Learning library
Make the foundations concrete.
Build working knowledge of robotics and machine learning through examples you can change, calculations you can check, and data you can inspect.
Start with the map of machine learning fields to connect tasks, data, learning signals, and model choices.
14 lessons found
Foundations firstFoundations / 10 min read
Derivatives and the chain rule: predict a small change
Understand derivatives as local rates, compare secant and tangent slopes, and multiply the correct factors through nested functions. Test a smooth curve and a corner with an interactive experiment.
Foundations / 13 min read
Partial derivatives and gradients: predict a multivariable change
Hold one input fixed to find a partial derivative, combine the partials into a gradient, and compare a directional derivative with the actual change from a finite step.
Foundations / 13 min read
Jacobian matrices: from joint rates to robot tip velocity
Read a Jacobian by its rows and columns, calculate a two-link arm's tip velocity, and compare a local prediction with a finite move. Includes singularities and the multivariate chain rule.
Foundations / 11 min read
Hessians: measure curvature in every direction
Differentiate a gradient to build the Hessian, calculate directional curvature, and classify stationary points. Explore coupled quadratics, saddles, and the limits of zero eigenvalues.
Foundations / 13 min read
Taylor expansion and linearization: predict locally and check the error
Build constant, linear, and quadratic approximations around a chosen center. Compare their errors, calculate a Taylor remainder bound, and connect the same idea to gradients, Hessians, and Jacobians.
Foundations / 12 min read
Ordinary differential equations: turn a rate law into a time course
Solve a cooling initial-value problem, compare its exact solution with Euler steps, and separate model behavior from numerical accuracy and stability.
Foundations / 12 min read
Numerical integration: compare drift, phase, and step cost
Advance an oscillator with forward Euler, velocity-first symplectic Euler, and classical RK4. Compare each method with the analytic solution and separate energy drift, phase error, step cost, and stability.
Foundations / 12 min read
ODE stability: equilibria, attraction, and basins
Classify equilibria of a nonlinear rate law, use a phase line to find basins of attraction, and compare exact trajectories without confusing model stability with numerical stability.
Foundations / 12 min read
Manifolds and tangent spaces: move along a constraint
Use the unit circle to understand local coordinates and tangent vectors. Compare straight steps, exact rotation, and normalization, then examine why averaging headings and rotations needs care.
Foundations / 13 min read
Geodesics: shortest arcs and longer routes on a circle
Compare a shortest circle arc, a longer constant-speed geodesic, and a straight chord. Work through angle wrapping, antipodal ties, coincident endpoints, and the metric that defines distance.
Foundations / 12 min read
Lie groups and Lie algebras: connect robot poses to local motions
Use planar robot poses to understand SE(2), its tangent space se(2), and the Lie bracket. Compare motion order, shrink a commutator loop, and reproduce the calculations in Python.
Foundations / 13 min read
Exponential and logarithm maps: turn a body twist into a pose
Exponentiate a constant planar body twist, calculate its coupled translation, and recover a chosen logarithm. Explore straight-motion limits, half-turn branch choices, and information lost in a full turn.