Simultaneous localization and mapping with infinite planes

Simultaneous localization and mapping with infinite planes is attractive because of the reduced complexity with respect to both sparse point-based and dense volumetric methods. We show how to include infinite planes into a least-squares formulation for mapping, using a homogeneous plane parametrization with a corresponding minimal representation for the optimization. Because it is a minimal representation, it is suitable for use with Gauss-Newton, Powell's Dog Leg and incremental solvers such as iSAM. We also introduce a relative plane formulation that improves convergence. We evaluate our proposed approach on simulated data to show its advantages over alternative solutions. We also introduce a simple mapping system and present experimental results, showing real-time mapping of select indoor environments with a hand-held RGB-D sensor.

Authors

• Michael Kaess

Keywords

• Simultaneous localization and mapping
• Quaternions
• Optimization
• Three-dimensional displays
• Convergence
• Estimation
• Infinite Plane
• Mapping System
• Real-time Mapping
• Present Experimental Results
• Minimal Representation
• RGB-D Sensor
• Least Squares Estimation
• Fisher Information
• Lie Algebra
• Unit Sphere
• Levenberg-Marquardt Algorithm
• Least Squares Problem
• Cholesky Decomposition
• Projective Space
• Local Frame
• Tangent Space
• Laser Ranging
• Global Frame
• Planar Graphs
• Factor Graph
• Unit Quaternion
• Planar Features
• Exponential Map
• Variable Nodes
• Normal Equations
• Estimation Problem
• Cost Function
• Planar System