This talk explores how partial differential equation (PDE)–based physics priors can provide a foundation for scalable and generalizable algorithms in robot motion learning. Rather than searching over discrete graphs or samples, it formulates and learns the solution to the motion-planning problem as a continuous value function governed by Hamilton–Jacobi (HJ) PDEs. These methods enable self-supervised value-function learning without reliance on expert trajectories or trial-and-error interaction. The learned value functions yield fast inference of motion plans and demonstrate strong scalability across complex, high-dimensional, and constraint-rich navigation and manipulation tasks. The talk also introduces an HJ PDE–derived mapping representation that unifies perception and planning: unlike occupancy grids or signed distance fields, it encodes motion-feasible geometry in a form naturally structured for continuous decision-making. Together, these developments outline a unified, numerically grounded framework for robot motion planning and control through the lens of physics-informed learning.

Robots show great promise if they can get out of the lab into the field and go beyond a single-operator per robot paradigm. However, the unstructured nature of the real-world requires nuanced decision making of the robot. In this talk I will outline some of our approaches, progress, and results on multi-modal sensing, providing nuanced perception inputs, as well as navigation in difficult terrain, and future directions of our research.

Deploying mobile robots in unstructured outdoor environments remains a fundamental challenge, requiring the ability to robustly perceive complex terrains, pedestrian flows, and general traffic rules. To effectively serve humans, especially older adults, these robots must go beyond simple navigation to also understand human behavior and enhance personal mobility. In this talk, I will review our previous approaches for long-range outdoor navigation, with a focus on scene understanding and planning. Then, I will present a high-level overview of what we are currently working on, where I aim to apply these navigation technologies to develop companion robots that support older adults.

Humanoid robots are entering human-centric environments, where they must not only move well but also understand people and interact safely through physical contact. In this talk, I will present two complementary directions toward human-centered embodied intelligence. First, I will introduce GentleHumanoid, a whole-body control policy that combines motion tracking with compliant, tunable force regulation, enabling contact-rich behaviors such as gentle hugging, assistive support, and safe object interaction on the Unitree G1. Second, I will show how large language models can be grounded in 3D human motion for behavior understanding and planning, highlighting ChatPose and ChatHuman as steps toward systems that interpret actions, anticipate intent, and connect high-level reasoning to executable motion. I will close with future directions on scaling human–humanoid interaction data, developing vision-language-action models for long-horizon interaction, and incorporating muscle-driven modeling for more realistic and adaptive humanoids. 

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