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S-Rolling: Steerable Rolling Gaits for Twistable Snake Robots in Low-Clearance Environments

Qingling Fan, Zhongqiang Ren

arXiv:2610.29478v1cs.RO

TL;DR

Low-clearance navigation requires snake robots to keep a small swept height while remaining steerable, a combination existing gaits do not readily provide. This paper develops S-rolling for twistable snake robots, using independently rolling body segments and a central twist joint. Real-robot tests show heading changes in low-clearance settings where the rolling arc baseline cannot change heading.

  • Problem

    Low-clearance environments require a small swept height, but rolling gaits generally offer limited steering while sidewinding’s vertical undulation may cause ceiling collisions.

    Source: §I · p. 1

  • Method

    S-rolling uses an S-shaped backbone with independently rolling head and tail segments, a central twist joint for their relative rotation, and a quasi-static model relating segment speeds to robot velocities.

    Source: §I · p. 2, 4) Piecewise Rolling Control and Twist… · p. 4, §V · p. 7

  • Results

    Approximately 90° and 180° heading changes were demonstrated in low-clearance tasks, whereas the rolling arc gait cannot change the robot’s heading.

    Source: §I · p. 2

  • Takeaways & Limitations

    S-rolling combines low-swept-height planar rolling with steering capability that existing rolling gaits lack.

    Source: §V · p. 7

Abstract

from arXiv · show

Snake robots can traverse complex environments with limbless locomotion, but maneuvering in low-clearance environments remains challenging because a gait must maintain a small swept height while also providing planar steering. Existing rolling gaits preserve a low swept height body configuration but generally provide limited steering, whereas steering gaits often introduce vertical undulation and require additional clearance. With that in mind, this paper develops S-rolling, a steerable rolling gait that combines low swept height locomotion with planar maneuverability for twistable snake robots. S-rolling is designed using an S-shaped planar backbone curve, whose head and tail segments roll with independently controlled angular velocities, producing different motion modes. We derive its joint space gait equation, in which a central twist joint realizes the relative rotation between the two segments. We also develop a quasi-static kinematic model relating the segment rolling speeds to the linear and angular velocities of the robot. Real-robot experiments demonstrate the various motion modes, traversal through a 10 cm clearance test track, and maneuvering tasks beneath a large workpiece and a car chassis. In these low-clearance scenarios, S-rolling successfully performs approximately 90$^\circ$ and 180$^\circ$ heading changes, whereas the baseline rolling arc gait cannot change the robot heading.

I. INTRODUCTION

Low-clearance navigation calls for both a small swept height and planar maneuverability, but existing low-height gaits offer limited steering while some steerable gaits add vertical undulation. The paper develops S-rolling for twistable snake robots and evaluates it in low-clearance experiments.

I. INTRODUCTION

  • Low-clearance navigation requires a small swept height, yet rolling and rectilinear gaits generally offer little steering and sidewinding’s vertical undulation may cause ceiling collisions.The paper frames the challenge as maintaining a small cross section while remaining maneuverable in restricted vertical space.Source: §I · p. 1
  • S-rolling uses an S-shaped backbone and independently controlled rolling speeds for the head and tail segments to enable steerable motion without additional vertical undulation.The S-shaped curve consists of two tangential circular arcs with opposite signed curvatures.Source: §I · pp. 1–2
  • The paper derives joint-space gait equations and a quasi-static kinematic model that maps segment rolling speeds to the robot’s linear and angular velocities.The model reduces locomotion control to a differential-drive-car representation for maneuvering.Source: §I · p. 2
  • S-rolling completes approximately 90° and 180° heading changes in low-clearance tasks, while the rolling arc baseline cannot change the robot’s heading.Real-robot tests include a 10 cm-clearance track and tasks beneath a large workpiece and a car chassis.Source: §I · p. 2

A. Gait Design Methods

  • Backbone-curve methods provide a geometric basis for designing S-rolling and deriving its joint-space equation.The paper positions this approach against gait-design methods that offer limited geometric interpretability.Source: A. Gait Design Methods · p. 2

B. Rolling and Low-Clearance Locomotion

Low-clearance settings restrict vertical motion while leaving the horizontal plane available for maneuvering, making steering a key challenge for low-height rolling gaits. The section introduces the geometric frame representation and method used to design and model S-rolling.

B. Rolling and Low-Clearance Locomotion

  • The rolling arc gait maintains low swept height but provides no steering, while steering some low-height gaits requires additional vertical waves or lifting.Sidewinding steers effectively but increases swept height.Source: B. Rolling and Low-Clearance Locomotion · p. 2
  • The proposed low-clearance setting constrains gravity-direction motion but not the horizontal plane, and defines a gap by 1 ≤ h_z/A_cd < 2.Here h_z is gap height and A_cd is the snake robot’s cross-sectional diameter.Source: B. Rolling and Low-Clearance Locomotion · p. 2

III. METHOD

  • The method designs the backbone curve, fits it to T-Snake’s discrete structure to derive gait equations, and then develops a kinematic model.These steps are described as Sections III-A through III-D.Source: §III · p. 2

A. Design of Backbone Curves

1) Dorsal Reference Curve:

  • The dorsal reference curve’s shape equation uses curvature functions for two axes perpendicular to the tangent and a torsion function along the curve.The passage identifies these shape functions as κ_a, κ_b, and τ.Source: 1) Dorsal Reference Curve · p. 3

2) Rolling Description:

The rolling description uses relative frame rotation to produce lateral rolling, while S-rolling’s backbone is a closed-form planar S made from two tangential circular arcs with opposite signed curvatures.

