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Understand how a robot works.

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45 lessons found

Foundations first

  1. Foundations / 12 min read

    Joint limits in inverse kinematics: solve a bounded velocity step

    Turn physical joint ranges and speed limits into bounds on a local inverse-kinematics command. Compare a constrained least-squares solution with clipping, and check the resulting finite arm position.

  2. Foundations / 13 min read

    Analytical inverse kinematics: find both arm configurations for a target

    Derive both joint-angle solutions for a two-link robot arm, check them with forward kinematics, and identify unreachable targets and merged boundary branches.

  3. Foundations / 11 min read

    Robot workspaces: derive the reachable position set

    Derive the exact position workspace of a two-link robot with elbow limits. Test targets against its annulus, recover a valid arm configuration, and separate position reach from orientation and path feasibility.

  4. Foundations / 13 min read

    Configuration space: follow joint paths across angle boundaries

    Represent a robot arm as a point in joint space, follow paths across periodic angle boundaries, and distinguish angular distance from workspace motion and collision clearance.

  5. Foundations / 11 min read

    Collision checking: test the motion between endpoints

    Check a translating disk against a circular obstacle, including every point between its endpoints. Derive the closest-point test, expose missed samples, and distinguish broad-phase box overlap from a collision.

  6. Foundations / 13 min read

    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.

  7. 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.

  8. 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.

  9. Foundations / 10 min read

    Multivariable control: manage coupling between outputs

    Move one output without disturbing another. Compare independent feedback with matrix decoupling, then test model mismatch and large actuator commands.