Position and Orientation Tracking Control of a Cable-Driven Tensegrity Continuum Robot

Trajectory tracking control of flexible continuum robots is challenging due to their inherent compliance and high nonlinearity. Many related works exclude the control of the end's orientation, i.e., only the end's position is considered. In this article, a differential-algebraic equations (DAEs) model-based instantaneous optimal control (IOC) framework for the end's position and orientation cooperative tracking of a cable-driven tensegrity continuum robot (TCR) is developed. Based on the tensegrity concept, a TCR is designed first as the control object, which can achieve multimode deformations such as bending, scoliosis, contraction, and the S- or J-shape. Then, the actuation of cables is introduced as the system kinematic constraints from the view of multibody dynamics so that a control-oriented model of the TCR can be built by DAEs. Subsequently, the original continuous trajectory tracking problem is approximated for a series of IOC problems at each discrete time slot. Finally, considering the constraints of control input saturation, a linear complementarity problem was derived for solving these IOC problems. The method provides an easy-to-implement and unified framework for addressing the trajectory tracking control issues of cable-driven continuum robots, which can improve the control performance of the position-only tracking controllers and exploit the TCR's advantages to handle more application scenarios. The advanced performance and potential applications of the proposed controller have been evaluated via several numerical simulations and experiments on the TCR prototype.