PaperlayerView exact revision on arXiv

Source-linked AI summary

Shape-adaptive Hysteresis Compensation for Tendon-driven Continuum Manipulators

Young-Ho Kim, Tommaso Mansi

arXiv:2109.06907v1cs.RO

TL;DR

Existing TDCM models do not account for changes in proximal shaft shape, despite their relevance to tip control. The paper uses motor current to detect and compensate hysteresis shifts, and reports improved tip-control performance across varied settings.

  • Problem

    Existing TDCM models omit varied proximal shaft shape, although it affects tip-control modeling.

    Source: §I · p. 1

  • Method

    The paper uses a gradient-based, motor-current method to detect hysteresis shifts and adapt compensation to proximal-shaft shape changes.

    Source: §I · p. 2, §V · p. 7

  • Results

    The hysteresis-shift compensator significantly improved tip-control performance across varied curvatures, periodic and non-periodic inputs, and 1-DoF and 2-DoF tests.

    Source: §V · p. 8

  • Takeaways & Limitations

    The detected hysteresis shift can be integrated with any hysteresis model that handles dead zone.

    Source: §V · p. 8

    The authors note that motor-current-only compensation may be limited for multi-DoF manipulation because it does not detect coupling effects as expected.

    Source: §IV · p. 7

Abstract

from arXiv · show

Tendon-driven continuum manipulators (TDCM) are commonly used in minimally invasive surgical systems due to their long, thin, flexible structure that is compliant in narrow or tortuous environments. There exist many researches for precise tip control of the articulating section. However, these models do not account for the proximal shaft shape of TDCM, affecting the tip controls in practical settings. In this paper, we propose a gradient-based shift detection method based on motor current that can easily find the offset of task space models (i.e., hysteresis). We analyze our proposed methods with multiple Intra-cardiac Echocardiography catheters, which are typical commercial example of TDCM. Our results show that the errors from varied proximal shape are considerably reduced, and the accuracy of the tip manipulation is improved when changing external environmental structures.

I. INTRODUCTION

Tendon-driven continuum manipulators support minimally invasive procedures, but existing kinematic models often omit changes in proximal shaft shape. This paper proposes motor-current-based hysteresis shift detection and compensation, and evaluates it across shaft shapes and catheter inputs.

I. INTRODUCTION

  • TDCMs use tendon-driven bending to navigate narrow, tortuous environments, making them useful in minimally invasive treatment.They are also used in therapeutic and real-time diagnostic manipulators.Source: §I · p. 1
  • Prior approaches include friction and hysteresis compensation, but some hysteresis models require many parameters and complicated identification procedures.A simplified model treats dead zone and backlash together.Source: §I · p. 1
  • Existing TDCM kinematic models commonly assume a straight or fixed proximal shaft, omitting shape-change effects on tip-control accuracy.Adding tip sensors for feedback is practically constrained by sterilization, cost, and size.Source: §I · p. 1
  • The paper proposes motor-current-based dead-zone detection to adapt hysteresis compensation to proximal-shaft shape changes.It also analyzes shaft-shape effects and evaluates periodic and non-periodic inputs on multiple catheters across varied shaft curvatures.Source: §I · p. 2

A. Tendon-driven continuum manipulator

The manipulator uses tendon-driven knobs to steer a distal bending section, while its flexible proximal shaft can change shape with surrounding anatomy. Those shape changes alter tendon lengths and the bending section’s initial state, motivating compensation for accurate tip control.

A. Tendon-driven continuum manipulator

  • A TDCM-based device has tendon-sheath pull mechanisms, a flexible proximal shaft, and a bending section controlled by wires from the handle.The robot’s two knob angles, φ1 and φ2, steer the tip in two planes.Source: A. Tendon-driven continuum manipulator · p. 2

B. The effect of the TDCM proximal shaft shape changes on tendon controls

  • Proximal-shaft shape changes can make tendon-length changes nonzero, altering the bending section’s initial state and requiring compensation for precise tip control.External shape sensing may use fiber Bragg grating or optical, CT, or MRI images, but cost and size constrain those sensors.Source: B. The effect of the TDCM proximal… · p. 3
  • The modeled frictional behaviors include backlash from sheath–tendon friction and dead zone from structural wire slack in the driving parts.The section frames the task as identifying hysteresis changes and compensating configuration states to minimize error.Source: B. The effect of the TDCM proximal… · p. 3

C. Shift controls of hysteresis compensation

The proposed method is associated with dead-zone detection in a simplified hysteresis model, and can also be applied to other dead-zone-capable hysteresis models under a straight-shaft condition.

C. Shift controls of hysteresis compensation

  • The method builds on a simplified model that represents dead zone and backlash together, while its dead-zone detection can apply to any hysteresis model that handles dead zone in a straight-shaft condition.The simplified model is described as prior work.Source: C. Shift controls of hysteresis… · p. 3

1) Review of a simplified hysteresis model:

The simplified hysteresis model represents dead zone and backlash with eight piecewise-linear equations, divided between positive- and negative-velocity motion. Its parameters are identified from motor current in the straight-shaft condition, so it does not account for proximal-shaft shape changes.

1) Review of a simplified hysteresis model:

2) Experimental validation for dead zone and motor current:

A sinusoidal sweep was used to compare tip output and motor current across shaft shapes. The observed hysteresis shifted in opposite directions with the bending direction, and the figure marks estimated dead-zone values.

