Robust pose-graph loop-closures with expectation-maximization

In this paper, we model the robust loop-closure pose-graph SLAM problem as a Bayesian network and show that it can be solved with the Classification Expectation-Maximization (EM) algorithm. In particular, we express our robust pose-graph SLAM as a Bayesian network where the robot poses and constraints are latent and observed variables. An additional set of latent variables is introduced as weights for the loop-constraints. We show that the weights can be chosen as the Cauchy function, which are iteratively computed from the errors between the predicted robot poses and observed loop-closure constraints in the Expectation step, and used to weigh the cost functions from the pose-graph loop-closure constraints in the Maximization step. As a result, outlier loop-closure constraints are assigned low weights and exert less influences in the pose-graph optimization within the EM iterations. To prevent the EM algorithm from getting stuck at local minima, we perform the EM algorithm multiple times where the loop constraints with very low weights are removed after each EM process. This is repeated until there are no more changes to the weights. We show proofs of the conceptual similarity between our EM algorithm and the M-Estimator. Specifically, we show that the weight function in our EM algorithm is equivalent to the robust residual function in the M-Estimator. We verify our proposed algorithm with experimental results from multiple simulated and real-world datasets, and comparisons with other existing works.

Authors

• Gim Hee Lee
• Friedrich Fraundorfer
• Marc Pollefeys

Keywords

• Equations
• Robustness
• Mathematical model
• Simultaneous localization and mapping
• Cost function
• Expectation Maximization
• Low Weight
• Bayesian Model
• Latent Variables
• Local Minima
• Simulated Datasets
• Weight Function
• Real-world Datasets
• Maximum Step
• Least-squares
• Sigmoid Function
• Uncertainty Estimation
• Nonlinear Least Squares
• Functional Equation
• Jacobian Matrix
• Mahalanobis Distance
• Penalty Term
• Fisher Information
• Pose Estimation
• Subset Of Clusters
• Robust Cost
• Relative Pose
• Current Pose
• Parking Garage
• Least Squares Problem
• Real Robot
• Local Constraints
• Equation In Step