Research at NVIDIA: RMPflow - A Computational Graph for Automatic Motion Policy Generation

In this work, researchers from NVIDIA, Georgia Institute of Technology, and the University of Washington, developed a new motion generation and control framework that enables globally stable controller design within intrinsically non-Euclidean spaces.

Non-Euclidean geometries are not often modeled explicitly in robotics, but are nonetheless common in the natural world. One important example is the apparent non-Euclidean behavior of obstacle avoidance. Obstacles become holes in this setting. As a result, straight lines are no longer a reasonable definition of shortest distance—geodesics must, therefore, naturally flow around them. This behavior implies a form of non-Euclidean geometry: the space is naturally curved by the presence of obstacles.