An analytical differential kinematics-based method for controlling tendon-driven continuum robots

Generic and high-performance feedback control is still challenging for tendon-driven continuum robots. Conventional model-based controllers, based on the piecewise constant curvature (PCC) assumption, explicitly require the arc parameters (bending angle and direction angle) to link the task (in Cartesian coordinates) and actuation spaces. However, the approaches' effectiveness remains to be explored when robot shapes deviate from circular arcs. This paper proposed a hybrid scheme for novel kinematic control of continuum robots. The error led by the slack state has been avoided through tension supervision, while analytical differential kinematics is further developed to avoid the explicit call of arc parameters by importing Cylindrical coordinates into task space and applying accurate piecewise linear approximation. Comparison between a conventional PCC-based controller and the proposed controller has been done by implementing them in a twin-pivot joint-based continuum section. An overall tip positioning accuracy of ±0.35mm has been reached, and a result of root-mean-square-error (RMSE): 0.3mm and Max error: 0.97mm has been observed when running two predefined path tracking. Further, in order to evaluate the versatility of the proposed controller, a dual-revolute joint-based and a 3D-printed continuum section were used to test for path tracking to prove the effectiveness of the controller on a wide range of continuum robotic systems.