Vehicle-mounted flexible robotic arms (VFRAs) are crucial in enhancing operational capabilities in sectors where human intervention is limited due to accessibility or safety concerns, such as hazardous environments or precision surgery. This paper introduces the latest generation of VFRAs that utilize advanced soft materials and are designed with elongated structures to provide greater flexibility and control. We present a novel mathematical model, derived using Hamilton’s principle, which simplifies the analysis of the arm’s dynamic behaviors by employing partial differential equations (PDEs). This model allows us to understand how these arms behave over time and space, classifying them as distributed parameter systems. Furthermore, we enhance the practical utility of these robotic arms by implementing a proportional-derivative (PD) based boundary control law to achieve precise control of movement and suppression of vibrations, which are critical for operations requiring high accuracy. Our approach’s effectiveness and practical utility are evidenced by numerical simulations, which verify that our advanced control strategy greatly enhances the performance and dependability of VFRAs in actual applications. These advancements not only pave the way for more sophisticated robotic implementations but also have broad implications for the future of automated systems in various industries.
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