Flexible manipulators offer several advantages over rigid manipulators, including light-in-weight, high payload-to-weight ratio, lower power consumption, and the ability to operate at high speeds. However, these manipulators are susceptible to structural vibrations, which can be effectively suppressed by implementing an appropriate controller. The paper presents a performance evaluation of such a controller for tracking a complex trajectory that combines curved and linear paths, in contrast to existing literature-focused on pure linear or circular trajectories without considering any payload. Before controlling, the dynamics of a two-flexible manipulator system are modeled using a hybrid Euler-Lagrangian formulation and DeNOC matrices, with validation. After that, to achieve precise trajectory tracking while suppressing vibrations, a hybrid controller is designed, integrating command shaping techniques with a proportional-derivative (PD) feedback controller. The results demonstrate the effectiveness of command shaping and its comparison to unshaped input commands. The controller’s performance is evaluated using a semicircular trajectory within a 3-second timeframe, considering both payload and non-payload cases. The proposed control scheme effectively suppresses vibrations in both payload scenarios. Detailed analysis of tip deflections for both links with shaped and unshaped input commands is provided, along with the quantification of vibration suppression along the trajectory. The impact of different configurations and payloads on the natural frequency during trajectory tracking is presented. The study also shows the tracking of B-Splines trajectories, highlighting the requirement of higher gains for such trajectories and evaluating the effect of link flexibility by tracking error analysis. Vibration suppression is achieved by implementing the controller while tracking such trajectories.

与刚性机械手相比，柔性机械手具有多种优势，包括重量轻、有效载荷重量比高、功耗更低以及能够高速运行。然而，这些机械臂容易受到结构振动的影响，可以通过采用适当的控制器来有效抑制结构振动。该论文提出了这种控制器的性能评估，用于跟踪结合了曲线和线性路径的复杂轨迹，这与现有文献（专注于纯线性或圆形轨迹而不考虑任何有效载荷）形成鲜明对比。在控制之前，使用混合欧拉-拉格朗日公式和 DeNOC 矩阵对双柔性机械臂系统的动力学进行建模，并进行验证。之后，为了在抑制振动的同时实现精确的轨迹跟踪，设计了一种混合控制器，将命令整形技术与比例微分（PD）反馈控制器相结合。结果证明了命令整形的有效性及其与未整形输入命令的比较。控制器的性能是在 3 秒时间内使用半圆轨迹进行评估，同时考虑有效负载和非有效负载情况。所提出的控制方案有效地抑制了两种有效负载情况下的振动。提供了对具有成形和非成形输入命令的两个连杆的尖端偏转的详细分析，以及沿轨迹的振动抑制的量化。介绍了轨迹跟踪期间不同配置和有效负载对固有频率的影响。该研究还展示了 B 样条轨迹的跟踪，强调了此类轨迹对更高增益的要求，并通过跟踪误差分析评估了链路灵活性的效果。通过在跟踪此类轨迹的同时实施控制器来实现振动抑制。