The term kinodynamic planning was introduced by Canny, Donald, Reif, and Xavier  to refer to motion planning problems for which velocity and acceleration bounds must be satisfied. This means that there are second-order constraints on . The original work used the double integrator model for and . A scalar version of this model appeared Example 13.3. More recently, the term has been applied by some authors to virtually any motion planning problem that involves dynamics. Thus, any problem that involves second-order (or higher) differential constraints can be considered as a form of kinodynamic planning. Thus, if includes velocity variables, then kinodynamic planning includes any system, .
Note that kinodynamic planning is not necessarily a form of nonholonomic planning; in most cases considered so far, it is not. A problem may even involve both nonholonomic and kinodynamic planning. This requires the differential constraints to be both nonintegrable and at least second-order. This situation often results from constrained Lagrangian analysis, covered in Section 13.4.3. The car with dynamics which was given Section 13.3.3 is both kinodynamic and nonholonomic.
Steven M LaValle 2020-08-14