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Image-Based Path-Planning for Navigation of Soft-Growing Robots in the Spinal Sub-Arachnoid Space

George Dimas, Panagiotis G. Kalozoumis, Panagiotis Vartholomeos, Dimitris K. Iakovidis

arXiv:2610.12631v1cs.ROeess.SY

TL;DR

Path planning in the complex 3D SSS must protect delicate tissue while meeting the navigation requirements of a soft-growing robot. The paper extends A* with image-based costs for obstacle proximity and anchor points. In the evaluated SSS model, the proposed method anchored the robot where traditional A* did not, supporting steering along the planned path.

  • Problem

    The robot needs a safe path through the complex SSS that protects delicate tissue while satisfying its navigation requirements.

    Source: §I · p. 1

  • Method

    The paper extends A* for image-based 3D planning, adding costs that favor anchor-capable nodes and account for obstacle proximity.

    Source: §I · p. 2, B. Extended A* Algorithm for… · p. 3

  • Results

    In the SSS model comparison, the proposed algorithm anchored the robot on opposite sides of the growing element, while traditional A* failed to meet that requirement.

    Source: C. Qualitative Results · p. 5

  • Takeaways & Limitations

    The detailed-model evaluation supports the additional cost functions’ capacity to enable navigation through delicate tissue while meeting robot movement requirements and maintaining path efficiency.

    Source: §IV · p. 6

    The study did not evaluate SSS phantoms, real-world MRI data from different individuals, finite element simulations, or the robot’s kinematics.

    Source: §IV · p. 6

Abstract

from arXiv · show

Recently, soft robotic procedures are being developed aiming at achieving targeted minimally invasive operations or drug administration in specific locations in the human body. Accordingly, specialized path-planning algorithms need to be investigated for the estimation of efficient paths that would protect the delicate tissue structures and simultaneously satisfy a set of requirements for the efficient navigation of the robot. In this context, we propose an image-based 3D pathplanning algorithm, which is an extension of the A* algorithm, for the navigation of a soft-growing robot inside the spinal subarachnoid space (SSS). The proposed algorithm is capable of estimating a safe pathway towards the goal location, while ensuring the establishment of anchor points that facilitate the efficient steering of the soft robot. The algorithm is evaluated using a highly detailed model of the SSS with respect to its capacity to satisfy the robot movement requirements and path efficiency.

I. INTRODUCTION

The paper addresses the challenge of planning safe paths through the complex 3D spinal sub-arachnoid space (SSS), where the robot must protect delicate tissues and meet its own navigation requirements. It extends A* for image-based planning that accounts for robot maneuverability and anchor points.

I. INTRODUCTION

  • The project envisions MRI-guided access through the SSS to deep brain regions, where a drug-loaded scaffold would attach to ventricle walls and release therapeutics.The stated motivation is localized delivery to brain regions that current therapies may not adequately address.Source: §I · p. 1
  • The SSS contains delicate neural tissues that a path must protect while meeting the robot’s requirements for successful navigation.The SSS includes structures such as the spinal cord, nerve rootlets, and blood vessels, and cerebrospinal fluid helps protect neural tissue.Source: §I · p. 1
  • Unlike many medical path-planning settings focused on avoiding tissue contact, the soft-growing robot needs its growing element to contact surrounding structures for anchor points.The catheter must avoid critical anatomy, while the growing element uses contact to support steering precision along the path.Source: §I · pp. 1–2
  • Prior work on contact-based robot navigation used a simplified 2D projection, whereas the SSS’s complex structure motivates planning in the actual 3D image volume.The paper uses MRI scans as the localization method, with the image stack forming a volume for path estimation.Source: §I · p. 2
  • The proposed method extends A* with costs that favor nodes near obstacles and nodes that can provide anchor points, then evaluates paths using a detailed SSS model.The study also counts actuation nodes—path nodes where the robot changes direction—to assess path efficiency.Source: §I · p. 2

II. METHODOLOGY

This section introduces the robot’s movement requirements and the additional A* cost functions used to support path estimation. The robot’s catheter can rotate, translate, and bend.

