The term *trajectory planning* has been used for decades in
robotics to refer mainly to the problem of determining both a path and
velocity function for a robot arm (e.g., PUMA 560). This corresponds
to finding a path in the phase space in which is
defined as
. Most often the problem is solved using
the refinement approach mentioned in Section 1.4 by
first computing a path through
. For each configuration
along the path, a velocity must be computed that satisfies
the differential constraints. An inverse control problem may also
exist, which involves computing for each , the action that
results in the desired
. The refinement approach is often
referred to as *time scaling* of a path through
[456]. In recent times, trajectory planning seems synonymous
with kinodynamic planning, assuming that the constraints are
second-order ( includes only configuration and velocity variables).
One distinction is that trajectory planning still perhaps bears the
historical connotations of an approach that first plans a path through
.

Steven M LaValle 2020-08-14