Profile

Represents a motion profile that maps from one parameter space to time with derivatives.

A profile defines how to traverse a path over time, typically encoding velocity and acceleration constraints. It maps from a displacement or other parameter \(x\) to time \(t\) along with time derivatives, enabling computation of velocities and accelerations.

Profiles are essential for trajectory generation, converting geometric paths into time-parameterized trajectories that respect kinematic and dynamic constraints.