Coordinated Particle Relocation Using Finite Static Friction With Boundary Walls

We present theoretical and practical methods for achieving arbitrary reconfiguration of a set of objects, based on the use of external forces, such as a magnetic field or gravity: Upon actuation, each object is pushed in the same direction until it collides with an obstruction. This concept can be used for a wide range of applications in which particles do not have their own energy supply. A crucial challenge for achieving any desired target configuration is breaking global symmetry in a controlled fashion. Previous work made use of specifically placed barriers; however, introducing precisely located obstacles into the workspace is impractical for many scenarios. In this letter, we present a different, less intrusive method: making use of the interplay between static friction with a boundary and the external force to achieve arbitrary reconfiguration. Our key contributions are a precise theoretical characterization of the critical coefficient of friction that is sufficient for rearranging two particles in triangles, convex polygons, and regular polygons; a method for reconfiguring multiple particles in rectangular workspaces, and deriving practical algorithms for these rearrangements. Hardware experiments show the efficacy of these procedures, demonstrating the usefulness of this novel approach.