There are many ways to classify motion planning problems under differential constraints. Some planning approaches rely on particular properties of the system; therefore, it is helpful to characterize these general differences. The different kinds of problems described here are specializations of Formulation 14.1. In spite of differences based on the kinds of models described below, all of them can be unified under the topic of planning under differential constraints.
One factor that affects the differential model is the way in which the task is decomposed. For example, the task of moving a robot usually requires the consideration of mechanics. Under the classical robotics approach that was shown in Figure 1.19, the motion planning problem is abstracted away from the mechanics of the robot. This enables the motion planning ideas of Part II to be applied. This decomposition is arbitrary. The mechanics of the robot can be considered directly in the planning process. Another possibility is that only part of the constraints may be considered. For example, perhaps only the rolling constraints of a vehicle are considered in the planning process, but dynamics are handled by another planning module. Thus, it is important to remember that the kinds of differential constraints that appear in the planning problem depend not only on the particular mechanical system, but also on how the task is decomposed.