Writing
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.
Start with the interactive foundationsShowing 73–84 of 151 posts
Explore joint flexibility with two rotary inertias joined by a spring and damper. Calculate transmitted torque, loaded deflection, elastic oscillation, and energy loss, then compare motor and load motion.
Turn uncertain inertia, damping, and disturbance torque into an acceleration range. Compare a nominal command with an actual model, handle negative acceleration correctly, and understand the assumptions behind a worst-case bound.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.