Manifold Optimization for Robotic Perception

Abstract

Robotic perception plays a crucial role in endowing a robot with human-like perception. This entails the ability to perceive and understand about the unstructured world from the sensor modalities, which would allow it to navigate autonomously through the environment to accomplish a task. Recent years have witnessed an unprecedented enthusiasm in robotic perception research as it promises a vast variety of compelling applications such as self-driving cars, drone technology, domestic robots, virtual and augmented reality. An essential task in robotic perception is state estimation. Generally, the task is concerned with inferring the state, such as the pose of an entity from observations in the form of inertial and/or visual measurements. Such an inverse problem can usually be formulated as an optimization problem, that seeks to select the best model from the imperfect sensor data. This thesis falls under the paradigm of state estimation, which aims to address the pose estimation and Simultaneous Localisation and Mapping (SLAM) problems. Solving pose estimation and SLAM problems typically involve estimating rotations. However, they naturally reside in the manifold space, i.e., the special orthogonal group SO(3), where Euclidean geometry with which we are familiar is no longer applicable. To reliably and accurately deploy state estimation algorithms for realworld applications, the underlying optimization problems must be able to properly address the inherent non-convexity of the manifold constraints, which is the main contribution of this thesis. Despite previous developments in state estimation, there remain unsatisfactorily solved problems, specifically, problems associated with outliers and large-scale input observations. This thesis is devoted to developing novel techniques to address these problems, in a manner that respects the manifold structure. The first part of the thesis is concerned with the sensor fusion problem in the context of INS/GPS fusion. While a ‘de-facto’ standard for the sensor fusion problem is the filtering technique, it is highly susceptible to outlier measurements. This thesis proposes a method to address the outlier-prone sensor fusion problem with a robust nonlinear optimization framework, underpinned by a novel pre-integration theory. An influential optimisation strategy in SLAM is rotation averaging, which aims to estimate the absolute orientation, given a set of relative orientations that are in general incompatible. It stems from the fact that if the rotations containing nonconvex constraints were solved first, then the remaining problem involving structure and translation would be easier to deal with. Inspired by Lagrangian duality, this thesis contributes a globally-optimal rotation averaging algorithm which is capable of handling large-scale input measurements much more efficiently. Finally, a specialised rotation averaging algorithm underpinned by a novel lifting technique, is proposed to resolve the fundamental ambiguity problem in markerbased SLAM. We demonstrate how to resolve the ambiguity problem by exploiting the special problem structure, which is then able to achieve a more accurate and/or complete marker-based SLAM.