Abstract-Legged robots require accurate models of their environment in order to plan and execute paths. We present a probabilistic technique based on Gaussian processes that allows terrain models to be learned and updated efficiently using sparse approximation techniques. The major benefit of our terrain model is its ability to predict elevations at unseen locations more reliably than alternative approaches, while it also yields estimates of the uncertainty in the prediction. In particular, our nonstationary Gaussian process model adapts its covariance to the situation at hand, allowing more accurate inference of terrain height at points that have not been observed directly. We show how a conventional 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. In experiments with a real quadruped robot equipped with a laser range finder, we demonstrate the usefulness of our approach and discuss its benefits compared to simpler terrain models such as elevations grids.

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 that (1) 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. To the best of our knowledge, this was the first legged robotics system to autonomously sense, plan, and traverse a terrain surface of the given complexity. C 2009 Wiley Periodicals, Inc.