One of the richest sources of interesting I-spaces is manipulation planning. As robots interact with obstacles or objects in the world, the burden of estimating the state becomes greater. The classical way to address this problem is to highly restrict the way in which the robot can interact with obstacles. Within the manipulation planning framework of Section 7.3.2, this means that a robot must grasp and carry objects to their desired destinations. Any object must be lying in a stable configuration upon grasping, and it must be returned to a stable configuration after grasping.
As the assumptions on the classical manipulation planning framework are lifted, it becomes more difficult to predict how the robot and other bodies will behave. This immediately leads to the challenges of uncertainty in predictability, which was the basis of Chapter 10. The next problem is to design sensors that enable plans to be achieved in spite of this uncertainty. For each sensing model, an I-space arises.
Section 12.5.1 covers the preimage planning framework [311,659], under which many interesting issues covered in Chapters 10 and 11 are addressed for a specific manipulation planning problem. I-states, forward projections, backprojections, and termination actions were characterized in this context. Furthermore, several algorithmic complexity results regarding planning under uncertainty have been proved within this framework.
Section 12.5.2 covers methods that clearly illustrate the power of reasoning directly in terms of the I-space. The philosophy is to allow nonprehensile forms of manipulation (e.g., pushing, squeezing, throwing) and to design simple sensors, or even to avoid sensing altogether. This dramatically reduces the I-space while still allowing feasible plans to exist. This contradicts the intuition that more information is better. Using less information leads to greater uncertainty in the state, but this is not important in some problems. It is only important is that the I-space becomes simpler.