Uncertainty-aware robot motion prediction is crucial for downstream traversability estimation and safe autonomous navigation in unstructured, off-road environments, where terrain is heterogeneous and perceptual uncertainty is high. Most existing methods assume deterministic or spatially independent terrain uncertainties, ignoring the inherent local correlations of 3D spatial data and often producing unreliable predictions. In this work, we introduce an efficient probabilistic framework that explicitly models spatially correlated aleatoric uncertainty over terrain parameters as a probabilistic world model and propagates this uncertainty through a differentiable physics engine for probabilistic trajectory forecasting. By leveraging structured convolutional operators, our approach provides high-resolution multivariate predictions at manageable computational cost. Experimental evaluation on a publicly available dataset shows significantly improved uncertainty estimation and trajectory prediction accuracy over aleatoric uncertainty estimation baselines.

Rovers require knowledge of terrain to plan trajectories that maximize safety and efficiency. Terrain type classification relies on input from human operators or machine learning-based image classification algorithms. However, high level terrain classification is typically not sufficient to prevent incidents such as rovers becoming unexpectedly stuck in a sand trap; in these situations, online rover-terrain interaction data can be leveraged to accurately predict future dynamics and prevent further damage to the rover. This paper presents a meta-learning-based approach to adapt probabilistic predictions of rover dynamics by augmenting a nominal model affine in parameters with a Bayesian regression algorithm (P-ALPaCA). A regularization scheme is introduced to encourage orthogonality of nominal and learned features, leading to interpretable probabilistic estimates of terrain parameters in varying terrain conditions.

(Simplified Abstract) To accomplish breakthroughs in dynamic whole-body locomotion, legged robots have to be terrain aware. Terrain-Aware Locomotion (TAL) implies that the robot can perceive the terrain with its sensors, and can take decisions based on this information. This thesis presents TAL strategies both from a proprioceptive and an exteroceptive perspective. The strategies are implemented at the level of locomotion planning, control, and state estimation, and using optimization and learning techniques. The first part is on TAL strategies at the Whole-Body Control (WBC) level. We introduce a passive WBC (pWBC) framework that allows the robot to stabilize and walk over challenging terrain while taking into account the terrain geometry (inclination) and friction properties. The pWBC relies on rigid contact assumptions which makes it suitable only for stiff terrain. As a consequence, we introduce Soft Terrain Adaptation aNd Compliance Estimation (STANCE) which is a soft terrain adaptation algorithm that generalizes beyond rigid terrain. The second part of the thesis focuses on vision-based TAL strategies. We present Vision-Based Terrain-Aware Locomotion (ViTAL) which is an online planning strategy that selects the footholds based on the robot capabilities, and the robot pose that maximizes the chances of the robot succeeding in reaching these footholds. ViTAL relies on a set of robot skills that characterizes the capabilities of the robot and its legs. The skills include the robot's ability to assess the terrain's geometry, avoid leg collisions, and avoid reaching kinematic limits. Our strategies are based on optimization and learning methods and are validated on HyQ and HyQReal in simulation and experiment. We show that with the help of these strategies, we can push dynamic legged robots one step closer to being fully autonomous and terrain aware.