Ex Situ Sensing Method for the End-Effector's Six-Dimensional Force and Link's Contact Force of Cable-Driven Redundant Manipulators

The cable-driven redundant manipulator (CDRM) possesses remarkable flexibility and holds substantial potential for application in constrained environments. To ensure both the smooth movement of the end-effector during delicate operations and the safety of interactions with the surrounding environment, real-time sensing of forces acting on both the end and links is imperative. Current in situ sensor-based methods face limitations in their applicability to CDRMs due to size and load capacity constraints. Moreover, these methods fall short in measuring contact force and its location along the entire arm. In this article, we introduce an ex situ sensing approach for capturing the six-dimensional (6-D) force at the end and the contact force on the linkages of a CDRM. First, a multispace recursive dynamic model of the CDRM is established using the Newton–Euler method. This model establishes mapping relationships among cable tensions, joint torques, and operational forces at the end-effector. Then, a simplified dynamic model for the recursive subsystem is derived based on joint motion transmission relationships and recursive equations. This model decouples the dynamic equations and provides a versatile force-sensing model. It enables the realization of 6-D force/torque sensing at the end-effector, as well as the determination of the magnitude and location of external forces acting on the links. Finally, compliant controllers are designed based on different external force-sensing methods to cater to diverse operational requirements. Experimental validation of the proposed methods is conducted on a CDRM prototype. The results demonstrate that the accuracy of end-effector force sensing exceeds 95%, torque sensing surpasses 90%, and the positioning error of the link's contact force sensing is less than 20 mm. Furthermore, the compliance controllers exhibit excellent smoothness in tasks involving human–robot interaction.