Pairwise Consistent Measurement Set Maximization for Robust Multi-Robot Map Merging

3 min read

PCM decides which inter-robot loop closures to trust when two robots merge their pose graphs. Single-robot robust SLAM judges a loop closure against the odometry chain, but between two robots there is no shared odometry and often no prior on their relative pose. PCM instead checks pairs: two inter-robot measurements are consistent if composing one, the two local trajectories and the inverse of the other gives something close to the identity, measured by Mahalanobis distance (which is chi-squared, so the threshold has a probabilistic meaning). The consistency matrix becomes a graph, and the largest set of mutually consistent measurements is its maximum clique, solved exactly for moderate sizes or with a heuristic for larger ones.

Findings

  • Synthetic city, 81 generated datasets with 15 inlier loop closures, two groups of 5 internally consistent “perceptual aliasing” outliers and 90 random outliers. PCM (11% threshold): translation MSE 0.276 m², TPR 0.997, FPR 0.001. RANSAC at 1%: 5.688 m² and FPR 0.006. SCGP: 623 m². DCS disabled every inter-robot measurement (TPR 0).
  • PCM’s TPR and FPR barely move with the threshold as long as it is below about 85%; RANSAC’s FPR changes with every threshold and is never zero.
  • The heuristic clique solver gave the same results as the exact one on these data.
  • NCLT, two sessions about two weeks apart, 10 “inliers” and 98 “outliers” from GICP scan matching: PCM accepted all 10 inliers and 3 labelled outliers and gave the best trajectory error and relative-pose translation error, the latter lower than the no-outlier graph (386.7 against 455.5 m²). On checking, the 3 were real matches that the ground-truth thresholding had mislabelled.

Limits

  • PCM assumes the largest consistent set is the true one. A big enough group of mutually consistent wrong measurements (repeated structure, or a robot lying in a coordinated way) wins.
  • The authors assume full-degree-of-freedom relative pose measurements. Pairwise consistency also does not imply that a whole set is jointly consistent. The later group-k extension (Forsgren, Mangelson and others, IJRR 2024) checks consistency over groups of k measurements instead of pairs.
  • Maximum clique is NP-hard; exact solving takes exponential time in the worst case.
  • It only handles inter-robot measurements. Each robot’s own trajectory is trusted.

Relevance

PCM’s pairwise check is often reused as the outlier filter in collaborative SLAM front ends, and the same maximum-clique step appears inside TEASER. Its blind spot is the coordinated liar, which is where outlier-robust estimation needs ideas from Byzantine fault tolerance. Map merging across sessions weeks apart also makes it relevant to long-term autonomy.