Duality-based verification techniques for 2D SLAM

While iterative optimization techniques for Simultaneous Localization and Mapping (SLAM) are now very efficient and widely used, none of them can guarantee global convergence to the maximum likelihood estimate. Local convergence usually implies artifacts in map reconstruction and large localization errors, hence it is very undesirable for applications in which accuracy and safety are of paramount importance. We provide a technique to verify if a given 2D SLAM solution is globally optimal. The insight is that, while computing the optimal solution is hard in general, duality theory provides tools to compute tight bounds on the optimal cost, via convex programming. These bounds can be used to evaluate the quality of a SLAM solution, hence providing a “sanity check” for state-of-the-art incremental and batch solvers. Experimental results show that our technique successfully identifies wrong estimates (i. e. , local minima) in large-scale SLAM scenarios. This work, together with [1], represents a step towards the objective of having SLAM techniques with guaranteed performance, that can be used in safety-critical applications.

Authors

• Luca Carlone
• Frank Dellaert

Keywords

• Simultaneous localization and mapping
• Optimization
• Convergence
• Upper bound
• Position measurement
• Standards
• Verification Techniques
• Local Minima
• Global Optimization
• Convex Optimization
• Optimal Cost
• Global Convergence
• Dual Theory
• Iterative Technique
• Map Reconstruction
• Sanity Check
• Local Convergence
• Safety-critical Applications
• Reconstruction Artifacts
• Lower Bound
• Optimization Problem
• Lagrange Multiplier
• Simulated Datasets
• Global Minimum
• Primal Problem
• Standard Solver
• Quadratic Constraints
• Semidefinite Programming
• Dual Problem
• Quadratic Programming
• Candidate Solutions
• Schur Complement
• Position Of The Robot
• Iterative Solver