Robotics you can drag around

Four propellers, all pointing the same way, and six degrees of freedom to cover with them. Fly one in 3D and watch the mixer decide what each motor gets.

Two wheels, two motors, and the one equation underneath skid steer, Ackermann steering and every trailer that ever jackknifed.

Drive a mecanum chassis, watch the four motor powers, and find out why mounting the rollers wrong costs a whole degree of freedom.

Four numbers per joint describe an entire arm. Type a table in and watch it appear.

Every reachable point has two arm configurations, and choosing between them is a real decision.

A robot with a lidar and the map of a building, tracking its own pose. Every scan is matched to the map, and the match is a sensor whose noise depends on what the scan could see: in a bare corridor it says where across, and nothing about where along.

Three filters localise the same robot from the same lidar. Where the scan pins the pose they are equally precise, at very different prices. Where it does not, the difference is what each one does with the wheels.

A robot woken up somewhere in a building it has the map of. Belief as two thousand guesses rather than a mean and a covariance, so it can hold two places at once until the map tells them apart.

A sensor that reports position only, fed into a filter that reports velocity too. Add a second, slower sensor and the same update fuses it in: precision adds, whichever one arrives first.

Noise, drift, and mains hum are three different problems wearing the same disguise. Four filters, and which corruption each one is actually for.

Robots locating each other by passing messages to their neighbours, with nobody solving the whole problem. On a graph with a loop the means come out exact and the uncertainties do not, and the tool shows how far out they are.

Belief propagation on a graph that branches, and what setting one variable does to the rest of it. Evidence usually creates independence. At one shape of junction it destroys it, and the algebra says why.

A robot switched on somewhere in a corridor it has the map of, with one bit of sensor. Belief as a table of fifteen numbers, moved by Bayes' rule and nothing else, so the posterior is exact and every step of the arithmetic is on screen.

Three gains, each one a trade. Tune a joint and watch the response change.

A robot patrols, breaks off to approach, breaks off that to recharge. No state machine is coded anywhere.

Throw a random point at the space, step toward it from the nearest thing you have already reached, and never enumerate the free space at all.

Grow every obstacle by the robot's own shape and the robot becomes a point. Every planner after that is simpler.

Dijkstra plus an estimate of the distance remaining, and far less of the map examined.

Every cell one step away, then every cell two steps away. The first route it finds is the shortest.

Change the queue to a stack and every guarantee disappears.

One neuron computes a weighted sum and thresholds it, which draws one straight line. Everything else follows from what that line cannot do.

A robot learns to pick and place by filling in a table of numbers, one cell at a time.

Bigger gears turn slower and push harder. Change the tooth counts and watch the train work it out.