Learning library
Probability
Sensors are noisy and outcomes are uncertain. These lessons cover conditional probability, Bayesian updating, common distributions, and Markov chains, each grounded in a robot that has to act on incomplete information.
10 lessons, in library order. Search within probability.
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Combine uncertain measurements
Use evidence to update a belief, describe uncertainty in more than one coordinate, and combine a prediction with a sensor reading.
- Conditional probability: reading a robot sensor
Calculate what a sensor detection means under a stated base rate.
- Bayesian inference: learning a robot's grasp success rate
Separate the prior, likelihood, and posterior in an evidence update.
- Covariance and uncertainty ellipses: read the shape of error
Read variance, correlation, and the geometry of a Gaussian uncertainty region.
- Kalman filter: predict position, then correct with measurements
Combine a motion prediction and measurement while checking the noise assumptions.
Foundations / 8 min read
Conditional probability: reading a robot sensor
Learn conditional probability with an interactive robot sensor example. Work through the formula, Bayes' rule, base rates, and common mistakes using counts.
Foundations / 9 min read
Bayesian inference: learning a robot's grasp success rate
Learn Bayesian inference through a robot grasp example. Update a Beta prior with successes and failures, then distinguish uncertainty from prediction.
Foundations / 10 min read
Logistic regression: turn a score into a probability
Explore logistic regression with synthetic robot observations. Calculate sigmoid probabilities and log loss, then change a threshold and inspect the confusion matrix.
Foundations / 9 min read
Markov chains: transitions and stationary distributions
Learn Markov chains with a robot example. Explore transition matrices, stationary distributions, periodic chains, and absorbing states with an interactive model.
Foundations / 9 min read
Laplace distribution: model sensor error and tolerance
Learn the Laplace distribution through sensor error. Explore location, scale, density, interval probabilities, and the link between absolute error and median fitting.
Foundations / 13 min read
SLAM in robotics: estimate a robot’s path and its map
Understand SLAM in robotics by solving a small landmark problem. Compare localization, mapping, and joint estimation, then see how anchoring and measurement weights change the answer.
Foundations / 10 min read
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.
Foundations / 12 min read
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.
Foundations / 11 min read
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.
Foundations / 12 min read
LQG control: connect a Kalman estimate to LQR feedback
Control a cart from noisy position readings. Connect Kalman filtering to LQR, compare matched disturbances, and test what changes when the model is wrong.