Aims

The aims of the course are to:

• To introduce students to simulation and control of partially observed dynamical systems.
• To give practical experience with classical methods for state estimation.
• To explore optimal feedback control in a closed-loop system.
• To develop collaborative coding, analysis, and presentation skills.
• To foster understanding of robustness in estimation and control under noise and model mismatch.

Objectives

As specific objectives, by the end of the course students should be able to:

• Understand and apply state-space models to simulate dynamic systems.
• Implement and tune models to decode noisy observations.
• Design and use controllers for optimal state feedback control.
• Integrate estimation and control in a closed-loop system.
• Conduct experiments to assess tracking accuracy, control effort, and robustness.
• Collaborate effectively to develop shared code and produce a joint presentation.
• Present technical results clearly using plots, metrics, and structured reports.

Content

This lab explores how brain-machine interface (BMI)-like systems can decode noisy neural activity to control movement. In this design project, small groups will simulate and control a simplified neural interface system. A 2D cursor moves in a plane based on a latent trajectory, observed indirectly through noisy neural-like signals. Students will estimate the cursor's hidden state and control its movement toward a dynamic target. Over four weeks, they will explore estimation accuracy, control performance, and system robustness to disturbances and model mismatch. The project blends inference, control, signal processing, and neural data simulation in a realistic, design-oriented lab. 

Week 1–2 (Group) 

Introduction to classical filtering and control methods (primer provided). 

Groups set up simulation environment and run example trajectories. 

Implement group simulation code with documentation. 

Deliverable: Group simulation code + brief documentation (group mark); interim report (individual mark). 

Week 3 (Individual) 

Implement control loops. 

Test closed-loop performance and robustness. 

Continue experiments for final analysis. 

Week 4 (Group & Individual) 

Group presentation: approach, results, lessons learned (group mark). 

Individual final report due end of Week 4: methods, results, discussion (individual mark). 

Objectives

As specific objectives, by the end of the course students should be able to:

• understand the principles of Structure from Motion, one of the most important algorithms in computer vision, through hands-on experimentation and implementation
• explain the role of feature detection, feature matching, and camera pose estimation in an SfM pipeline
• use a professional SfM tool such as COLMAP to reconstruct sparse 3D structure and camera poses from a set of images
• design and analyse image-capture strategies for successful 3D reconstruction
• implement key components of a simplified SfM pipeline in Python

Content

The aim of this project is to understand Structure from Motion through a combination of professional tools, mathematical foundations, and hands-on implementation. Structure from Motion is the process of recovering both the 3D structure of a scene and camera paraemeters from multiple overlapping images.

The project will begin by treating COLMAP as a professional reference system. Students will run COLMAP on both standard datasets and their own captured image sets, producing sparse reconstructions and visualising the estimated camera poses and 3D point clouds. They will perform controlled capture experiments to understand when SfM succeeds or fails, for example by varying the number of images, image overlap, texture, lighting, and camera motion. They will also inspect intermediate outputs such as detected keypoints and matched image pairs.

Students will then implement and analyse key steps of a simplified SfM pipeline in Python that includes feature detection, descriptor matching, and relative pose recovery. Modular utilities will be provided so that the focus remains on understanding and experimentation, rather than low-level software infrastructure.

The project culminates in a short group presentation and an individual final report, showcasing the reconstruction pipeline, visual results, quantitative and qualitative analysis, and lessons learned about the strengths and limitations of Structure from Motion.

Week 1:

• setting up the Python/COLMAP environment and running COLMAP sparse reconstruction
• visualising sparse point clouds and estimated camera poses
• creating controlled ablations, such as fewer images, lower overlap, poor texture, or challenging lighting
• reading introductory material on multiview geometry and SfM

Week 2:

• extracting descriptors
• matching descriptors between image pairs
• estimating the fundamental matrix

Week 3:

• recovering relative camera rotation and translation
• triangulating sparse 3D points
• visualising reconstructed sparse points and camera poses

Week 4:

• analysing failure cases 
• preparing and delivering final presentation and report.