Simultaneous Localisation and Mapping with Quadric Surfaces

There are many possibilities for how to represent the map in simultaneous localisation and mapping (SLAM). While sparse, keypoint-based SLAM systems have achieved impressive levels of accuracy and robustness, their maps may not be suitable for many robotic tasks. Dense SLAM systems are capable of producing dense reconstructions, but can be computationally expensive and, like sparse systems, lack higher-level information about the structure of a scene. Human-made environments contain a lot of structure, and we seek to take advantage of this by enabling the use of quadric surfaces as features in SLAM systems. We introduce a minimal representation for quadric surfaces and show how this can be included in a least-squares formulation. We also show how our representation can be easily extended to include additional constraints on quadrics such as those found in quadrics of revolution. Finally, we introduce a proof-of-concept SLAM system using our representation, and provide some experimental results using an RGB-D dataset.