Trajtime

Trajtime is a term used in motion planning and robotics to describe the time required to execute a specified trajectory under a given set of constraints. It is a measure of execution efficiency that depends on the trajectory geometry, the available actuation, and the dynamic model of the system. In practice, trajtime can refer either to the time associated with a fixed speed profile along the path or to the minimum achievable time under acceleration, velocity, and control limits.

Mathematically, for a trajectory parameterized by arc length s in [0, S] and a speed profile v(s), the trajtime is T = ∫_0^S ds / v(s). In discrete representations, this becomes a sum over trajectory segments. In the context of time-optimal control, trajtime denotes the smallest total time to complete the trajectory subject to dynamic constraints; solving for this time typically involves optimal control methods such as Pontryagin's maximum principle, direct collocation, or convex optimization.

Trajtime is used to compare candidate trajectories, to schedule motions within a robot's control loop, and to optimize planners for safety margins, energy use, or coordination in multi-agent systems. It is common in autonomous driving, robotic manipulation, and aerial robotics.

Limitations include sensitivity to model accuracy and disturbances, since actual execution time can deviate from the predicted trajtime. Consequently, practical systems often report trajtime as an estimate with bounds or use robust or adaptive planning to account for uncertainties.