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Understand how a robot works.

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15 lessons found

Foundations first

  1. Foundations / 13 min read

    Trajectory time scaling: choose when a robot follows its path

    Separate a robot’s geometric path from its timing. Compare cubic and quintic profiles, derive joint speed and acceleration through the chain rule, and choose a duration that meets explicit limits.

  2. Foundations / 12 min read

    Trapezoidal velocity profiles: accelerate, cruise, and stop

    Build a rest-to-rest motion for one linear joint. Derive triangular and trapezoidal velocity profiles, calculate braking distance, and inspect exact position, velocity and acceleration within explicit limits.

  3. Foundations / 9 min read

    Lyapunov stability: prove convergence with a function

    Build a Lyapunov function, check its derivative, and prove convergence. See why a failed candidate can coexist with a stable system.