Input Shaping for Point-to-Point Motion with a Continuum Robot Arm

Cable-driven manipulators exhibit strong nonlinearities and low structural stiffness, which make precise control challenging under time-varying uncertainties and external disturbances. This paper presents a time-delay-estimation (TDE)-based adaptive fractional-order nonsingular terminal sliding mode (AFONTSM) control strategy for cable-driven robots. A robust controller is constructed within a TDE-based model-free framework by combining fractional-order nonsingular terminal sliding mode error dynamics with a fast terminal sliding mode reaching law. The main contribution is a new adaptive law that introduces an adaptive exponential term into the update gain to form a nonlinear adaptive mechanism. This design improves adaptive regulation under different operating conditions by suppressing noise-induced chattering during smooth tracking while preserving or enhancing the adaptive gain during trajectory reversal. Lyapunov analysis proves the ultimate uniform boundedness of the tracking error. Experimental results show that, compared with the baseline method, the proposed controller reduces RMSE by 34.52% and 31.11%, ITAE by 33.79% and 32.97%, and ISCT by 6.69% and 17.77% for the two joints, respectively. Further comparisons with recently reported adaptive laws demonstrate that the proposed law provides faster adaptive response, more stable gain evolution, and improved chattering suppression. Additional payload tests further verify the robustness and repeatability of the proposed method.

Shape and force sensing have long been critical bottlenecks in the development of compact capstan-driven continuum surgical robots, primarily due to the difficulty of obtaining cable tension information within the confined capstan assembly. To overcome these challenges, this paper presents an integrated design-modeling-sensing approach based on the concept of actuation-perception co-design. A compliant element is introduced into the motor mounting bracket of the drive system, enabling micro-deformation under the cable reaction force and thereby allowing real-time cable tension measurement without occupying the compact capstan space. To address the modeling complexity arising from unconventional joint configurations introduced by the spatial cable routing strategy, a parallel computation framework based on a multibody short-thick-beam model is proposed, which captures shear effects in short beam segments and synergistic multi-cable interactions while achieving real-time performance. Building on this framework, stable shape and force sensing is achieved by incorporating a proximal multi-axis force/torque sensor as an additional measurement anchor. Following this design-modeling-sensing framework, capstan-driven continuum surgical robots with single- and dual-segment configurations are developed. Experimental results validate the proposed framework in both single- and dual-segment continuum robots, demonstrating real-time tip pose estimation together with contact force and location perception. By enabling cable tension feedback without compromising the compact capstan architecture, the proposed framework makes integrated perception feasible for capstan-driven continuum surgical robots.

In this paper, we discuss a novel continuum robot design that enables the online tuning of the magnetic response at its tip. The proposed method allows for the change of both effective magnetic direction and intensity, introducing steering DOF without the need to control the external fields. This is unattainable with classical designs, which rely on fixed internal magnetic content and steer solely under the effect of a controllable magnetic field. The proposed robot design can be used in both controllable and fixed magnetic fields, potentially widening the clinical applicability of these robots. We experimentally show a max tip deflection of 33.8 mm from the resting state (23 % of the length of the robot). We discuss a model based on modified beam theory that captures the mechanical behavior of the continuum robot, with a mean absolute tip tracking error of 1.86 mm (1.2 % of the length) and maximum errors of less than 4.8 mm (3.2 % of the length) for all experimental points.