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.

Search lesson titles, concepts, and the explanations themselves.

Explore topics

Choose any topics, then search. Results can match any selected topic.

99 lessons to explore

Foundations first

  1. Foundations / 14 min read

    Open-loop and closed-loop control: compare plans with position feedback

    Explore open-loop and closed-loop control by moving an axis along a planned path. Calculate how gain errors, drift, initial position, and sensor bias change tracking, then connect or disconnect the feedback path.

  2. Foundations / 14 min read

    Transfer functions: predict joint speed from torque

    Derive a robot joint transfer function with the Laplace transform. Separate zero-state and natural responses, calculate a pole and time constant, and compare torque steps with pulses.

  3. Foundations / 15 min read

    Block diagrams: trace signals and derive the feedback loop

    Read control block diagrams by naming signals and checking each junction. Combine series and parallel paths, derive feedback transfer functions, and compare reference, disturbance, and sensor-error responses.

  4. Foundations / 13 min read

    Poles and zeros: connect root locations to a step response

    Explore poles and zeros by changing one numerator zero in a stable second-order system. Calculate inverse response, compare real and complex poles, and distinguish canceled factors from hidden internal modes.

  5. Foundations / 12 min read

    Stability criteria: find the feedback gain limit

    Connect the Routh-Hurwitz criterion, Nyquist stability test, and gain and phase margins. Find when a three-lag feedback system settles, sustains oscillation, or becomes unstable.

  6. Foundations / 12 min read

    Step response characteristics: measure rise, overshoot, and settling

    Read step response characteristics from an exact second-order model. Compare rise time, overshoot, settling time, and steady error without mistaking the end of a plot for the final value.

  7. Foundations / 13 min read

    PID control: build a command from error and measured motion

    Build a PID controller from proportional, integral, and derivative terms. Compare tracking and load rejection, calculate each command contribution, and check the stability limit of integral gain.

  8. Foundations / 13 min read

    PID tuning: calculate gains, then test the response

    Tune a PID controller against explicit response and effort targets. Convert Ziegler–Nichols settings into parallel gains, understand relay auto-tuning, and compare manual adjustments.

  9. Foundations / 11 min read

    Integral windup: what happens when the actuator runs out of effort

    Explore integral windup in a sampled PI controller. Compare requested effort, actuator limits, and integral memory as an impossible reference returns to a feasible value.

  10. Foundations / 11 min read

    Derivative kick and filtering: choose what D responds to

    Explain derivative kick and filtering with a target step and measured noise. Compare derivative on error with derivative on measurement, calculate filtered command peaks, and weigh noise gain against lag.

  11. Foundations / 12 min read

    Feedforward control: predict torque, then correct error

    Calculate model-based torque from a smooth speed reference, then add feedback correction. Compare feedforward, proportional feedback, and their combination under inertia error, drag error, and unknown external torque.

  12. Foundations / 12 min read

    Cascade control: let position request velocity and velocity request torque

    Build cascade control from nested position and velocity loops. Follow command units, compare finite inner dynamics with ideal velocity tracking, and calculate the effect of an opposing load.