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.
99 lessons found
Foundations firstFoundations / 13 min read
Kinematic singularities: find the tip velocities an arm can produce
Use a two-link robot arm to distinguish exact rank loss from near-singular conditioning. Calculate the minimum-norm joint rates for a requested tip velocity and identify the component the arm cannot produce.
Foundations / 11 min read
Manipulability: read a robot’s velocity ellipse
Map a joint-rate budget into a robot’s possible tool velocities. Read the ellipse’s singular values, compare area with conditioning, and understand singular poses, units, and the limits of force duality.
Foundations / 14 min read
Numerical inverse kinematics: solve a tool position with local steps
Use a position Jacobian and damped least squares to refine a two-joint arm toward a target. Inspect accepted steps, compare starting guesses, and distinguish convergence, a stalled solve, and unreachable geometry.
Foundations / 14 min read
Differential inverse kinematics: turn a tip-velocity command into a joint step
Calculate damped joint rates for a robot tip-velocity command, measure the resulting speed and direction error, and compare an instantaneous prediction with one finite joint step.
Foundations / 12 min read
Kinematic redundancy: use the motion a task leaves free
Split a three-link arm’s joint rates into a primary solution and null-space motion. Check the exact projector, compare damping leakage, and measure why a finite step can move a tool with zero initial velocity.
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.
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.
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.
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.
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.
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.
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.