Robot dynamics: separate the torques that move an arm
Explore robot dynamics through a two-link arm's torque budget. Separate inertia, velocity coupling, gravity, and friction, then check holding torque, link mass, and mechanical power.
Writing
Clear accounts of what was tried and learned.
Explanations, tutorials, build notes, and essays grounded in work that can be examined. Explore a concept, try an experiment, and follow the reasoning behind it.
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Ackermann steering: calculate wheel angles and turning radius
Derive the inner and outer front-wheel angles for ideal Ackermann steering. Connect bicycle steering, wheelbase, and track width to turning radius, reverse motion, and the rear axle's path.
Differential-drive kinematics: from wheel rates to pose
Convert left and right wheel rates into robot speed, turning rate, and an exact constant-rate pose update. Explore straight travel, arcs, spins, and reverse motion, then check the limits of wheel odometry.
Dubins paths: shortest routes with a turning limit
Connect two robot poses with forward motion and a minimum turning radius. Compare all six Dubins path families, calculate arc lengths, and see why matching position alone misses the heading constraint.
Instantaneous center of rotation: find the center from a planar velocity
Calculate a planar rigid body's instantaneous center of rotation from its linear and angular velocity. Check point velocities, move the reporting reference, and distinguish turning, translation, and rest.
Nonholonomic constraints: move sideways without sliding
Derive a wheeled robot’s no-sideways-slip constraint and trace a feasible maneuver that changes its lateral position. Separate instantaneous velocity limits from reachable poses, and see why the motion rules depend on the robot.
Omnidirectional drives: move sideways with three omniwheels
Derive the wheel speeds for a three-wheel Kiwi drive. Command forward, sideways, and turning motion, preserve direction when motors saturate, and integrate the resulting world path.
Path smoothing: shorten a route with checked shortcuts
Shorten a robot path by removing unnecessary waypoints while checking every replacement segment for collision. Compare length and clearance, trace accepted and rejected shortcuts, and separate a simpler path from smooth robot motion.
Probabilistic roadmaps: reuse a graph for new routes
Build a probabilistic roadmap from collision-free samples, attach new start and goal queries, and search the same graph for routes. Explore neighbor counts, missed connections, and what a finite roadmap can prove.
Reeds–Shepp paths: shortest car routes with reverse gear
Add reverse travel to a car with a minimum turning radius. Read signed motion primitives, calculate a three-arc turnaround, and compare complete Reeds–Shepp solutions with forward-only Dubins paths.
RRT*: improve a path by rewiring the tree
Follow RRT* as it chooses cheaper parents, rewires nearby nodes, and updates every descendant's cost. Compare the first path with later improvements and understand what asymptotic optimality does and does not promise.
Skid steering: why turning requires wheel slip
Derive why four fixed wheels must scrub sideways during a turn. Compare a chosen effective-track model with differential-drive odometry, calculate contact slip speeds, and distinguish equivalent side rotation centers from the body's turning center.