Trajectory tracking of multi-section tendon-driven continuum robots using virtual actuation space control

Tendon-driven Continuum Robots (TDCRs) excel at operating in confined and complex environments due to their inherent flexibility and high degrees of freedom. Despite these advantages, achieving precise control in multi-section TDCRs remains challenging because of their infinite degrees of freedom, nonlinear behaviour, and coupled tendon actuation. This paper introduces a generalised virtual actuation space framework that significantly simplifies kinematic modelling and control of multi-section TDCRs. By formulating a novel concept of virtual actuation space that converts each bending section of the TDCR two-input actuation system, the proposed method reduces the complexity of TDCR modelling and control, enabling unique and simplified representations of each section. Furthermore, the formulation decouples each section via a generalised tendon mapping matrix that handles coupling effects. Experimental validation on a two-section TDCR demonstrates tracking performance with a root mean square error below 3 mm, corresponding to approximately 1% of the robot’s length. These results confirm the method’s efficacy in improving TDCR precision for minimally invasive surgery, industrial applications, and other constrained environments.