The enhanced mobility brought by legged locomotion empowers quadrupedal robots to navigate through complex and unstructured environments. However, optimizing agile locomotion while accounting for the varying energy costs of traversing different terrains remains an open challenge. Most previous work focuses on planning trajectories with traversability cost estimation based on human-labeled environmental features. This human-centric approach is insufficient because it does not account for the varying capabilities of the robot locomotion controllers over challenging terrains. To address this, we introduce a novel real-world learning pipeline that unifies offline demonstrations, online reinforcement learning, and multi-modal perception to achieve robust legged navigation. The framework employs multiple training stages to develop a planner that guides the robot in avoiding obstacles and hardto- traverse terrains while reaching its goals. We first develop a novel traversability estimator in a robot-centric manner. The training of the navigation planner is directly performed in the real world using a sample efficient reinforcement learning method. With the proposed method, a quadrupedal robot learns to perform traversability-aware navigation through realworld interactions in diverse offroad and unstructured environments. Moreover, the robot demonstrates the ability to generalize the learned navigation skills to unseen scenarios.

Interacting with the world is a multi-sensory experience: achieving effective general-purpose interaction requires making use of all available modalities - including vision, touch, and audio - to fill in gaps from partial observation. For example, when vision is occluded reaching into a bag, a robot should rely on its senses of touch and sound. However, state-of-the-art generalist robot policies are typically trained on large datasets to predict robot actions solely from visual and proprioceptive observations. In this work, we propose FuSe, a novel approach that enables finetuning visuomotor generalist policies on heterogeneous sensor modalities for which large datasets are not readily available by leveraging natural language as a common cross-modal grounding. We combine a multimodal contrastive loss with a sensory-grounded language generation loss to encode high-level semantics. In the context of robot manipulation, we show that FuSe enables performing challenging tasks that require reasoning jointly over modalities such as vision, touch, and sound in a zero-shot setting, such as multimodal prompting, compositional cross-modal prompting, and descriptions of objects it interacts with. We show that the same recipe is applicable to widely different generalist policies, including both diffusion-based generalist policies and large vision-language-action (VLA) models. Extensive experiments in the real world show that FuSe is able to increase success rates by over 20% compared to all considered baselines.

We present an algorithm, based on the Differential Dynamic Programming framework, to handle trajectory optimization problems in which the horizon is determined online rather than fixed a priori. This algorithm exhibits exact one-step convergence for linear, quadratic, time-invariant problems and is fast enough for real-time nonlinear model-predictive control. We show derivations for the nonlinear algorithm in the discrete-time case, and apply this algorithm to a variety of nonlinear problems. Finally, we show the efficacy of the optimal-horizon model-predictive control scheme compared to a standard MPC controller, on an obstacle-avoidance problem with planar robots.