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 37–48 of 101 posts
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.
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.
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.