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 . 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 2012-04-20