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In complex environments, a spherical robot has great application value. When the pendulum spherical robot is stopped or disturbed, there will be a periodic oscillation. This situation will seriously affect the stability of the spherical robot. Therefore, this paper aims to propose a control method based on backstepping and disturbance observers for oscillation suppression.

This paper analyzes the mechanism of oscillation. The oscillation model of the spherical robot is constructed and the relationship between the oscillation and the internal structure of the sphere is analyzed. Based on the oscillation model, the authors design the oscillation suppression control of the spherical robot using the backstepping method. At the same time, a disturbance observer is added to suppress the disturbance.

It is found that the control system based on backstepping and disturbance observer is simple and efficient for nonlinear models. Compared with the PID controller commonly used in engineering, this control method has a better control effect.

The proposed method can provide a reliable and effective stability scheme for spherical robots. The problem of instability in real motion is solved.

In this paper, the oscillation model of a spherical robot is innovatively constructed. Second, a new backstepping control method combined with a disturbance observer for the spherical robot is proposed to suppress the oscillation.

The objective of the present study was to investigate the impacts of familiarity with and awareness of Florida as a snowbird destination, and satisfaction with the snowbird experience on Florida's image and on snowbirds' permanent relocation intention to Florida. Additionally, the influence of Florida's image on snowbirds' behavioral intention to move to Florida permanently was investigated.

Data gathered from 304 snowbirds were utilized in employing structural equation modeling to assess the research model.

The study results showed that awareness of and familiarity with Florida as a snowbird destination, and satisfaction with the snowbird experience significantly influenced participants' image perceptions of Florida. In addition, awareness of and familiarity with Florida as a snowbird destination, and participants' image of Florida had a significant influence on snowbirds' intentions to move to Florida permanently.

The findings of the study provide significant insights for destination marketing and management organizations and local policymakers in formulating and enacting policies in snowbird destinations to efficiently address migration trends.

This study is one of the first papers to empirically investigate and successfully construct a comprehensive model that explicate the determinants of snowbird tourists' permanent relocation intention.