7.5 Folding Problems in Robotics and Biology

A growing number of motion planning applications involve some form of folding. Examples include automated carton folding, computer-aided drug design, protein folding, modular reconfigurable robots, and even robotic origami. These problems are generally modeled as a linkage in which all bodies are connected by revolute joints. In robotics, self-collision between pairs of bodies usually must be avoided. In biological applications, energy functions replace obstacles. Instead of crisp obstacle boundaries, energy functions can be imagined as ``soft'' obstacles, in which a real value is defined for every $q \in {\cal C}$, instead of defining a set ${\cal C}_{obs}\subset {\cal C}$. For a given threshold value, such energy functions can be converted into an obstacle region by defining ${\cal C}_{obs}$ to be the configurations that have energy above the threshold. However, the energy function contains more information because such thresholds are arbitrary. This section briefly shows some examples of folding problems and techniques from the recent motion planning literature.