ScaleFree Approximate Motion Planning For Modular Robots Michael

Scale-Free, Approximate Motion Planning For Modular Robots Michael De Rosa CMU

Algorithm Overview • • Hole Motion Hole Growth/Deletion Smoothing (Self-Organizing Criticality) Region-based Planning

Hole Motion • Uniform hexagonal holes • Holes collide and reflect off of object boundary, other holes • Holes can move 1 row at a time (not shown)

Hole Creation/Deletion • Creation/deletion regions are designated on the perimeter • Creation raises the contour of the object • Deletion lowers the contour

Smoothing-Overview >1 >1 • Smoothing algorithm based on Oslo model of sand-pile collapse • As grains of sand are added, local slope increases • If slope exceeds a threshold, collapses occur

Smoothing, continued • Smoothing is constantly active in all creation/deletion regions • “gravity” is determined on a per-region basis (either as one of the 6 hex directions, or w. r. t. an origin point) • This smoothing approach provides bounds on maximum surface roughness as a function of time

Regions • Triangular regions are created either manually, or by keyframing between two images • Ex: simple example with one growth region & smoothing

Challenges (1) • Holes bind to closer regions, pinching off areas farther away from center of mass • Pinched off region becomes detached from central mass

Attempted Solutions • Force regions to wait for further regions to complete before activating – Created deadlock • Holes bind to deletion regions based on distance from desired contour – Some improvement, but much slower • Still an open problem, several techniques under study…

Challenges (2) • Creation of holes very sensitive to small perturbations in surface roughness • Solution: • Allow creation of holes that are not fully enclosed initially • Resulted in a 3 x speed-up in hole creation

Morphing Objects Bending Bar Circle Into Rectangle

Global vs Distributed • Current algorithm assumes only local communication between neighbors • …but requires synchronized clocks, and implicit locks/transactions between catoms • We are developing a distributed version that operates asynchronously, and tolerates moderate clock skew