Vibration driven robots such as the so called bristlebot and kilobot utilize periodic forced vibration of an internal mass to achieve directed locomotion. These robots are supported on an elastic element such as bristles or cilia and contain an internal mass that is driven to oscillate at a high frequency. Besides well known applications in investigating swarming behavior, such robots have potential applications in rescue operations in rubble, inspections of pipes and other inaccessible confined areas and in medical devices where conventional means of locomotion is ineffective. Bristlebot or its commercially available variants such as hexbugs are popular toy robots. Despite the apparent simplicity of these robots, their dynamic behavior is very complex. Vibration robots have attracted surprisingly few analytical models, those models that exist can only explain some regimes of locomotion. In this paper, a wide range of motion dynamics of a bristlebot is explored using a mathematical model which accounts for slip-stick motion of the bristles with the substrate. Analytical conditions for the system to exhibit a particular type of motion are formulated and the system of equations defining the motion are solved numerically using these conditions. The numerical simulations show transitions in the kinds of locomotion of a bristlebot as a function of the forcing frequency. These different kinds of locomotion include stick-slip and pure slip motions along with the important phenomenon of the reversal of the direction of motion of the robot. In certain ranges of frequencies, the robot can lose contact with the ground and ‘jump’. These different regimes of locomotion are a result of the nonlinear vibrations of the robot and the friction between the robot’s bristles and the ground. The results of this paper can potentially lead to more versatile vibration robots with predictable and controllable dynamics.

Terrestrial locomotion that is produced by creating and exploiting frictional anisotropy is common amongst animals such as snakes, gastropods, limbless lizards. In this paper we present a model of a bristle bot that locomotes by generating frictional anisotropy due to the oscillatory motion of an internal mass and show that this is equivalent to a stick-slip Mathieu oscillator. Such vibrational robots have been available as toys and theoretical curiosities and have seen some applications such as the well known kilobot and in pipe line inspection, but much remains unknown about this type of terrestrial locomotion. In this paper, motivated by a toy model of a bristle bot made from a toothbrush, we derive a theoretical model for its dynamics and show that its dynamics can be classified into four modes of motion : purely stick (no locomotion), slip, stick-slip and hopping. In the stick mode, the dynamics of the system are those of a nonlinear Mathieu oscillator and large amplitude resonance oscillations lead to the slip mode of motion. The mode of motion depends on the amplitude and frequency of the periodic forcing. We compute a phase diagram that captures this behavior, that is reminiscent of the tongues of instability seen in a Mathieu oscillator. The broader result that emerges in this paper is that mobile limbless continuum or soft robots can exploit high frequency parametric oscillations to generate fast and efficient terrestrial motion.