Toward robust multi-agent autonomous underwater inspection with consistency and global optimality guarantees

Summary

Abstract

Teams of autonomous robotic systems have the potential to have a dramatic positive effect on our society. In the underwater domain specifically, collaborative multi-agent autonomous systems have the potential to lead to significant increases in efficiency, safety, and data quality. However, while autonomous systems have been widely accepted within structured environments such as manufacturing plants and distribution facilities, they have not been nearly as widely adopted in unstructured environments. The primary reason for this is that the reliability of autonomous systems in unstructured environments has not yet reached a level where it is cost and time effective to widely adopt such platforms. One key element of the reliability of autonomous systems is the robustness of navigation and localization algorithms to common failure cases such as outlier measurements, bad initialization, and inaccurate characterizations of uncertainty. Accordingly, this thesis proposes methods for simultaneous localization and mapping (SLAM), multi-agent map merging, trajectory alignment, and uncertainty characterization that seek to address some of these failure cases.

First, we propose an algorithm for robust map merging that takes two pose graphs and a set of potential loop-closures between them and selects a set of those potential loop-closures that can be used to consistently align and merge the two maps. Our proposed algorithm requires no initial estimate of alignment and can handle outlier ratios of over 90%. We take advantage of existing maximum clique algorithms for increased efficiency and show that our algorithm outperforms existing state-of-the-art methods.

Second, we propose an algorithm for localizing a query trajectory to a reference trajectory based solely on low-dimensional data describing the environment around the robotic agent at each position it visited. Our approach takes advantage of convex relaxation techniques to avoid the need for initialization and data association, making it useful in cases where high-dimensional data is unavailable. We compare our proposed method to other existing convex optimization techniques and show that it better enforces a rigid body transformation than other existing methods.

Third, we formulate the planar pose graph SLAM and landmark SLAM problems as polynomial optimization problems and prove that the globally optimal solution to both can always be found by solving a semidefinite program (SDP). Since SDPs are convex, this enables to guarantee that we can find the true maximum likelihood estimate (MLE) without any initial estimate of the trajectory.

Fourth, we propose a framework for modeling the uncertainty of jointly correlated poses using the Lie algebra of the Special Euclidean group. We then derive first order uncertainty propagation formulas for the pose composition, pose inverse, and relative pose operations when using the proposed framework. We evaluate using both simulated data and data extracted from an existing SLAM dataset and show that our method leads to more consistent uncertainty estimates than commonly used methods. Finally, we release a C++ library implementation of the proposed method.

In summary, this thesis presents four methods for multi-agent map merging, trajectory alignment, globally optimal SLAM, and pose uncertainty characterization that seek to address some of the common failure cases of existing localization and mapping methods. Furthermore, we demonstrate the performance of all of our proposed methods when compared with other methods in the field.

Bibtex entry