Transcript 슬라이드 1
Vision-based SLAM Enhanced by Particle Swarm Optimization on the Euclidean Group Vision seminar : Dec. 30. 2009 Young Ki BAIK Computer Vision Lab. ComputerVisionLab Seoul National University Outline Introduction Related works Problem statement Proposed algorithm PSO-based visual SLAM Single camera SLAM using ABC algorithm Demonstration Conclusion ComputerVisionLab Seoul National University What is SLAM? SLAM : Simultaneous Localization And Mapping ComputerVisionLab Seoul National University 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 ComputerVisionLab Seoul National University How to solve SLAM problem? 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 ComputerVisionLab Seoul National University Previous works EKF-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 ComputerVisionLab Seoul National University RBPF-SLAM State equation (Process noise) (User input or odometry) (Nonlinear stochastic difference equation) Measurement equation (Measurement noise) (Camera projection function) ComputerVisionLab Seoul National University Problem of RBPF-SLAM How to choose importance function? ? t Odometry Naive motion model Constant position Xt+1=Xt+N Angle Change + Distance Change Left Encoder Distance t+1 Right Encoder Distance Constant velocity Xt+1=Xt+∇t(Vt+N) ComputerVisionLab Seoul National University Problem of RBPF-SLAM Sampling by transition model Landmark Particle Robot t ComputerVisionLab Seoul National University Problem of RBPF-SLAM Sampling by transition model t t+1 ComputerVisionLab Seoul National University Problem of RBPF-SLAM Sampling by transition model t t+1 ComputerVisionLab Seoul National University Problem of RBPF-SLAM Sampling by transition model t+1 (Gaussian) ComputerVisionLab Seoul National University Problem of RBPF-SLAM Sampling by transition model t+1 ComputerVisionLab Seoul National University Problem of RBPF-SLAM How to choose importance function? Hand-held camera case ? t t+1 ComputerVisionLab Seoul National University RBPF-SLAM Sampling by transition model t t+1 ComputerVisionLab Seoul National University Problem of RBPF-SLAM Particle impoverishment Mismatch between proposal and likelihood distribution. Likelihood Proposal ComputerVisionLab Seoul National University 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 !! ComputerVisionLab Seoul National University Optimal Importance Function (OIF) Sampling by optimal importance function OIF t t+1 ComputerVisionLab Seoul National University Problem of OIF-based SLAM Linearization Error Smooth camera motion Abrupt camera motion Linearization Error : Real camera state : Estimated camera state by linearization : Predicted camera state by a motion model ComputerVisionLab Seoul National University Problem statement OIF-based visual SLAM State of the art Weak to abrupt camera motion Novel visual SLAM robust to abrupt camera motion ComputerVisionLab Seoul National University 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 ComputerVisionLab Seoul National University Our contribution We propose … 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!! ComputerVisionLab Seoul National University Special Euclidean group SE (3) Conventional State 6-D vector by local coordinates Geometric as a Lie group SE(3) State Equation Ignores geometry of the underlying space Considers geometry of the curved space! ComputerVisionLab Seoul National University 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 Exp Log se(3) Identity SE(3) Exp: se(3) SE(3) Log: SE(3) se(3) ComputerVisionLab Seoul National University 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 se(3) Exp SE(3) ComputerVisionLab Seoul National University Main idea We use optimization method for better proposal distribution… Particle Swarm Optimization Propagate particles using motion prior Prior PSO Moves Particles with high likelihood ComputerVisionLab Seoul National University Particle Swarm Optimization Developed in evolutionary computation community Sampling-based optimization method Uses the relationship between particles PSO OIF Interaction Linearization ComputerVisionLab Seoul National University Particle Swarm Optimization Particle from motion prior ComputerVisionLab Seoul National University Particle Swarm Optimization Initialization (current optimum) (individual best) ComputerVisionLab Seoul National University Particle Swarm Optimization Particle from motion prior (current optimum) (individual best) ComputerVisionLab Seoul National University Particle Swarm Optimization Particle from motion prior (current optimum) (individual best) (Inertia) (Coefficient) (Random) ComputerVisionLab Seoul National University Particle Swarm Optimization Velocity updating (current optimum) (individual best) ComputerVisionLab Seoul National University Particle Swarm Optimization Moving (current optimum) (individual best) ComputerVisionLab Seoul National University Particle Swarm Optimization Global and local best updating (current optimum) (individual best) ComputerVisionLab Seoul National University Particle Swarm Optimization For all Particles ComputerVisionLab Seoul National University Geometric Particle Swarm Optimization Tangent space at X iold log Xi Xiold old old log Xi Pgb old log Xi Pibi Manifold v i X iold v iold Pgb exp Xi old X i new Pibi Random perturbation & coefficient multiplication ComputerVisionLab Seoul National University Experiments System environment CPU : Intel Core-2 Quad 2.4 GHz process Real-time with C++ implementation Synthetic sequence Real sequence Virtual stereo camera Quantitative analysis Bumblebee stereo camera (BB-HICOL-60) ComputerVisionLab Seoul National University Demonstration ComputerVisionLab Seoul National University Demonstration ComputerVisionLab Seoul National University 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 ComputerVisionLab Seoul National University 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 ComputerVisionLab Seoul National University 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 ) ComputerVisionLab Seoul National University Q & A ComputerVisionLab Seoul National University