mobile Robot Swarms: Algorithms
- Self-organizing Mobile Robot Swarms: Implementation
Kalman filter
: estimates system states that can only be observed indirectly or inaccurately by the system itself.
: estimates the variables of a wide range of processes.
: estimates the states of a linear system.
: minimizes the variance of the estimation error
Linear system
x: state of the system
u: known input to the system
y: measured output
w: process noise
z: measurement noise
http://wiki.answers.com/Q/What_is_a_feedback_system
A feedback system, in general engineering terms, is a system whose
output if fed back to the input, and depending on the output, your
input is adjusted so as to reach a steady-state. In colloquial
language, you adjust your input based on the output of your system so
as to achieve a certain end, like minimizing disturbance, cancelling
echo (in a speech system) and so on.
Criteria of an Estimator
1) The expected value of the estimate should be equal to the expected value of the state.
2) The estimator should be with the smallest possible error variance.
Requirement of Kalman filter
1) The average value of w is zero and average value of z is zero.
2) No correlation exists between w and z. w_k and z_k are independent random variables.
Kalman filter equations
K matrix: Kalman gain
P matrix: estimation error covariance
http://en.wikipedia.org/wiki/Three_sigma_rule
In statistics, the 68-95-99.7 rule, or three-sigma rule, or empirical rule, states that for a normal distribution, nearly all values lie within 3 standard deviations of the mean.
"steady state Kalman filter"
- K matrix & P matrix are constant
"extended Kalman filter"
: an extension of linear Kalman filter theory to nonlinear systems
"Kalman smoother"
: to estimate the state as a function of time so to reconstruct the trajectory after the fact
H infinity filter
=> correlated noise problem
=> unknown noise covariances problem
spacecraft navigation for the Apollo space program
> applications
all forms of navigation (aerospace, land, and marine)
nuclear power plant instrumentation
demographic modeling
manufacturing
the detection of underground radioactivity
fuzzy logic and neural network training
Gelb, A. Applied Optimal Estimation. Cambridge, MA: MIT Press, 1974.
Anderson, B. and J. Moore. Optimal Filtering. Englewood Cliffs, NJ: Prentice-Hall, 1979.
Grewal, M. and A. Andrews. Kalman Filtering Theory and Practice. Englewood Cliffs, NJ: Prentice-Hall, 1993.
Sorenson, H. Kalman Filtering: Theory and Application. Los Alamitos, CA: IEEE Press, 1985.
Peter Joseph’s Web site @http://ourworld.compuserve.com/homepages/PDJoseph/
IEEE Transactions on Systems, Man and Cybernetics, Part A, vol. 31, no. 1, pp. 43–54, 2001.
Abstract - This paper describes a visual tool for teleoperative experimentation involving remote manipulation and contact tasks. Using modest hardware, it recovers in real-time the pose of moving polyhedral objects, and presents a synthetic view of the scene to the teleoperator using any chosen viewpoint and viewing direction. The method of line tracking introduced by Harris is extended to multiple calibrated cameras, and afforced by robust methods and iterative ltering. Experiments are reported which determine the static and dynamic performance of the vision system, and its use in teleoperation is illustrated in two experiments, a peg in hole manipulation task and an impact control task.
Line tracking http://en.wikipedia.org/wiki/Passive_radar#Line_tracking
The line-tracking step refers to the tracking of target returns from individual targets, over time, in the range-Doppler space produced by the cross-correlation processing. A standard Kalman filter is typically used. Most false alarms are rejected during this stage of the processing.
- Three difficulties using the Harris tracker
First it was found to be easily broken by occlusions and changing
lighting. Robust methods to mitigate this problem have been
investigated monocularly by Armstrong and Zisserman [20], [21].
Although this has a marked effect on tracking performance, the second
problem found is that the accuracy of the pose recovered in a single
camera was poor, with evident correlation between depth and rotation
about axes parallel to the image plane. Maitland and Harris [22] had
already noted as much when recovering the pose of a pointing device
destined for neurosurgical application [23].
They reported much improved accuracy using two cameras; but the object
was stationary, had an elaborate pattern drawn on it and was visible at
all times to both cameras. The third difficulty, or rather uncertainty,
was that the convergence properties and dynamic performances of the
monocular and multicamera methods were largely unreported.
"Harris' RAPiD tracker included a constant velocity Kalman filter."
