Vision-based SLAM Enhanced by Particle Swarm Optimization on the Euclidean Group Vision seminar : Dec. 30. 2009 Young Ki BAIK Computer Vision Lab.

Single camera SLAM using ABC algorithm Outline Introduction Related works Problem statement Proposed algorithm PSO-based visual SLAM Single camera SLAM using ABC algorithm Demonstration Conclusion

SLAM : Simultaneous Localization And Mapping What is SLAM? SLAM : Simultaneous Localization And Mapping

Laser rangefinders, Sonar sensors Why visual SLAM? To acquire observation data Use many different type of sensor Laser rangefinders, Sonar sensors Too expensive : about 2000$ Scanning system : complex mechanics Camera Low price : about 30$ Acquire large and meaningful information from one shot measure

How to solve SLAM problem? Solved by filtering approaches Extended Kalman Filter (EKF) has scalability problem of the map Rao-Blackwellised Particle Filter (RBPF) handles nonlinear and non-Gaussian reduces computation cost by decomposing sampling space

Previous works EKF-based visual SLAM RBPF-based visual SLAM Andrew Davison (1998) Stereo camera + odometry Andrew Davison (2002) Single camera without odometry RBPF-based visual SLAM Robert Sim (2005) Stereo camera + odometry Mark Pupilli (2005) Single camera without odometry

RBPF-SLAM State equation Measurement equation (Process noise) (User input or odometry) (Process noise) (Nonlinear stochastic difference equation) Measurement equation (Camera projection function) (Measurement noise)

? + Problem of RBPF-SLAM How to choose importance function? t+1 t Odometry Naive motion model Constant position Xt+1=Xt+N Angle Change + Distance Change Left Encoder Distance Right Encoder Distance Constant velocity Xt+1=Xt+∇t(Vt+N)

Problem of RBPF-SLAM Sampling by transition model t Landmark Particle Robot t

Problem of RBPF-SLAM Sampling by transition model t t+1

Problem of RBPF-SLAM Sampling by transition model t t+1

Problem of RBPF-SLAM Sampling by transition model t+1 (Gaussian)

Problem of RBPF-SLAM Sampling by transition model t+1

? Problem of RBPF-SLAM How to choose importance function? Hand-held camera case ? t t+1

RBPF-SLAM Sampling by transition model t t+1

Problem of RBPF-SLAM Particle impoverishment Mismatch between proposal and likelihood distribution. Likelihood Proposal

Optimal Importance Function (OIF) For better proposal distribution Use observation for proposal distribution Optimal importance function approach (Doucet et al., 2000) Observation incorporated proposal Linearize the optimal importance function Used in FastSLAM 2.0 (Montemerlo et al.) The state of the art !!

Optimal Importance Function (OIF) Sampling by optimal importance function OIF t t+1

Problem of OIF-based SLAM Linearization Error Smooth camera motion Linearization Error Abrupt camera motion : Real camera state : Estimated camera state by linearization : Predicted camera state by a motion model

Problem statement OIF-based visual SLAM State of the art Weak to abrupt camera motion Novel visual SLAM robust to abrupt camera motion

Target Proposed SLAM system 6-DOF SLAM Hand-held camera Single or stereo camera No odometry RBPF-based SLAM Robust to sudden changes Real-time system

Our contribution We propose … Robust to abrupt camera motion!! Novel particle filtering framework combined with geometric PSO Based on special Euclidean group SE (3) Reformulating original PSO in consideration of SE (3) Applying Quantum particles to more actively explore the problem space Robust to abrupt camera motion!!

Special Euclidean group SE (3) Conventional Geometric State 6-D vector by local coordinates as a Lie group SE(3) State Equation Ignores geometry of the underlying space Considers geometry of the curved space!

Special Euclidean group SE (3) 6D vector  Euclidean group SE(3) Lie group  Group + Differentiable manifold Lie algebra  Tangent space at the identity (se(3)) Origin se(3) Exp Log Exp: se(3)  SE(3) Log: SE(3)  se(3) Identity SE(3)

Special Euclidean group SE (3) 6D vector  Euclidean group SE(3) Sampling on Tangent space at the identity (se(3)) Reasonable to consider the geometry of motion Sampling Exp se(3) SE(3)

Main idea We use optimization method for better proposal distribution… Particle Swarm Optimization Prior Propagate particles using motion prior PSO Moves Particles with high likelihood

Particle Swarm Optimization Developed in evolutionary computation community Sampling-based optimization method Uses the relationship between particles PSO OIF Interaction Linearization

Particle Swarm Optimization Particle from motion prior

Particle Swarm Optimization Initialization (current optimum) (individual best)

Particle Swarm Optimization Particle from motion prior (current optimum) (individual best)

Particle Swarm Optimization Particle from motion prior (current optimum) (individual best) (Inertia) (Coefficient) (Random)

Particle Swarm Optimization Velocity updating (current optimum) (individual best)

Particle Swarm Optimization Moving (current optimum) (individual best)

Particle Swarm Optimization Global and local best updating (current optimum) (individual best)

Particle Swarm Optimization For all Particles

Geometric Particle Swarm Optimization Tangent space at Manifold Random perturbation & coefficient multiplication

Bumblebee stereo camera Experiments System environment CPU : Intel Core-2 Quad 2.4 GHz process Real-time with C++ implementation Synthetic sequence Real sequence Virtual stereo camera Bumblebee stereo camera (BB-HICOL-60) Quantitative analysis

Demonstration

Demonstration

Artificial Bee Colony Additional work !! Visual Odometry Determining the position and orientation of a robot by analyzing the associated camera images … David Nister (2004) Monocular or binocular camera Yang Cheng et al. (2008) Stereo camera

Propagate particles using motion prior Artificial Bee Colony Additional work !! Propagate particles via visual odometry Propagate particles using motion prior PSO Moves PSO Moves Particles with high likelihood Artificial Bee Colony

Conclusion Novel visual SLAM is presented !! RBPF based on the special Euclidean group SE (3) Geometric Particle Swarm Optimization Robust to abrupt camera motion Real-time system Novel monocular SLAM will be presented !! Geometric Artificial Bee Colony Combined proposal ( VO + Naive motion model )

Q & A