@Article{Matter_Robotica,
AUTHOR = {Byoungkwon An and Nadia Benbernou and Erik D. Demaine and Daniela Rus},
TITLE = {Planning to Fold Multiple Objects from a Single Self-Folding Sheet},
JOURNAL = {Robotica},
journalurl = {http://journals.cambridge.org/action/displayJournal?jid=ROB},
VOLUME = 29,
NUMBER = 1,
YEAR = 2011,
PAGES = {87--102},
NOTE = {Special issue on Robotic Self-X Systems.},
withstudent = 1,
length = {29 pages},
doi = {https://dx.doi.org/10.1017/S0263574710000731},
dblp = {https://dblp.org/rec/journals/robotica/AnBDR11},
comments = {This paper is also available from <A HREF="http://dx.doi.org/10.1017/S0263574710000731">Cambridge Journals Online</A>.},
}
We describe the planning algorithms underlying these self-folding sheets, forming a new family of reconfigurable robots that fold themselves into origami by actuating edges to fold by desired angles at desired times. Given a flat sheet, the set of hinges, and a desired folded state for the sheet, the algorithms (1) plan a continuous folding motion into the desired state, (2) discretize this motion into a practicable sequence of phases, (3) overlay these patterns and factor the steps into a minimum set of groups, and (4) automatically plan the location of actuators and threads on the sheet for implementing the shape-formation control.