Techniques for Generating Consistent Maps
• Scan matching
• EKF SLAM
• Fast-SLAM
• Probabilistic mapping with a single map and a posterior about poses Mapping + Localization
• Graph-SLAM, SEIFs
Approximations for SLAM
• Local submaps
[Leonard et al.99, Bosse et al. 02, Newman et al. 03]
• Sparse links (correlations)
[Lu & Milios 97, Guivant & Nebot 01]
• Sparse extended information filters
[Frese et al. 01, Thrun et al. 02]
• Thin junction tree filters
[Paskin 03]
• Rao-Blackwellisation (FastSLAM)
[Murphy 99, Montemerlo et al. 02, Eliazar et al. 03, Haehnel et al. 03]
EKF-SLAM Summary
•Quadratic in the number of landmarks: O(n2)
• Convergence results for the linear case.
• Can diverge if nonlinearities are large!
• Have been applied successfully in large-scale environments.
• Approximations reduce the computational complexity.
Mark Paskin
Java library with several SLAM variants, including Kalman filter, information filter, and thin junction tree forms. Includes a MATLAB interface. http://www.stanford.edu/~paskin/slam/
Radish (The Robotics Many and varied indoor datasets, including large-area Data Set Repository) data from the CSU Stanislaus Library, the Intel Research Lab in Seattle, the Edmonton Convention Centre, and more. http://radish.sourceforge.net/
IJRR (The International Journal of Robotics Research)
IJRR maintains a Web page for each article, often containing data and video of results. A good paper example is by Bosse et al. [3], which has data from Killian Court at MIT. http://www.ijrr.org/contents/23\_12/abstract/1113.html
ICARCV 2010 - The 11th International Conference on Control, Automation, Robotics and Vision http://www.icarcv.org/2010/
History
- 1986, probabilistic SLAM problem (IEEE Robotics and Automation Conference)
Peter Cheeseman, Jim Crowley, and Hugh Durrant-Whyte, Raja Chatila, Oliver Faugeras, Randal Smith
> estimation-theoretic methods, consistent mapping
- consistent probabilistic mapping
Smith and Cheesman [39] and Durrant-Whyte [17]
> statistical basis
"There must be a high degree of correlation between estimates of the location of different landmarks in a map"
- visual navigation & sonar-based navigation
Ayache and Faugeras [1], Crowley [9] and Chatila and Laumond [6]
> Kalman filter-type algorithms
"The estimations of the landmarks are all necessarily correlated with each other because of the common error in estimated vehicle location."
> joint state (of the vehicle pose and every landmark position) to be updated following each landmark observation & estimator (state vector)
- random-walk behavior with unbounded error growth (without knowledge of the convergence behavior of the map)
> single estimation problem: "The combined mapping and localization problem is convergent."
"The more the correlations between landmarks grew, the better the solution."
- 1995, coining of SLAM (a paper at the International Symposium on Robotics Research) or called CLM (concurrent mapping and localization)
Csorba [10], [11]. the Massachusetts Institute of Technology [29], Zaragoza [4], [5], the ACFR at Sydney [20], [45], and others [7], [13]
> computational efficiency, addressing in data association, loop closure
- 1999 ISRR, convergence between the Kalman-filter-based SLAM methods and the probabilistic localisation and mapping methods introduced by Thrun
- 2000 IEEE ICRA
> algorithmic complexity, data association, implementation
Formulation
SLAM = process by which a mobile robot can build a map of an environment and at the same time use this map to deduce its location
(In SLAM, both the trajectory of the platform and the location of all landmarks are estimated online without the need for any a priori knowledge of location.)
Probabilistic SLAM
The SLAM probability distribution = the joint posterior density of the landmark locations and vehicle state (at time k) given the recorded observations and control inputs up to and including time k together with the initial state of the vehicle
recursive solution
: observation model + motion (state transition) model == Bayes theorem ==> estimate of SLAM distribution
observation model -> prediction (; measurement update)
+ motion model -> correction (; time update)
+ Markov process
=> map building problem + localization problem
: joint posterior density of the landmark locations and vehicle state
As the map is built, the location accuracy of the robot measured relative to the map is bounded only by the quality of the map and relative measurement sensor.
: Robot relative location accuracy becomes equal to the localization accuracy achievable with a given map.
2)
a set of samples of a more general non-Gaussian probability distribution to describe vehicle motion
Rao-Blackwellized particle filter or FastSLAM algorithm
> definition
mapping: 환경을 인식가능한 정보로 변환하고
localization: 이로부터 자기 위치를 추정하는 것
> issues
- uncertainty <= sensor
- data association (데이터 조합): 차원이 높은 센서 정보로부터 2-3차원 정도의 정보를 추려내어 이를 지속적으로 - 대응시키는 것
- 관찰된 특징점 자료들을 효율적으로 관리하는 방법
> localization (위치인식)
: 그 위치가 미리 알려진 랜드마크를 관찰한 정보를 토대로 자신의 위치를 추정하는 것
: 초기치 x0와 k-1시점까지의 제어 입력, 관측벡터와 사전에 위치가 알려진 랜드마크를 통하여 매 k시점마다 로봇의 위치를 추정하는 것
- 로봇의 위치추정의 불확실성은 센서의 오차로부터 기인함.