II. METHODOLOGY

  • The methodology analyzes additional A* cost functions intended to improve path estimation in line with the robot’s movement requirements.The section covers the robot specification, movement requirements, navigation configuration space, and cost functions.Source: §II · p. 2
  • The growing element’s anchor points and the catheter’s maneuverability are the movement requirements that the added costs are intended to address.The section frames the cost functions as tools for satisfying those requirements during path estimation.Source: §II · p. 2
  • The catheter can rotate around the Z-axis, translate along it, and bend over the X-Z plane when tendon tension is applied.The robot comprises a growing element and a steerable catheter with tendon.Source: Figure 1 · p. 2

A. Soft-Robot Growing & Navigation Principles

The robot combines a pressurized soft growing element with a tendon-driven catheter, and its tip is planned under a follow-the-leader assumption. Candidate anchors arise from contact between opposite sides of the growing element and surrounding structures.

A. Soft-Robot Growing & Navigation Principles

  • Pressurizing the saline-filled growing element enables eversion and translation of its active channel, while the tendon bends the catheter tip in one direction.Combining translation, longitudinal rotation, and tendon-driven bending enables navigation in multiple directions.Source: A. Soft-Robot Growing & Navigation… · p. 2
  • The path-planning model considers only the robot tip, assuming the rest of the catheter follows the tip’s path.This is the paper’s follow-the-leader navigation assumption.Source: A. Soft-Robot Growing & Navigation… · p. 2
  • The robot tip is modeled as a catheter disk inside a soft growing-element annulus, with their radii denoted r_c and r_g.The model uses a co-centered cross-section.Source: A. Soft-Robot Growing & Navigation… · p. 2
  • A node can serve as an anchor when the growing element contacts obstacles simultaneously on opposite sides; excessive intersection area makes the path nontraversable.The intersection area is assessed relative to the total cross-sectional area.Source: A. Soft-Robot Growing & Navigation… · p. 3

B. Extended A* Algorithm for Image-based Path-Planning

The extended A* method uses image-based path costs to account for anchor availability and proximity to obstacles. Its anchor cost adapts according to whether a node is anchored.

B. Extended A* Algorithm for Image-based Path-Planning

  • A* evaluates nodes using a path cost g(n) and heuristic h(n), which estimate distances from the node to the start and target, respectively.The usual implementation combines them as f(n) = g(n) + h(n).Source: B. Extended A* Algorithm for… · p. 3
  • Because A* can produce paths near obstacles without guaranteeing anchors, the method adds a parametric cost c_a to favor nodes that can provide anchor points.The distance-based behavior of A* is accepted, but anchor availability requires an additional cost.Source: B. Extended A* Algorithm for… · p. 3
  • The adaptive parameter k(n) resets to zero at anchored nodes and increments at nodes that are not anchored.This parameter changes according to the node’s anchoring status.Source: B. Extended A* Algorithm for… · p. 3
  • A separate cost c_b favors proximity to obstacles by penalizing nodes farther from the nearest obstacle.The robot cross-section and segmented SSS slice illustrate how overlapping regions indicate safe anchoring.Source: B. Extended A* Algorithm for… · p. 3, Figure 2 · p. 3

C. Navigation Configuration Space

The navigation space is built from a binary stack of SSS segmentation maps, with separate free and obstacle spaces for the catheter and growing element. The path also distinguishes anchor points and catheter-actuation nodes to represent robot movement requirements.

