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As the demand for human–robot collaboration in manufacturing applications grows, the necessity for collision detection functions in robots becomes increasingly paramount for safety. Hence, this paper aims to improve the existing method to achieve efficient, accurate and sensitive robot collision detection.

The external torque is estimated by momentum observers based on the robot dynamics model. Because the state of the joints is more accessible to distinguish under the action of the suppression operator proposed in this paper, the mutated external torque caused by joint reversal can be accurately attenuated. Finally, time series analysis (TSA) methods can continuously generate dynamic thresholds based on external torques.

Compared with the collision detection method based only on TSA, the invalid time of the proposed method is less during joint reversal. Although the soft-collision detection accuracy of this method is lower than that of the symmetric threshold method, it is superior in terms of detection delay and has a higher hard-collision detection accuracy.

Owing to the mutated external torque caused by joint reversal, which seriously affects the stability of time series models, the collision detection method based only on TSA cannot detect continuously. The consequences are disastrous if the robot collides with people or the environment during joint reversal. After multiple experimental verifications, the proposed method still exhibits detection capabilities during joint reversal and can implement real-time collision detection. Therefore, it is suitable for various engineering applications.

Given the growing significance of contemporary socio-economic and infrastructural conversations of Public-Private Partnerships (PPP), this research seeks to provide a general overview of the academic landscape concerning PPP.

To offer a nuanced perspective, the study adopts the Latent Dirichlet Allocation (LDA) methodology to meticulously analyse 3,057 journal articles, mapping out the thematic contours within the PPP domain.

The analysis highlights PPP's pivotal role in harmonising public policy goals with private sector agility, notably in areas like disaster-ready sustainable infrastructure and addressing rapid urbanisation challenges. The emphasis within the literature on financial, risk, and performance aspects accentuates the complexities inherent in financing PPP and the critical need for practical evaluation tools. An emerging focus on healthcare within PPP indicates potential for more insightful research, especially amid ongoing global health crises.

This study pioneers the application of LDA for an all-encompassing examination of PPP-related academic works, presenting unique theoretical and practical insights into the diverse facets of PPP.

The impact of technological transformations in all sectors is undeniably significant, especially in fitness family business. The aim is to examine the digital transformation perceptions of fitness centre employees and the effects of perceived empowerment on their job performance in family business in Turkey.

The sample was 334 fitness centre employees. Four variables were evaluated (digital transformation, meaning competence, self-determination and job performance), and PLS-SEM was used.

The digital transformation process in the fitness sector can be considered as an important factor in terms of creating new business ventures. Our results showed that digital transformation perceived by family business employees had a significantly influence on the meaning competence of the employees. Also, the meaning competence of employees was a mediator between the digital transformation and job performance.

Managers of family businesses must take into account that an appropriate digital transformation of their products and/or services has an impact on the meaning competence of their employees. Thus, through increased competence in employee performance, the digitization of family business fitness will lead to higher employee performance and productivity.

This study innovates by linking digital transformation as a factor influencing the coach's own motivation and self-perceived competence in the use of technology to their job performance.