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Model-Less Feedback Control of Space-based Continuum Manipulators using Backbone Tension Optimization

Shrreya Rajneesh, Nikita Pavle, Rakesh Kumar Sahoo, Manoranjan Sinha

TL;DR

The paper tackles the challenge of controlling space-based continuum manipulators without detailed kinematic models. It introduces a model-less control framework that initializes and online-refines an empirical Jacobian, supplemented by backbone tension optimization to regulate axial loading. A real-time dual convex optimization pipeline computes actuator commands while adapting the Jacobian and enforcing tendon slack and geometric constraints. Validated on circular, pentagonal, and square planar trajectories, the approach achieves sub-millimeter accuracy with stable tension evolution, offering a scalable alternative to model-dependent continuum manipulation in constrained environments.

Abstract

Continuum manipulators offer intrinsic dexterity and safe geometric compliance for navigation within confined and obstacle-rich environments. However, their infinite-dimensional backbone deformation, unmodeled internal friction, and configuration-dependent stiffness fundamentally limit the reliability of model-based kinematic formulations, resulting in inaccurate Jacobian predictions, artificial singularities, and unstable actuation behavior. Motivated by these limitations, this work presents a complete model-less control framework that bypasses kinematic modeling by using an empirically initialized Jacobian refined online through differential convex updates. Tip motion is generated via a real-time quadratic program that computes actuator increments while enforcing tendon slack avoidance and geometric limits. A backbone tension optimization term is introduced in this paper to regulate axial loading and suppress co-activation compression. The framework is validated across circular, pentagonal, and square trajectories, demonstrating smooth convergence, stable tension evolution, and sub-millimeter steady-state accuracy without any model calibration or parameter identification. These results establish the proposed controller as a scalable alternative to model-dependent continuum manipulation in a constrained environment.

Model-Less Feedback Control of Space-based Continuum Manipulators using Backbone Tension Optimization

TL;DR

The paper tackles the challenge of controlling space-based continuum manipulators without detailed kinematic models. It introduces a model-less control framework that initializes and online-refines an empirical Jacobian, supplemented by backbone tension optimization to regulate axial loading. A real-time dual convex optimization pipeline computes actuator commands while adapting the Jacobian and enforcing tendon slack and geometric constraints. Validated on circular, pentagonal, and square planar trajectories, the approach achieves sub-millimeter accuracy with stable tension evolution, offering a scalable alternative to model-dependent continuum manipulation in constrained environments.

Abstract

Continuum manipulators offer intrinsic dexterity and safe geometric compliance for navigation within confined and obstacle-rich environments. However, their infinite-dimensional backbone deformation, unmodeled internal friction, and configuration-dependent stiffness fundamentally limit the reliability of model-based kinematic formulations, resulting in inaccurate Jacobian predictions, artificial singularities, and unstable actuation behavior. Motivated by these limitations, this work presents a complete model-less control framework that bypasses kinematic modeling by using an empirically initialized Jacobian refined online through differential convex updates. Tip motion is generated via a real-time quadratic program that computes actuator increments while enforcing tendon slack avoidance and geometric limits. A backbone tension optimization term is introduced in this paper to regulate axial loading and suppress co-activation compression. The framework is validated across circular, pentagonal, and square trajectories, demonstrating smooth convergence, stable tension evolution, and sub-millimeter steady-state accuracy without any model calibration or parameter identification. These results establish the proposed controller as a scalable alternative to model-dependent continuum manipulation in a constrained environment.

Paper Structure

This paper contains 13 sections, 16 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Kinematic Modeling of Continuum Manipulators
  3. Constant Curvature Approximation
  4. Surrogate Forward–Kinematics Model
  5. Empirical Jacobian Estimation
  6. Backbone Tension Optimization
  7. Optimal Actuation Using Convex Optimization
  8. Online Jacobian Adaptation
  9. Results and Discussion
  10. Tip Trajectory Tracking
  11. Tendon Tension Evolution
  12. Tracking Error Evolution
  13. 3D Manipulator Snapshots

Figures (5)

  • Figure 1: Flowchart of the proposed dual convex-optimization control pipeline with backbone tension regulation.
  • Figure 2: Tracked versus reference trajectories for the (a) circle, (b) pentagon, and (c) square paths
  • Figure 3: Tendon–tension evolution for the three reference paths: (a) circle, (b) pentagon, and (c) square paths.
  • Figure 4: Error Vs Distance traversed on the trajectories for the (a) circle, (b) pentagon, and (c) square paths
  • Figure 5: 3D manipulator snapshots at different timestamps for the three reference trajectories: (a) circle, (b) pentagon, and (c) square.