# Rida T. Farouki: Pythagorean-hodograph curves in real-time motion control applications

Source: Numerical analysis seminar

Pythagorean-hodograph curves incorporate special algebraic structures that permit exact computation of properties (arc length, offset curves, rotation-minimizing frames, etc.) which otherwise require numerical approximation. Such properties provide significant advantages in terms of the flexibility and reliability of algorithms for real-time motion control. These advantages are illustrated in the context of a selection of recent projects, including (1) real-time interpolators for constant or variable feedrates along curvilinear paths; (2) inverse dynamics compensation for axis inertia and damping; (3) cross-coupled control of multi-axis machines; (4) corner smoothing of piecewise-linear paths; (5) real-time offset curve trimming; and (6) optimal tool orientation control in 5-axis CNC machining.