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 85–96 of 151 posts
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.
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.
Convert wheel encoder increments into a differential-drive robot's position and heading. Replay measured counts, calculate exact arc updates, and see how calibration errors and wheel slip change the estimate.
Use A* to find a low-cost route across a weighted grid. Calculate g, h, and f, compare Manhattan distance with Dijkstra, and see how an overestimate can return a worse path.
Trace Dijkstra’s algorithm through a weighted grid, update route estimates, and see why the goal must leave the priority queue before its cost is final. Reproduce a complete search in Python.
Build an RRT for a disk robot, check every new branch for collision, and connect the tree to a goal. Explore seeded sampling, step length, narrow passages, and the limits of a finite search budget.
Derive both joint-angle solutions for a two-link robot arm, check them with forward kinematics, and identify unreachable targets and merged boundary branches.
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.
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.
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.
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.
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.