Expand description
Stage C — time-parameterise a joint path at a commanded constant TCP speed.
This is a CNC-style constant-feedrate planner. The timing is found by a
discrete convex program: the variable is the cumulative arc length
σ[k] at each output tick k·dt, and the per-joint velocity/acceleration/
jerk limits are written directly as bounds on the finite differences of the
emitted joint samples — the exact quantities a downstream controller
reconstructs. So the limits are honoured by construction rather than by a
continuous bound plus a margin, and the solver never touches a fragile
joint-space third derivative.
The joint path is first smoothed (a cubic spline, densely resampled) so the
chord-linear interpolation the solver times is C²-smooth at the tick scale;
σ is solved with a small banded LP (Clarabel); the result is reconstructed,
and a final finite-difference check against the true limits is the airtight
backstop. A path that physically cannot fit under the limits fails.
Structs§
- Constant
Speed Retimer - Constant-feedrate, jerk-limited retimer over a joint path.