Trajectory planning

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 $ X$ in which $ x \in X$ is defined as $ x = (q,{\dot q})$. Most often the problem is solved using the refinement approach mentioned in Section 1.4 by first computing a path through $ {\cal C}_{free}$. For each configuration $ q$ along the path, a velocity $ {\dot q}$ must be computed that satisfies the differential constraints. An inverse control problem may also exist, which involves computing for each $ t$, the action $ u(t)$ that results in the desired $ {\dot q}(t)$. The refinement approach is often referred to as time scaling of a path through $ {\cal C}$ [456]. In recent times, trajectory planning seems synonymous with kinodynamic planning, assuming that the constraints are second-order ($ x$ 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 $ {\cal C}_{free}$.

Steven M LaValle 2012-04-20