Command shaped trajectory tracking control for a two-link flexible manipulator

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.