Dynamic modelling and PFL-based trajectory tracking control for underactuated cable-driven truss-like manipulator

In recent years, an innovative underactuated robot was developed, named as underactuated cable-driven truss-like manipulator (UCTM), to be suitable in aerospace applications. However, there has been strong consensus that the stabilization of planar underactuated manipulators without gravity is a great challenge since the system includes a second order nonholonomic constraint and most classical control methods are not suitable for this kind of system. Furthermore, the complexity of the truss-like structure results in tremendous difficulty of computational complicacy and high nonlinearity during dynamic modelling in addition to controller design. It is paramount to solve these difficulties for UCTM’s future applications. To solve the above difficulties, this paper presents a dynamic modelling method for UCTM and a trajectory tracking control method based on partial feedback linearization (PFL) that fulfills the control goal of moving UCTM from its original position to a desired position by tracking a given trajectory of the joint angles. To achieve this, a model equivalent method is proposed to make UCTM equivalent with a three-link manipulator in the sense of dynamic behavior. Then the Lagrangian equation combined with complex vector method is proposed in the dynamic modelling process of UCTM, which simplifies the derivation procedure. Based on the established dynamic model, a coordinate transformation method is proposed to transform the control force matrix into the conventional form of an underactuated system, so that the control force can be separated from the unactuated term. The PFL method in combination with the LQR control method is then proposed to realize the targets that the joint angles can track given desired trajectory. Simulation experiments are conducted to verify the correctness and effectiveness of the proposed methods.