Natural Oscillations of Underactuated Cable-Driven Parallel Robots - Complete Experiments Data

Underactuated Cable-Driven Parallel Robots (CDPR) employ a number of cables smaller than the degrees of freedom (DoFs) of the end-effector (EE) that they control. As a consequence, the EE is underconstrained and preserves some freedoms even when all actuators are locked, which may lead to undesirable oscillations. This paper proposes a methodology for the computation of the EE natural oscillation frequencies, whose knowledge has proven to be convenient for control purposes. This procedure, based on the linearization of the system internal dynamics about equilibrium configurations, can be applied to a generic robot suspended by any number of cables comprised between 2 and 5. The kinematics, dynamics, stability, and stiffness of the robot free motion are investigated in detail. The validity of the proposed method is demonstrated by experiments on 6-DoF prototypes actuated by 2, 3, and 4 cables. Additionally, to highlight the interest of this modelling strategy in a robotic context, we apply it to the trajectory planning of a 6-Dof 4-cable CDPR by means of a frequency-based method (multi-mode input shaping) and experimentally compare the latter with traditional non-frequency-based motion planners.

非驱动电缆驱动的平行机器人（CDPR）采用若干条小于其末端执行器（EE）自由度（DoFs）的电缆进行控制。由此，即便所有执行器均已锁定，末端执行器仍处于欠约束状态，保留部分自由度，这可能导致不希望的振荡。本文提出了一种计算末端执行器自然振荡频率的方法，该方法的掌握已被证明对于控制目的极为便利。该方法基于对系统内部动力学在平衡配置附近的线性化，可应用于由2至5条电缆悬挂的通用机器人。对机器人的自由运动学、动力学、稳定性和刚度进行了详细的研究。通过在由2、3和4条电缆驱动的6-DoF原型机上的实验验证了所提方法的可行性。此外，为了凸显该建模策略在机器人领域的应用价值，我们采用基于频率的方法（多模式输入整形）对6自由度4电缆CDPR的轨迹规划进行了应用，并通过实验将其与传统的非频率基础运动规划进行了比较。