ROS 2 tf2: transform a laser point at the right time
Connect an odometry message to a transform tree, convert a timestamped laser point, and reproduce missing-frame and extrapolation errors in ROS 2 Jazzy.
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ROS 2 QoS: fix a topic that delivers no messages
Reproduce a ROS 2 reliability mismatch, inspect the publisher and subscriber profiles, and restore delivery. Run the checked Jazzy example in one isolated container.
SLAM Toolbox in ROS 2: build a map from laser scans
Run SLAM Toolbox on supplied laser scans and odometry. Reproduce a missing-transform failure, repair the frame tree, and inspect the map produced by the real ROS node.
State-space models: connect states, inputs, and outputs
Build a cart state-space model from Newton’s law. Read A, B, C, and D, separate initial motion from force response, and choose position, velocity, or acceleration as the output.
World models for robotics: learn dynamics, then plan
Fit a small action-conditioned world model, use it to choose a plan, and check what actually happens. See how perfect training predictions can hide a poor decision.
Behavior cloning: learn robot actions from demonstrations
Learn behavior cloning with an interactive robot example and downloadable Python exercise. Split episodes, fit a policy, and compare action error with rollouts.
Covariance and uncertainty ellipses: read the shape of error
Read a covariance matrix as a geometric description of spread. Rotate an uncertainty ellipse, compare a Gaussian model with a finite sample, and calculate what a 95% contour means.
Diffusion Policy: generate robot actions by denoising
See how Diffusion Policy represents several possible actions, learns to remove noise, and executes action chunks. Follow an exact teaching denoiser and separate sampling steps from robot time.
Extended Kalman filter: localize a robot with range and bearing
Predict a robot's nonlinear motion, linearize with Jacobians, and correct its pose from a known landmark. Inspect angle wrapping, covariance, and a poor initial heading that challenges the local approximation.
ICP algorithm explained: align two scans step by step
Learn how ICP aligns two point sets. Step through the lab, download the same data and Python solver, and compare a correct fit with misleading residuals.
ICP failure cases: when a smaller residual gives the wrong pose
Diagnose ICP failure cases with repeated geometry, partial overlap, and unmatched points. Compare the fitting residual with a known pose error, change the starting estimate, and see which evidence each metric uses.
Kalman filter: predict position, then correct with measurements
Work through a scalar Kalman update, then estimate position and velocity from noisy readings. Explore missing measurements, covariance, and a biased sensor that defeats the filter’s assumptions.