Whereas dedicated scene representations are required for each different task in conventional robotic systems, this paper 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, localisation 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 optimisation-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 2D and 3D 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.

翻译：尽管传统机器人系统中不同任务需要专门的场景表征，但本文证明，一种统一的表征可直接用于多个关键任务。我们提出Log-高斯过程隐式表面用于地图构建、里程计与路径规划（Log-GPIS-MOP）：一种基于统一表征的表面重建、定位与导航概率框架。该框架对高斯过程隐式表面（GPIS）公式应用对数变换，以恢复能够同时准确捕获具有梯度的欧几里得距离场以及隐式表面的全局表征。通过Log-GPIS推理直接估计距离场及其梯度，所提出的增量式里程计技术能够计算输入帧的最优对齐，并将其全局融合以生成地图。与此同时，基于优化的路径规划器利用相同的Log-GPIS表面表征计算安全无碰撞路径。我们在二维和三维的仿真与真实数据集上验证了所提框架，并与现有最先进方法进行了基准测试。实验表明，Log-GPIS-MOP在序列里程计、表面地图构建与障碍物规避任务中均取得了竞争性结果。