Modeling of continuum robots with twisted tendon actuation systems

In contrast to traditional articulated robots, continuum robots do not have any joints. The backbone of these robots can be bent, twisted and stretched by environmental and actuation forces. A group of continuum robotic arms use tendon-driven actuation systems. In this group, the shape of robot backbone can be controlled by pulling the tendons. Generally, exact modeling of the forces and moments produced by tendon-driven systems has no closed form solution. However, for a simplified case where the backbone shape is a planar curve with a constant curvature, some closed-form solutions have been introduced. Such solutions are valuable, especially in control applications where Jacobian matrices must be calculated. For exact modeling of elastic rods in spatial deformations, constant curvature models are not accurate. In such cases, the theory of Cosserat rod can be used for backbone modeling. Continuum robots usually consist of an elastic rod as the backbone and an actuation system. The effects of the actuation systems must be included to the model of Cosserat rod. The effects of the actuation systems are more complicated, when the tendon passages are not parallel to the backbone. In this paper, a model for continuum robotic arms is presented, which considers both, the elastic backbone and the effects of the actuation system. Furthermore, the tendons can twist around the backbone, in an arbitrary passage. The presented model is more compact than other solutions, and will be validated in a case study, by comparison with numerical results obtained from existing models.