Trajectdelen

Trajectdelen, in Dutch, refer to the constituent parts or segments of a trajectory—the path traced by a moving object through space (and often time). The term is used in fields such as robotics, biomechanics, traffic and air navigation, computer animation, and signal processing to describe how a full trajectory can be decomposed into smaller, more manageable pieces.

Formally, if a trajectory is a map gamma from a time interval [t0, tf] to a state space, a trajectdeel is obtained by choosing a partition of the interval: 0 = t0 < t1 < ... < tn = tf. Each trajectdeel is the restriction gamma|[ti-1, ti], representing the path of the object during that sub-interval. Trajectdelen can be described by simple models, such as linear or polynomial interpolations, or by more complex parametric forms. In practice, a trajectory may be explicitly piecewise-defined, with distinct dynamics or control laws governing each segment.

The segmentation serves several purposes. It enables modular planning and control, allows analysis of different motion primitives, and supports estimation and optimization by reducing a complex path to simpler units. In robotics, trajectdelen may correspond to distinct motion primitives or waypoints; in biomechanics, they can align with phases of a gait cycle; in transportation, segments often run between waypoints or control regions.

Segmentation criteria vary and may be time-based, distance-based, or event-driven, depending on constraints such as continuity of position, velocity, or acceleration. The choice of segment length and number affects computational efficiency and the smoothness of the resulting trajectory. See also trajectory planning and trajectory optimization.