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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
⇝Zoom Link for Tutorials

This course covers fundamentals of physics-based modelling and numerical optimization from the perspective of character animation and robotics applications. The methods discussed in class derive their theoretical underpinnings from applied mathematics, control theory and computational mechanics, and they will be richly illustrated using examples ranging from locomotion controllers and crowd simulation to robotic manipulation of elastically-deforming objects.

Times

Day What Time Location
Wednesdays Class 14:15 - 16:00 HG E 1.2
Thursdays Tutorial 16:15 - 18:00 ML F 40

Content

Introduction

23/02/2025
Slides

Kinematic Modeling

02/03/2025
Slides

Unconstrained optimization and Inverse Kinematics

09/03/2025
Slides
NumericalOptimizationReview
IKNotes

Dynamics

16/03/2025
Slides

Computational Elasticity

23/03/2025
Slides

Constrained Optimization and Sensitivity Analysis

30/03/2025
Slides

3D Orientations and Rigid Body Dynamics

06/04/2025
Slides
ImpulseBasedCollisions

Articulated Rigid Body Dynamics

13/04/2025
Slides
MaximalCoordinatesFormulations

Contact Modeling

27/04/2025
Slides

Trajectory Optimization

04/05/2025
Slides

Feedback Control

11/05/2025
Slides

Deep Reinforcement Learning

18/05/2025
Recording
Slides

Q&A

25/05/2025
Recording
Questions you should have answers to

Assignments

The accompanying programming assignments are meant to deepen the concepts covered in class. For each programming sheet, we will provide a C++ code framework with basic functionality already in place. This allows you to get straight to the point and implement only the technically interesting and relevant parts.

Getting ready ...

Hand out: 03/03/22
Hand in: 11/03/22, 18:00 CEST
An (ungraded) assignment that sets up the code base and makes sure everything compiles and runs on your machine. Also, you will get familiar with how to submit assignments.
github classroom invitation
github issues
Tutorial slides
Tutorial recording

Unconstrained optimization and IK

Hand out: 10/03/22
Hand in: 18/03/22, 18:00 CEST
Formulate inverse kinematics as an unconstrained optimization problem and solve it with gradient-based minimization strategies.
github classroom invitation
github issues
Tutorial slides
Tutorial recording

Kinematic walking controller

Hand out: 17/03/22
Hand in: 01/04/22, 18:00 CEST

github classroom invitation
github issues
Tutorial slides
Tutorial recording

Boids

Hand out: 31/03/22
Hand in: 15/04/22, 18:00 CEST

github classroom invitation
github issues
Assignment Writeup
Tutorial Recording

Soft body simulation and control

Hand out: 14/04/22
Hand in: 29/04/22, 18:00 CEST

github classroom invitation
github issues
Assignment Writeup
Tutorial Slides
Tutorial Recording

Rigid body dynamics

Hand out: 28/04/22
Hand in: 13/05/22, 18:00 CEST
github classroom invitation
github issues
Tutorial Slides
Tutorial Recording
Tutorial Slides 05/05
Tutorial Recording 05/05

Trajectory Optimization

Hand out: 12/05/22
Hand in: 27/05/22, 18:00 CEST

Github Classroom Repo
Issues
Assignment Writeup
Recording
Slides
Related Paper (Video)
Additional Trajectory Optimization Reading


Evaluation

The evaluation is based on the exam (50%) and assignments (50%).
Exam: The exam will take place at 14:15, CEST, June 1st.
Assignments: Assignments need to be handed in no later than the deadline and will be graded.