Dynamic Control of Multisection Three-Dimensional Continuum Manipulators Based on Virtual Discrete-Jointed Robot Models

Despite the rise of development in continuum manipulator technology and application, a model-based feedback closed-loop control appropriate for continuum robot designs has remained a significant challenge. Complicated by the soft and flexible nature of the manipulator body, control of continuum structures with infinite dimensions proves to be difficult due to their complex dynamics. In this paper, a novel strategy is designed for trajectory control of a multi-section continuum robot in three-dimensional (3D) space to achieve accurate orientation, curvature, and section length tracking. The formulation connects the continuum manipulator dynamic behavior to a virtual discrete-jointed robot whose degrees of freedom are directly mapped to those of a continuum robot section under the hypothesis of constant curvature. Based on this connection, a computed torque control architecture is developed for the virtual robot, for which kinematics and dynamic equations are constructed and exploited, with appropriate transformations developed for implementation on the continuum robot. The control algorithm is implemented on a six Degree-of-Freedom two-section OctArm continuum manipulator. Experiments show that the proposed method could manage simultaneous extension/contraction, bending, and torsion actions on multi-section continuum robots with decent performance (arc length and curvature error of ±4mm and ±0.35 m $-1$ ). The designed dynamic controller can reduce the curvature tracking error and rise time by up to 48.1% and 94.8% compared to the traditional PID controller during two-section maneuvers.