Dynamics of a Vibration Driven Bristlebot

Abstract

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.

On the Forward and Backward Motion of Milli-Bristle-Bots

“…Then, a gap of zero or very small speed appears, followed by the backward motion region at higher frequencies, around 70 to 80 kHz, but with lower peak speeds. Note that this backward region does not correspond to the backward behavior that has been predicted or observed in [11] or [1]. Unlike this work, in the two latter cases, the backward frequency is lower than the forward frequency and in the case of [1], there is a well-defined transition frequency.…”

“…The possibility of backward locomotion in bristlebots was first predicted in [6] using a wet friction model, and further theoretically analyzed in [7], and experimentally observed for a macro-scale bristlebot (with > 10 cm feature size) using an external shaker [1]. Our work reports on the theoretical analysis of the bidirectional motion using Coulomb dry friction model, similar to the model used in [11]. Taking the analysis further, a fundamental upper limit on the robot speed as a function of actuation frequency is derived in this work for the first time.…”

“…9g and eq. 9h, that θp > θ > θn (11) Next, note that the asymptotic solution of the robot motion (once all the transient solutions die out) cannot be exclusively in the regime ẋl > 0, or exclusively in the regime ẋl < 0. In other words one cannot have ẋl (t) > 0, ∀t > T .…”

Mechanically driven active and passive grains as models for egress dynamics

“…Vibration-driven granular particles have been studied in a variety of experiments, e. g. [1][2][3][4][5][6][7][8][9][10][11][12][13]. In many of these, the excitation leads to a diffusive motion of the individual particles.…”