Modeling and Dynamics Analysis of a Beam-Hoverboard Self-Transportation System

Abstract

In recent years, self-balancing personal transportation devices have gained significant popularity, the most popular ones being the “Hoverboard” systems. These systems utilize the dynamics of an inverted pendulum to create stable lateral motion. In this paper, the dynamic behavior of a hoverboard system with an attached flexible beam is investigated. By introducing a flexible beam, the vibrational characteristics of the system created by both the rider and the environment can be measured and accounted for. The beam is a continuous system modeled as an n degree of freedom (DOF) inverted pendulum. The resulting system becomes an n+2 DOF (n DOF for the beam, one DOF for the rotation of the beam about the wheel axis, and one DOF for the horizontal motion of the system). A mathematical model is developed to simulate the vibrations of the beam when excited by a piezoelectric actuator at the base, and to simulate the horizontal motion necessary to balance the beam as it is excited.

A New Dynamic Model of a Two-Wheeled Two-Flexible-Beam Inverted Pendulum Robot

“…( 24)-(33), it is sufficient to omit the ϕ and one of these beams. Then, the final equations will convert to [23].…”

“…The first idea of using flexible structure as an inverted pendulum in robot was created by Nguyen et al They studied a linearized mathematical model and controller for a single flexible inverted pendulum, this model only accounted for lateral movement in one direction rather than in the two directions and it has four wheels [22]. In another robot Mehrvarz et al modeled a two-wheeled flexible inverted pendulum which can move in one direction [23]. They also designed a MPC controller for their robot and showed that the percision of their modeling [24].…”

“…Here, to solve the problem of two-wheeled flexible beam inverted pendulum which is used in [23], two-wheeled twoflexible beam inverted pendulum model is addressed. This robot is designed to move in-plane and has not the previous problem.…”

Boundary Vibration Control of Strain Gradient Timoshenko Micro-Cantilevers Using Piezoelectric Actuators

“…Many flexible systems are modeled using a linear PDE and a set of BCs. To achieve the control purposes of flexible structures, most engineers rely on discretizing the governing PDE into a set of ordinary differential equations (ODEs) [4], [34], [35]. This is because of the abundance of control design techniques available for ODEs and mathematical complexities of boundary control of PDE models.…”

“…One of the important continuous systems in mechanical engineering is the micro-beam. Micro-beams have many applications in transportation [4], MEMS and NEMS [5],atomic force microscopy (AFM) [6], micro switches [7]- [10], mass sensors, micro-accelerometers, micro-mirrors [11], [12], grating light valves (GLV) [13]- [15] and cell contraction assays [16].…”