P01Active
Drone Ranger
Perception and mapping on a drone platform — from sensor selection and frame setup to flight-log replay.
A personal field guide to seeing the world
Start from geometry,
learn how machines
see the world.
Connecting mathematical intuition, robot coordinate frames, 3D perception and world models into one continuous thread — notes on how I move from first principles to real sensors and embodied systems.
- Tracks
- 5
- Notes
- 18
- Thread
- Geometry → Perception → Action
Knowledge Map
Knowledge Map
From mathematical foundations to how robots perceive and act. Each stop stands alone, and links to the others.
- 01 / Foundations
Geometry & Math
Linear algebra and vector calculus through geometric intuition, plus the statistical and information-theoretic tools for measuring relationships.
- Vectors & matrices
- Change of coordinates
- Gradient / divergence / curl
- Where quaternions came from
- From inner products to attention
- 02 / Transforms
Robot Transforms
Getting every sensor and every joint to speak the same coordinate language.
- SO(3) / SE(3)
- Frame conventions
- ROS 2 TF
- Camera–LiDAR calibration
- 03 / Perception
3D Perception
From pixels and point clouds to spatial representations a machine can reason about.
- RGB-D / LiDAR
- SLAM
- 3D reconstruction
- Occupancy / 3DGS
- 04 / World Models
World Models
From knowing what the world looks like to predicting how it will change.
- Spatial understanding
- Prediction & planning
- Physical AI
- Embodied intelligence
- 05 / Projects
Projects & Practice
Putting concepts back into real sensors, real data and failed experiments.
- Drone Ranger
- Data collection
- Mapping
- Simulation & lab logs
How each note is built
Every note follows the same path
- 01QuestionThe one question this note answers
- 02IntuitionA picture before any formula
- 03FormalismThe precise math or geometry
- 04RoboticsWhere it shows up in a robot
- 05ExperimentVisuals, code or video
- 06ReferencesOriginal papers and further reading
Recent Thinking
Recent Thinking
Long-form essays and concept breakdowns
- 3D PerceptionImaging Model: Camera Geometry and CalibrationPlaceholder, to be written.
- Geometry & MathInner products, covariance and correlationStarting from the inner product, centering gives covariance and normalizing gives correlation; the correlation coefficient is the cosine of the angle between the centered vectors. This chapter derives the chain in full and shows where these quantities appear in state estimation and point-cloud processing.
- Geometry & MathThe Jacobian and the gradient: the derivative as a local linear mapExtend the one-variable derivative to several variables and it turns from a number into a matrix, the Jacobian; the transpose of a scalar field's Jacobian is the gradient. This chapter derives why the gradient points uphill fastest and is normal to level sets, and works out the Jacobians of camera projection and pose optimization.
- Geometry & MathCross-correlation and convolution: the sliding inner productAdding a shift to the inner product gives cross-correlation; flipping the kernel gives convolution. This chapter derives how the two relate, why linear time-invariant systems are exactly convolutions, and why normalized cross-correlation is the correlation coefficient over a window, with uses in template matching and stereo.
- Geometry & MathDivergence and curl: what they extract from the JacobianThe Jacobian fully describes what a vector field does near a point, and divergence and curl extract two parts of it. Divergence is the trace and reads off the local change of volume; curl comes from the antisymmetric part and equals twice the local angular velocity. This chapter derives both, their integral forms and the two zero identities, and uses optical-flow divergence to estimate time to contact.
Projects & Practice
Projects & Practice
Putting concepts back into real sensors, real data — and failed experiments.
P02Planned
Sensor Rig
Joint RGB-D and LiDAR capture, time synchronization and an extrinsic calibration workflow.
P03Planned
Sim Lab
Reproducing mapping and planning experiments in simulation, logging every failure and fix.
Videos
See the figures, the experiments — and the derivations
Short explainers and project demos live on YouTube, embedded next to the formulas, code and references of each note.
Math intuition
Quaternions: from complex numbers to 3D rotation
An animation of why q v q⁻¹ rotates a vector.
Robotics
ROS 2 TF: giving every sensor an address
Building and debugging a transform tree on real hardware.