Actuation space reduction to facilitate insightful shape matching in a novel reconfigurable tendon driven continuum manipulator
Authors: Sabyasachi Dash, John Golden, Girish Krishnan
Organizations: Department of Industrial and Enterprise Systems Engineering, University of Illinois Urbana-Champaign · Department of Mechanical Science and Engineering, University of Illinois, Urbana-Champaign
In tendon driven continuum manipulators (TDCMs), reconfiguring the tendon routing enables tailored spatial deformation of the backbone. This work presents a design in which tendons can be rerouted either prior to or after actuation by actively rotating the individual spacer disks. Each disk rotation thus adds a degree of freedom to the actuation space, complicating the mapping from a desired backbone curve to the corresponding actuator inputs. However, when the backbone shape is projected into an intermediate space defined by curvature and torsion (C-T), patterns emerge that highlight which disks are most influential in achieving a global shape. This insight enables a simplified, sequential shape-matching strategy: first, the proximal and intermediate disks are rotated to approximate the global shape; then, the distal disks are adjusted to fine-tune the end-effector position with minimal impact on the overall shape. The proposed actuation framework offers a model-free alternative to conventional control approaches, bypassing the complexities of modeling reconfigurable TDCMs.
Figures & tables
Fig. 1: Conventional TDCMs (a) rely on fixed tendon routing which limits the range of achievable spatial defomration modes. The proposed Reconfigurable TDCM (RTDCM) design (b) enables local tendon rerouting via controlled rotation of intermediate spacer disks, allowing more versatile backbone spatial configurations. (c) The geometric Curvature-Torsion (C-T) space provides an intermediate mapping between the manipulator’s spatial deformation and the corresponding actuation space.
Fig. 2: (a) RTDCM design with each disk assembly capable of rotating the tendon locally. The servo motor (1) sits on the fixed mount (2) which is attached to the backbone using epoxy. The fixed mount is connected to the rotating disk (5) through a bearing (4), and a gear (3) attached to the servo motor-head rotates (5) which holds the tendon. (b) Experimental setup with stepper motor (1) to actuate the tendon, and a magnetic stylus (3) with reference at (2) to retrieve track coordinates of the backbone.
Fig. 3: Continuous rotation of (a) second, (b) fourth, (c) eighth disk from 90∘ clockwise to 90∘ anticlockwise direction, where (a) proximal actuation yields behavior similar to entire base rotation, (b) intermediate actuation induces a more pronounced global shape change of the backbone, and (c) distal actuation enables local tip maneuvering with minimal effect on the overall shape
Fig. 4: (a) Parallel tendon routing yields a planar deformation profile of the backbone, which is signified by zero torsion throughout, and a rising curvature due to gravity. (b) Spatial deformation induced by local rotation of the fifth disk in (I) clockwise and (II) counterclockwise direction. Torsion plot demonstrates a sign change near the rotated disk, with the signs flipped between the clockwise and anticlockwise case. (c) Torsion plots for 90∘ clockwise rotation of (I) third through (V) seventh disk. The torsion flips sign from positive to negative in close proximity of each rotated disk. (d) Torsion plots for combination of two disks (third and sixth) rotated in opposite directions demonstrate two distinct sign changes. (e) Increasing tendon displacement directly correlates with a steeper curvature for both (I) parallel routing, and (II) routing with a rotated disk, while the peak curvature and slope reduce for the latter case. (f) For a fixed tendon displacement, the fifth disk is rotated incrementally from 30∘ to 90∘ , both in (I) clockwise and (II) anticlockwise directions. The resulting curvature profiles remain close to each other in both cases.
Fig. 5: Sequential Actuation Framework for Target Shape Matching
Fig. 6: (a) Target shape (I) with its corresponding torsion (II) profile demonstrating clear sign reversal from negative to positive near the fifth disk implying a counterclockwise rotation. (b) (I) With the fifth disk rotated to 90∘ , a tendon pull of 103 mm minimizes error from target curvature. (II) An exact angle of 78∘ in the fifth disk minimizes the global shape error, and (III) a counterclockwise rotation of the eighth disk to 10∘ minimizes the end-effector error. (c) Overlay of spatial curves obtained when Disk 5 is rotated iteratively till error with target shape is minimized, and Disk 8 is adjusted to match the tip. (d) A second target shape (I) with its torsion profile in (II), demonstrates a significant sign change near the fourth disk, and a minor sign change around the sixth/seventh disk. (e) (I) Both the fourth and sixth disks are rotated to 90∘ clockwise and counterclockwise directions respectively, and a tendon displacement of 131 mm minimizes the curvature error. Required disks are rotated sequentially: (II) fourth disk first to 87∘ clockwise, and (III) sixth disk next 55∘ counterclockwise to minimize overall shape error. (IV) End effector is adjusted by rotating the eighth disk clockwise by 16∘ . (f) Overlay of Target shape with shapes obtained after rotation of fourth disk, fourth + sixth disk, and fourth + sixth + end effector.
Department of Industrial & Enterprise Systems Engineering, University of Illinois Urbana-Champaign · Department of Mechanical Science & Engineering, University of Illinois Urbana-Champaign