Overview of Part IV: Planning Under Differential Constraints

Part IV is a continuation of Part II. It is generally not necessary to read Part III before starting Part IV. In the models and methods studied in Part II, it was assumed that a path can be easily determined between any two configurations in the absence of obstacles. For example, the sampling-based roadmap approach assumed that two nearby configurations could be connected by a “straight line” in the configuration space. The constraints on the path are global in the sense that the restrictions are on the set of allowable configurations.

The next few chapters introduce differential constraints, which restrict the allowable velocities at each point. These can be considered as local constraints, in contrast to the global constraints that arise due to obstacles. Some weak differential constraints, such as smoothness requirements, arose in Chapter 8. Part IV goes much further by covering differential consraints in full detail and generality.

Differential constraints arise everywhere. In robotics, most problems involve differential constraints that arise from the kinematics and dynamics of a robot. One approach is to ignore them in the planning process and hope that the differential constraints can be appropriately handled in making refinements. This corresponds to applying the techniques of Part II in robotics applications and then using control techniques to ensure that a computed path is executed as closely as possible. If it is practical, a better approach is to consider differential constraints in the planning process.