Riemannian Geometry: Robot Motion Learning and Control

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Explores data-driven approaches to improve robot design, focusing on compliance, soft materials, and complex interactions.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Presents the fundamental theorem of Riemannian geometry and demonstrates the uniqueness of the Riemannian connection.

Covers optimality conditions in optimization on manifolds, focusing on global and local minimum points.

Introduces optimization on manifolds, covering classical and modern techniques in the field.

Covers connections on manifolds, symmetric connections, Lie brackets, and compatibility with the metric in Riemannian geometry.

Delves into the rigidity of negatively curved manifolds and the interplay between curvature and symmetry.

Covers challenges and solutions for robots to work safely with humans, emphasizing adaptability and predictability.

Explains Riemannian submanifolds, metrics, and gradients computation on manifolds.

Explores the use of Center Pathet Generators for agile locomotion in medium-sized robots.