2) Experimental validation for dead zone and motor current:

3) Algorithm for shape-adaptive hysteresis compensation:

The method treats proximal-shaft shape changes as shifts in hysteresis and estimates the offset from motor-current gradients to update the dead-zone model. It requires suitable motions and does not detect dynamic dead-zone changes in real time.

3) Algorithm for shape-adaptive hysteresis compensation:

III. EXPERIMENT AND RESULT

The validation used motorized ICE catheters, with electromagnetic sensing to obtain tip pose as ground truth. Each catheter's hysteresis parameters were identified at the straight-shaft condition.

III. EXPERIMENT AND RESULT

  • Two electromagnetic sensors attached at the bending section's ends provided real-time tip position and orientation as ground truth via inverse kinematics.Source: §III · p. 5
  • The experiments used an ICE catheter on a motorized system that manipulated two knobs, φ1 and φ2.Source: §III · p. 5
  • Each catheter received a hysteresis model identified at the straight-shaft condition using motor-current estimates of Dpos, Dneg, Bpos, and Bneg, with ω set to the average value 1.45.Source: §III · p. 5

A. Experimental Setup: controllers, shape scenarios, input motions, conditions

The experiments compare three controllers across shaft shapes, input motions, and one- or two-degree-of-freedom operation. They assess tip-angle errors using PTPE and RMSE.

A. Experimental Setup: controllers, shape scenarios, input motions, conditions

  • Three controllers were compared: No Compensation, Compensation-Only, and Compensation+Shift, across straight, α = 45°, and α = 90° shaft scenarios.The tests used two ICE catheters and three trials.Source: A. Experimental Setup: controllers,… · p. 5
  • Tests covered one-DoF AP and LR bending and simultaneous two-DoF knob operation, with one knob moving twice as fast.Two-DoF operation was tested only with non-periodic inputs; the shaft curvature for each scenario was treated as fixed during testing.Source: A. Experimental Setup: controllers,… · pp. 5–6
  • The method updated the dead-zone shift for each shape scenario before testing, and performance was evaluated using mean and standard deviation of PTPE and RMSE.PTPE and RMSE improvements were measured relative to No Compensation and Compensation-Only.Source: A. Experimental Setup: controllers,… · pp. 5–6

B. Result of the non-linear hysteresis compensation

Compensation+Shift reduced tip-control errors across changing shaft shapes in one-DoF periodic tests and also improved results in two-DoF non-periodic tests. The two-DoF gains were smaller than the one-DoF gains in the reported comparison.

B. Result of the non-linear hysteresis compensation

  • Across straight, α = 45°, and α = 90° shaft conditions, No Compensation and Compensation-Only errors increased with shaft angle, while Compensation+Shift improved results.Figure 5 shows time-versus-output-angle and input-versus-output-angle traces for one catheter.Source: B. Result of the non-linear hysteresis… · p. 6
  • In one-DoF periodic tests, Compensation+Shift improved PTPE by 60% to 65% and RMSE by 69% and 79% against No Compensation.Table I reports PTPE and RMSE by shaft-shape scenario and controller; the text also reports PTPE improvements of 20% to 42% and RMSE improvements of 67% and 74%.Source: B. Result of the non-linear hysteresis… · p. 6, Table I · p. 7
  • In two-DoF non-periodic tests, PTPE improved by 17.7% to 45% and RMSE improved by 37.5% to 44%.Table II reports RMSE for two-DoF non-periodic inputs; Figure 6 depicts simultaneous knob manipulation.Source: B. Result of the non-linear hysteresis… · p. 7, Table II · p. 7, Figure 6 · p. 7

IV. DISCUSSION

The experiments support motor-current detection of hysteresis shifts and integration with existing dead-zone models. The discussion notes weaker two-DoF performance and workspace constraints on searching for the dead-zone boundary.

IV. DISCUSSION

  • Motor-current detection was effective at finding hysteresis shifts and was easy to integrate into a basic hysteresis model.The authors focused on updating existing model shifts without external sensors; they report tendon-curvature effects on backlash as negligible in dynamic motions.Source: §IV · p. 7
  • Two-DoF results improved, but less than one-DoF results; the authors attribute the shortfall to coupling effects that motor current did not capture as much as expected.They caution that motor-current-only compensation may be limited for higher-DoF manipulation in highly nonlinear coupled mechanisms.Source: §IV · p. 7
  • The search needs a small motion and enough bending-section workspace; dead zones are usually near knob neutral and below 20°.The straight-condition model can provide an initial dead-zone value for the search.Source: §IV · p. 7
  • At least one side of the dead zone must be free of collision, but a high motor-current gradient can signal contact and prompt a search in the other direction.The authors state that the ε upper boundary allows a safe motion and that the overall sweep need not require a large workspace.Source: §IV · p. 7

V. CONCLUSION

The paper uses motor-current-based gradient detection to identify hysteresis shifts caused by proximal-shaft shape changes, without external sensors. The compensator significantly improved tip-control performance across varied curvature, motion, and degree-of-freedom settings.

V. CONCLUSION

  • Gradient-based detection uses motor current to identify hysteresis shifts from arbitrary proximal-shaft shapes without external sensors, facilitating short calibration for varied environmental structures.Source: §V · pp. 7–8
  • Hysteresis-shift compensation significantly improved tip-control performance across varied curvature conditions, periodic and non-periodic inputs, and 1-DoF and 2-DoF settings.Without accounting for the shift, performance might be worse.Source: §V · p. 8
  • The detected hysteresis shift can be integrated with any hysteresis model that handles a dead zone.Source: §V · p. 8
Loading 2109.06907v1…