Log-GPIS-MOP: A Unified Representation for Mapping, Odometry, and Planning

Whereas dedicated scene representations are required for each different task in conventional robotic systems, this article demonstrates that a unified representation can be used directly for multiple key tasks. We propose the log-Gaussian process implicit surface for mapping, odometry, and planning (Log-GPIS-MOP): a probabilistic framework for surface reconstruction, localization, and navigation based on a unified representation. Our framework applies a logarithmic transformation to a Gaussian process implicit surface (GPIS) formulation to recover a global representation that accurately captures the Euclidean distance field with gradients and, at the same time, the implicit surface. By directly estimating the distance field and its gradient through Log-GPIS inference, the proposed incremental odometry technique computes the optimal alignment of an incoming frame and fuses it globally to produce a map. Concurrently, an optimization-based planner computes a safe collision-free path using the same Log-GPIS surface representation. We validate the proposed framework on simulated and real datasets in 2-D and 3-D, and benchmark against the state-of-the-art approaches. Our experiments show that Log-GPIS-MOP produces competitive results in sequential odometry, surface mapping, and obstacle avoidance.