Splines and Bézier curves

SKIDADDLE is a path-following library for FTC robots, written in Java, that I built to fix inefficiencies in Road Runner, the usual FTC path library, and get better paths. It plans with a physics model of the robot, and I derived all of its math by hand, myself, without AI or earlier work to build on. A path, a cubic Bézier for autonomous or a Hermite spline built on the fly in tele-op, is flattened into straight segments by adaptive De Casteljau subdivision, and a curve whose turns would need more than the robot's acceleration is relaxed until they don't. Every loop it splits the robot's velocity into a convergent part, toward the goal, and a transverse part, everything else. It first spends its acceleration budget cancelling the transverse part, then speeds up the convergent part, so from any starting position or velocity the robot converges on the path. A look-ahead over the stopping distance sets the fastest speed for each corner, and the robot switches segments when its braking distance says it must. Heading is a separate controller, and the result goes through PIDF and feedforward to the four wheels. A simulator draws the field and graphs every step.

Our chassis followed paths with pure pursuit: aim at a point a fixed distance down the path and ramp the speed up toward it. The robot's accelerations stay implicit in that, so it has no idea how hard it can brake or how fast it can take a corner, and at speed it swings wide of turns and overshoots where it should stop. I proposed replacing it with path tracking that models those accelerations explicitly, and led the feature from idea to implementation: I wrote the design and gathered the resources behind it, from spline fitting and arc-length reparametrization to the Riccati equation and a study that found LQR tracks more accurately than pure pursuit. First, a cubic spline through the waypoints is reparametrized by arc length, the speed at each point is capped by its curvature, and a forward and a backward pass keep every speed-up and every stop within what the robot can deliver. Then an LQR tracks that profile on a world-frame model of the chassis, where its dynamics stay constant, and its force is rotated into the robot's frame. I designed it and built the framework; the comparison here runs the finished MVP against our pure pursuit in simulation.