Lectures related to Riemannian Geometry: Robot Motion Learning and Control

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Explores training robots through reinforcement learning and learning from demonstration, highlighting challenges in human-robot interaction and data collection.

Algebraic Topology and Differential Geometry

Explores algebraic topology and differential geometry in understanding robot dynamics and global behavior.

Riemannian Trust Regions framework

Introduces the Riemannian Trust Regions (RTR) framework, covering conjugate directions, Newton's method, and model improvement.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Robot Learning and Control

Covers learning and adaptive control for robots, focusing on real-time reactivity and path planning using dynamical systems.

Compliant Control for Robots: Impedance and Variable Stiffness

Explores compliant control for robots through impedance and variable stiffness, enabling safe and adaptive interactions with the environment.

Riemannian connections: What they are and why we care

Covers Riemannian connections, emphasizing their properties and significance in geometry.

Symmetry Property: Riemannian Connection in Geometry

Explores symmetries, Riemannian connection, vector fields, and Lie bracket in geometry.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Improving Robot Design: Data-Driven Approaches

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

Differential Forms Integration

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

Riemannian connections: Proof sketch

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

Optimality Conditions: First Order

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

Optimization on Manifolds: Context and Applications

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

Riemannian Hessians: Connections and Symmetry

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

Rigidity in Negative Curvature

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

Robots: Safe Collaboration

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

Riemannian metrics and gradients: Riemannian gradients

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

Center Pathet Generators for Agile Locomotion

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