> mapping (지도작성)
: 기준점과 상대좌표로 관찰된 결과를 누적하여 로봇이 위치한 환경을 모델링하는 것
: 위치와 관측정보 그리고 제어입력으로부터 랜드마크 집합을 추정하는 것
- 지도의 부정확성은 센서의 오차로부터 기인함.
> Simultaneous Localization and Mapping (SLAM, 동시간 위치인식 및 지도작성)
: 위치한 환경 내에서 로봇의 위치를 추정하는 것
: 랜드마크 관측벡터와 초기값 그리고 적용된 모든 제어입력이 주어진 상태에서 랜드마크의 위치와 k시점에서의 로봇 상태벡터 xk의 결합확률
- 재귀적 방법 + Bayes 정리
- observation model (관측 모델) + motion model (상태 공간 모델, 로봇의 움직임 모델)
- motion model은 상태 천이가 Markov 과정임을 의미함. (현재 상태는 오직 이전 상태와 입력 벡터로서 기술되고, 랜드마크 집합과 관측에 독립임.)
- prediction (time-update) + correction (measurement-update)
- 불확실성은 로봇 주행거리계와 센서 오차로부터 유발됨.
Klein, G. and Murray, D. 2007. Parallel Tracking and Mapping for Small AR Workspaces
In Proceedings of the 2007 6th IEEE and ACM international Symposium on Mixed and Augmented Reality - Volume 00
(November 13 - 16, 2007). Symposium on Mixed and Augmented Reality.
IEEE Computer Society, Washington, DC, 1-10. DOI=
http://dx.doi.org/10.1109/ISMAR.2007.4538852
1. parallel threads of tracking and mapping
2. mapping from smaller keyframes: batch techniques (Bundle Adjustment)
3. Initializing the map from 5-point Algorithm
4. Initializing new points with epipolar search
5. mapping thousands of points
affine warp
warping matrix <- (1) back-projecting unit pixel displacements in the source keyframe pyramid level onto the patch's plane and then (2) projecting these into the current (target) frame
This paper appears in: Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on
Publication Date: 13-16 Oct. 2003
On page(s): 1403-1410 vol.2
ISBN: 0-7695-1950-4
INSPEC Accession Number: 7971070
Digital Object Identifier: 10.1109/ICCV.2003.1238654
Current Version Published: 2008-04-03
This paper appears in: Computer Vision and Pattern Recognition, 2006 IEEE Computer Society Conference on
Publication Date: 17-22 June 2006
Volume: 1, On page(s): 469- 476
ISSN: 1063-6919
ISBN: 0-7695-2597-0
Digital Object Identifier: 10.1109/CVPR.2006.263
Current Version Published: 2006-07-05
monocular SLAM
particle filter + top-down search => real-time, large number of landmarks
the first to apply this FastSLAM-type particle filter to single-camera SLAM
1. Introduction
SLAM = Simultaneous Localization and Mapping
: process of causally estimating both egomotion and structure in an online system
SLAM using visual data in computer vision
SFM (= structure from motion): reconstructing scene geometry
+ causal or recursive estimation techniques
perspective-projection cameras
filtering methods to allow indirect observation models
Kalman filtering framework
Extended Kalman filter = EKF (-> to linearize the observation and dynamics models of the system)
causal estimation with recursive algorithms (cp. estimation depending only on observations up to the current time)
=> online operation (cp. SFM on global nonlinear optimization)
Davision's SLAM with a single camera
> EKF estimation framework
> top-down Bayesian estimation approach searching for landmarks in image regions constrained by estimate > uncertainty (instead of performing extensive bottom-up image processing and feature matching)
> Bayesian partial-initialization scheme for incorporating new landmarks
- cannot scale to large environment
EKF = the Extended Kalman filter
- N*N covariace matrix for N landmarks
- updated with N*N computation cost
> SLAM system using a single camera as the only sensor
> frame-rate operation with many landmarks
> FastSLAM-style particle filter (the first use of such an approach in a monocular SLAM setting)
> top-down active search
> an efficient algorithm for discovering the depth of new landmarks that avoids linearization errors
> a novel method for using partially initialized landmarks to help constrain camera pose
FastSLAM
: based on the Rao-Blackwellized Particle Filter
2. Background
2.1 Scalable SLAM
> submap
bounded complexity -> bounded computation and space requirements
Montemerlo & Thrun
If the entire camera motion is known then the estimates of the positions of different landmarks become independent of each other.
Generic constraints on underspecified target trajectories.pdf
