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We investigate the problem of finding collision-free paths for two planar robots which coordinately carry a rectangular object from an initial position and orientation to a destination position and orientation in a cluttered 2-D environment. The robot arms and the carried object construct a 6-link closed chain. The path planning problem for the 6-link closed chain is solved by using two major algorithms: the collision-free feasible configuration finding algorithm and the collision-free path finding algorithm. The collision-free feasible configuration finding algorithm finds all collision-free feasible configurations (CFFCs) of the 6-link closed chain in each discrete interval of two joint angles. The collision-free path finding algorithm builds a connection graph by CFFCs and the transitions between any two groups of CFFCs at adjacent joint intervals. Then a graph search method is used to find a collision-free path for each joint of the robots.

This paper presents an advanced control strategy based on Fractional-Order Sliding Mode Control (FO-SMC), which introduces a robust solution to significantly improve the reliability of robotic manipulator systems and increase its control performance. The proposed FO-SMC strategy includes a two-key term-based Fractional Sliding Function (FSF) that presents the main contribution of this work. Additionally, a fractional-order-based Lyapunov stability analysis is developed for a class of nonlinear systems to guarantee the asymptotic stability of the closed loop system. Four FSF-based versions of the designed FO-SMC are studied and discussed. Various scenarios of the proposed control strategy are tested on a 3-degree-of-freedom SCARA robotic arm and compared to recent FO-SMC works, demonstrating the effectiveness of the new proposed control strategy to (i) ensure the asymptotic stability, (ii) achieve a smooth start-up, (iii) cancel the static error, giving a good tracking trajectory, and (iv) reduce the control torques, yielding a consumed energy minimization.