C. Navigation Configuration Space

  • The SSS volume is represented as an image stack of segmentation maps derived from the 3D object.The stack records anatomical structures and free space as binary labels.Source: C. Navigation Configuration Space · p. 3, Figure 3 · p. 4
  • The configuration space assigns each voxel in the segmentation stack a unique integer-coordinate position, with free and obstacle subspaces determined by its binary label.The stack uses 1 for anatomical structures and 0 for free space.Source: C. Navigation Configuration Space · p. 3
  • The catheter's free and obstacle spaces are defined separately, while a growing-element node is possible when its obstacle-intersection area ratio is below threshold v.The growing-element annulus area is evaluated around the node; its free and obstacle spaces depend on design factors such as pressure.Source: C. Navigation Configuration Space · p. 4
  • A growing-element node is an anchor when the element contacts obstacles on opposite sides, either left–right or up–down.The annulus's outer circle is divided into four arcs to identify opposite contact regions.Source: C. Navigation Configuration Space · p. 4
  • A catheter node is an actuation node when its angle relative to the preceding and following path nodes is non-zero.The angle is estimated from three consecutive nodes.Source: C. Navigation Configuration Space · p. 4

A. Experimental Setup

The method was evaluated on a processed digital SSS model using randomly selected start and end points. Across 200 runs, the variants trade off anchor frequency against path complexity and actuation.

A. Experimental Setup

  • The digital SSS model was converted in 3D Slicer into a stack of segmentation-like images to shorten validation time on actual data.Of 574 maps at 223×128 resolution, 413 were retained after segments outside the robot's intended operating region were discarded; slices had 0.547×0.547 mm2 in-plane resolution and 1 mm thickness.Source: A. Experimental Setup · p. 4
  • The catheter radius was 0.5 mm, the GE radius was 1 mm, the safe-passage threshold v was 80%, and the k(n) steepness factor z was 5.Source: A. Experimental Setup · p. 4
  • The comparison measured APAP, ADT, and APAN; higher APAP indicates more stable maneuvering, while lower ADT and APAN indicate lower path complexity.The compared variants were full A*, original A* using g and h, and A* using only ca and cb.Source: A. Experimental Setup · pp. 4–5
  • Both full A* and A* using only ca achieved the highest anchor-point percentage, while ca alone yielded a lower actuation-node percentage.Simple A* had lower ADT and APAN but also lower APAP, so the authors identify a balance among anchoring and path complexity as necessary for feasible navigation.Source: A. Experimental Setup · p. 5
  • The evaluation used 200 runs, with random start and end points selected from the first and last segmentation maps and restricted to catheter and GE free space.The results compare the proposed method with original A* and A* using only ca and cb.Source: A. Experimental Setup · p. 5

C. Qualitative Results

Qualitative checks in the SSS model show the proposed path avoiding obstacles while maintaining GE anchoring. Unlike traditional A*, it satisfies the opposite-side anchoring requirement; its abrupt turns are described as amenable to smoothing.

C. Qualitative Results

  • Rendered as a 2 mm tube in the SSS model, the proposed path avoided obstacles and showed stable wall anchoring.The tube diameter matched the GE's outer diameter.Source: C. Qualitative Results · p. 5
  • The path’s direction changes appeared abrupt, but post-processing smoothing could correct them without affecting anchoring points.Source: C. Qualitative Results · p. 5
  • The proposed path anchored the GE on opposite sides, whereas traditional A* failed this requirement and left locations where steering could be compromised.Fig. 5 compares the paths in cross-section; blue lines indicate intersections that ensure safe anchoring.Source: C. Qualitative Results · p. 5, Figure 5 · p. 5

IV. CONCLUSIONS

On a highly detailed SSS model, the image-based A* extension’s additional cost functions supported safe navigation through delicate tissues while meeting robot movement requirements and maintaining path efficiency. Phantom and real-world MRI-derived data, finite-element simulations, and robot kinematics are identified as future work.

IV. CONCLUSIONS

  • On a highly detailed SSS model, additional cost functions enabled navigation through delicate tissues while fulfilling robot movement requirements and maintaining path efficiency.Source: §IV · p. 6
  • The image-based A* extension estimates safe paths toward targets and anchor points for soft-growing robot steering and maneuverability.Source: §IV · p. 6
  • Future work will evaluate SSS phantoms, MRI-derived anatomy, finite-element simulations, and robot kinematics not considered in this study.Source: §IV · p. 6
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