8. Feedback Motion Planning

So far in Part II it has been assumed that a continuous path sufficiently solves a motion planning problem. In many applications, such as computer-generated animation and virtual prototyping, there is no need to challenge this assumption because models in a virtual environment usually behave as designed. In applications that involve interaction with the physical world, future configurations may not be predictable. A traditional way to account for this in robotics is to use the refinement scheme that was shown in Figure 1.19 to design a feedback control law that attempts to follow the computed path as closely as possible. Sometimes this is satisfactory, but it is important to recognize that this approach is highly decoupled. Feedback and dynamics are neglected in the construction of the original path; the computed path may therefore not even be usable.

Section 8.1 motivates the consideration of feedback in the context of motion planning. Section 8.2 presents the main concepts of this chapter, but only for the case of a discrete state space. This requires less mathematical concepts than the continuous case, making it easier to present feedback concepts. Section 8.3 then provides the mathematical background needed to extend the feedback concepts to continuous state spaces (which includes C-spaces). Feedback motion planning methods are divided into complete methods, covered in Section 8.4, and sampling-based methods, covered in Section 8.5.

- 8.1 Motivation
- 8.2 Discrete State Spaces
- 8.2.1 Defining a Feedback Plan
- 8.2.2 Feedback Plans as Navigation Functions
- 8.2.3 Grid-Based Navigation Functions for Motion Planning

- 8.3 Vector Fields and Integral Curves

- 8.4 Complete Methods for Continuous Spaces
- 8.4.1 Feedback Motion Planning Definitions
- 8.4.2 Vector Fields Over Cell Complexes
- 8.4.3 Optimal Navigation Functions
- 8.4.4 A Step Toward Considering Dynamics

- 8.5 Sampling-Based Methods for Continuous Spaces