profile

Rest-to-rest motion profiles for a single axis. C++17 core, Python plotter.

Two generators

Trapezoidal. Ramp up at amax, cruise at vmax, ramp down. Acceleration steps instantly, so jerk is unbounded at four instants in the move. Nearly every hobby motion library does this, and it is why cheap gantries ring after every move: the step in acceleration is a broadband input that hits the first structural mode of the machine.

Double-S, jerk limited. Acceleration itself ramps at jmax, so jerk stays bounded. Seven segments: jerk up, hold amax, jerk down, cruise, and the mirror image on the way down.

On a 400 unit move at vmax 300, amax 1200, jmax 9000, the jerk-limited profile takes 1.717 s against the trapezoid's 1.583 s. That is 8.4 percent slower on paper, and settles far faster in reality.

The cases that break naive implementations

Both generators handle all of them:

• the move is too short to reach vmax, so the cruise phase disappears
• the move is too short to reach amax either, so acceleration becomes a pure triangle and the peak never touches the limit
• the move runs in the negative direction

The double-S planner works these out in closed form rather than searching. The key identity is that a symmetric ramp from rest to v covers exactly v * Ta / 2 whatever shape the acceleration takes, because velocity is antisymmetric about v/2 across the phase. That turns the no-cruise case into a quadratic in v, and the no-amax case into a cube root.

Build and run

make test                # 13 checks
make plot                # writes move.csv and move.png
./profile --csv --distance 5 --vmax 300 --amax 1200 --jmax 9000 > short.csv

Implementation note

A profile is stored as a list of constant-jerk segments. Sampling integrates a cubic exactly, so there is no accumulated error no matter how finely you sample, and the same evaluator serves every case.

Tests

Thirteen checks: exact landing on target for both generators, every limit respected, the profile ending at rest with zero acceleration, the short-move and very-short-move collapses, negative direction, the time penalty staying inside a sane bound, and numerically integrating velocity over 200,000 steps to reproduce the commanded position to within 1e-4.

Built With

• c++
• makefile
• python