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Computational Models of Motion

A hands-on approach to understanding the mathematical models used in animation and robotics.

About this Course

⇝Moodle

This course will introduce mathematical foundations and computational tools that are required to generate motions for digital humans, virtual creatures and robots. The methods discussed in class derive their theoretical underpinnings from applied mathematics, control theory, and machine learning, and they will be richly illustrated using examples and hands-on exercises ranging from locomotion controllers to physics-based animation for physical robots and digital avatars.

Content

Introduction, Kinematic Modeling

Unconstrained Optimization and Inverse Kinematics

Data-driven Models of Motion

Constrained Optimization and Sensitivity Analysis

Data-driven Models of Motion

Constrained Optimization and Sensitivity Analysis

Trajectory Optimization

Feedback Control and Locomotion

Foundations of Deep RL (part 1)

Foundations of Deep RL (part 2)

Learning Methods for Motion Synthesis (part 1)

Learning Methods for Motion Synthesis (part 2)

Invited Lecture

Assignments

Warm up

• Git & GitHub classroom
• Cmake & C++ environment

Kinematic waking controller

• Inverse Kinematics
• Base trajectory planning
• Quadruped in sim
• Hexpod in sim & real hardware

Trajectory optimization for quadruped robots

• Kinematic to dynamically feasible trajectory
• Agile motion generation through keyframes
• Evaluation in physics-based simulation

Deep RL for humanoid motion imitation

• Reward design and motion imitation
• Train RL agents in a physics simulator
• Modulate inputs to generate new motions

Evaluation

Assignments (50%):

● Starter code provided (C++ or Python)
● Opportunity to go beyond and have fun
● Late policy: -20% if up to one day late
● Assignment grades provided most likely within a week of submission
● Students have one week after receiving their grades to ask for corrections

End of semester evaluation (50%):

● Written test during the last lecture of the semester
● Multiple-choice / short answer questions
● Designed to test your understanding of concepts covered in lecture