A Bayesian regression approach to terrain mapping and an application to legged robot locomotion

We deal with the problem of learning probabilistic models of terrain surfaces from sparse and noisy elevation measurements. The key idea is to formalize this as a regression problem and to derive a solution based on nonstationary Gaussian processes. We describe how to achieve a sparse approximation of the model, which makes the model applicable to real-world data sets. The main benefits of our model are (1) that it does not require a discretization of space, (2) it also provides the uncertainty for its predictions and (3) it adapts its covariance function to the observed data, allowing more accurate inference of terrain elevation at points that have not been observed directly. As a second contribution, we describe how a legged robot equipped with a laser range finder can utilize the developed terrain model to plan and execute a path over rough terrain. We show how a motion planner can use the learned terrain model to plan a path to a goal location, using a terrain-specific cost model to accept or reject candidate footholds.