1. Real-Time Simultaneous Localization and Mapping with a Single Camera (Mono SLAM)
Young Ki Baik
Computer Vision Lab.
Seoul National University

2. Contents References Kalman filter and SLAM Mono-SLAM Simulation Demo
Conclusion

3. References
Real-Time Simultaneous Localisation and Mapping with a Single Camera
Andrew J. Davison (ICCV 2003)
A Solution to the Simultaneous Localization and Map Building (SLAM) problem
Gamini Dissanayake. Et. Al. (IEEE Trans. Robotics and Automation 2001)
An Introduction to the Kalman Filter
G. Welch and G. Bishop (SIGGRAPH 2001)
Site for Quaternion

4. Kalman filter What is a Kalman filter? Applications
Mathematical power tool
Optimal recursive data processing algorithm
Noise effect minimization
Applications
Tracking (head, hands etc.)
Lip motion from video sequences of speakers
Fitting spline
Navigation
Lot’s of computer vision problem

5. Kalman filter Kalman filter Example Sensor noise Measurement error
Landmark
Kalman filter
How can we obtain optimal pose of robot and landmark simultaneously?
Real location
Robot
Location with error
Movement noise
Refined location
Localizing error (Processing error)

6. Kalman filter Example (Simple Gaussian form) Assumption
All error form Gaussian noise
Estimated value
Measurement value

7. Kalman filter Example (Simple Gaussian form) Optimal variance
Optimal value
Innovation
Kalman gain

8. SLAM SLAM If we have the solution to the SLAM problem…
Simultaneously Localization and map building system
EKF(Extended Kalman filter)-based framework
If we have the solution to the SLAM problem…
Allow robots to operate in an environment without a priori knowledge of a map
Open up a vast range of potential
application for autonomous vehicles
and robot
Research over the last decade has
shown that SLAM is indeed possible

9. SLAM Kalman filter and SLAM problem
Extended Kalman filter form for SLAM
Prediction
Observation
Update
: Previous value
: Input and measure
: Function
: Computed value

10. Mono SLAM ? What is Mono SLAM? User input
EKF-SLAM framework (EKF : Extended Kalman Filter)
Single camera
Unknown user input
User input
Known control input
Encoder information of robot or vehicle (odometry) ?
Most case of localization system,
odometry information is used as initial moving value.
Mono- slam don't use odometry information and it can be new feature.

11. Mono SLAM World frame model Camera frame R W : World coordinate
World Frame W
R : Local coordinate r
r : Camera position vector in W frame
y : Landmark position vector in W frame y

12. Mono SLAM Motion model 3D position and orientation
This state vector is parameters for conventional SLAM .

13. Mono SLAM
Motion model
Key difference between Mono- and conventional-SLAM
In the robot case, there is in possession of the control inputs driving the motion, such as “moving forward 1m with steering angle 5 degree”
In the hand helded camera case, we do not have such prior information about a person’s movement.
Assumption (Mono SLAM)
In the case of a camera attached to a person, it takes account of the unknown intentions of the person, but these too can be statistically modeled.
Constant velocity, constant angular velocity model are chosen as initial value and added undetermined accelerations occur with a Gaussian profile.

14. The total dimension of state vector is 13.
Mono SLAM
Motion model (Mono SLAM)
3D position and orientation
The total dimension of state vector is 13.

15. Mono SLAM Motion model (Mono SLAM)
Unknown user input (or noise vector)
In each time step, unknown acceleration and angular acceleration processes of zero mean and Gaussian distribution.

16. Mono SLAM Motion model (Mono SLAM) State update function
Quaternion trivially defined by the angle-axis rotation vector
: Previous value
: Unknown user input

17. Mono SLAM Motion model (Mono SLAM) Covariance update
In the EKF, the new state estimate must be accompanied by the increase in state uncertainty (process noise covariance) for the camera after this motion.
Qv is found via the Jacobian calculation

18. Mono SLAM Motion model (Mono SLAM) Covariance of noise vector
The rate of growth of uncertainty in this motion model is determined by the size of , and setting these parameters to small or large values defines the smoothness of the motion we expect.
small
- We expect a very smooth motion with small accelerations, and would be well placed to track motion but unable to cope with sudden rapid movements
High
- The uncertainty in the system increases significantly at
each time step.
- This can be cope with rapid accelerations.

19. Simulation Demo Condition 3D view 2D view Simple circular motion
Five 3D landmarks
Observation is 2D using projective camera model
3D view
2D view
Estimated LM
Real LM
Estimated Pos
& Covariance
Projected LM

20. Conclusion Conclusion Simulation result
Localization is possible with out control input.
Simulation result
3D position can be estimated using SLAM through the projected landmark information.
It needs more debuging for perfect simulation.

22. Mono SLAM Quaternion form for orientation (or rotation) Eular angle
Arbitrary 3D rotation is equal to one rotation (by scalar angle) around an axis.
The result of any sequence of rotation is equal to a single rotation around an axis.
3 degree of freedom in 3D space
Gimbal lock problem

23. Mono SLAM Quaternion form for orientation (or rotation) Axis angle
Arbitrary 3D rotation composed by 3-d unit vector and 1-d angle value
4 degree of freedom in 3D space
Singularity problem

24. Mono SLAM Quaternion form for orientation (or rotation)
Quaternion angle
Arbitrary 3D rotation composed by 3-d unit vector and 1-d angle value
4 degree of freedom in 3D space
Why quaternion?
Simpler algebra
Easy to fix numerical error
No singularity and Gimbal lock problem