Self-positioning ability of a sphericon-shaped magnetic millirobot rolling on an inclined surface

This paper introduces the novel self-positioning ability of a sphericon-shaped magnetic millirobot (SSMM) on an inclined surface. The SSMM is comprised of four identical half cones with a cylindrical magnet inserted into the geometric center, and it can roll along a straight line on a surface with repeated rolling cone motions actuated by an external wobbling magnetic field (EWMF). Due to the restoring moment induced by a conservative gravitational force, the SSMM can maintain (self-position) its equilibrium position on the surface, even when the EWMF is removed. This paper derived several equations to quantify the condition in which the SSMM can steadily generate self-positioning motions. It also examined the self-positioning ability of the SSMM by constructing a prototype SSMM and demonstrating its rolling and self-positioning motions by using a magnetic navigation system.