2) Rolling Description:

  • In the torsion-free bellows model, the robot can bend but not twist, and time-varying relative frame rotation generates lateral rolling.The relative rotation is spatially invariant along the curve at any given time.Source: 2) Rolling Description · p. 3

3) Backbone Curve of S-Rolling:

  • S-rolling’s backbone comprises two tangential arcs of equal length and curvature magnitude but opposite signed curvatures, forming an S-shaped curve for kinematic analysis.Its closed-form parametric representation is given in Eq. (8).Source: 3) Backbone Curve of S-Rolling · p. 3
  • Placing the curve midpoint at the origin and its endpoints on opposite x-axis sides removes arbitrary translation and rotation, yielding a unique world-frame representation.The endpoints lie on the negative and positive x-axis, respectively.Source: 3) Backbone Curve of S-Rolling · p. 3
  • The tangent angle is integrated under endpoint conditions ψ(L/4) = ψ(3L/4) = 0, then the tangent vector is integrated to obtain the backbone curve.The midpoint condition cr(L/2) = 0 fixes the resulting parametric expression.Source: 3) Backbone Curve of S-Rolling · pp. 3–4

4) Piecewise Rolling Control and Twist Angle:

S-rolling assigns separate tangent-axis frame rotations to the head and tail segments, whose independently controlled rolling produces distinct motion modes and a relative twist at their junction.

4) Piecewise Rolling Control and Twist Angle:

  • The head and tail occupy s ∈ [0, L/2] and s ∈ (L/2, L], respectively, and each segment’s frame rotates about its tangent by a separate angle.The resulting frames are denoted Dh and Dt.Source: 4) Piecewise Rolling Control and Twist… · p. 4
  • The time derivatives of the head and tail rotation angles define their rolling speeds, ωh and ωt, respectively.The derivation considers constant rates of change for both angles.Source: 4) Piecewise Rolling Control and Twist… · p. 4
  • Unequal segment rotations create a finite tangent-axis rotation jump at s = L/2, defined as the twist angle and incorporated into the gait equation.Different rolling directions and speeds across the segments produce different locomotion modes.Source: 4) Piecewise Rolling Control and Twist… · p. 4

B. Discrete Mechanism of T-Snake

The T-Snake mechanism is built from identical three-joint modules whose dorsal, twist, and lateral axes are arranged relative to the backbone. Their rotations discretely represent the backbone’s curvature and torsion.

B. Discrete Mechanism of T-Snake

  • Each of the n identical modules contains three 1-DoF revolute joints in a dorsal-twist-lateral sequence.The dorsal and lateral axes pass through the cross-sectional center, span the backbone’s normal plane, and are mutually orthogonal when straight; the twist axis follows the backbone tangent.Source: B. Discrete Mechanism of T-Snake · p. 4
  • In the straight configuration, the dorsal and lateral bending axes are mutually orthogonal, and the twist axis is orthogonal to both.The twist axis is locally aligned with the backbone tangent.Source: B. Discrete Mechanism of T-Snake · p. 4
  • The dorsal and lateral joint rotations represent accumulated curvatures κb and κa, respectively, while twist rotation represents accumulated torsion τ.Each module has length L0; the complete mechanism has 3n DoFs and length L = nL0.Source: B. Discrete Mechanism of T-Snake · p. 4

C. Gait Equations

S-rolling’s gait equations convert the designed backbone shape into joint-angle commands for the T-Snake. A central twist joint realizes the relative twist between the head and tail segments.

C. Gait Equations

  • The central twist joint of the (k + 1)-th module realizes the relative twist between the head and tail segments.The design uses an odd number of modules so the body midpoint aligns with that joint.Source: C. Gait Equations · pp. 4–5
  • Integrating the backbone shape functions between adjacent joints yields the corresponding dorsal and lateral joint angles.These angles are used to control the T-Snake.Source: C. Gait Equations · pp. 4–5
  • Equations (12b), (13b), and (14) jointly govern the T-Snake’s dorsal, lateral, and twist joint angles.Source: C. Gait Equations · p. 5

D. Kinematic Modeling

The paper derives a quasi-static kinematic model relating the head and tail segments’ rolling speeds to the T-Snake’s planar motion. Equal rolling speeds produce straight travel, while unequal speeds produce turning.

D. Kinematic Modeling

  • The kinematic model is derived under a quasi-static approximation, assuming uniform mass per arc-length and spatially invariant rolling speed within each segment.The uniform-density assumption places the center of mass at the backbone’s geometric centroid.Source: D. Kinematic Modeling · p. 5
  • The world-frame kinematic model relates the head and tail rolling speeds to the T-Snake’s planar pose velocity.The model expresses the pose using the center-of-mass position and body heading; its coefficients are defined in the text.Source: D. Kinematic Modeling · p. 5
  • Equal head and tail rolling speeds yield straight motion, while unequal speeds yield turning.The paper reports hardware demonstrations of these motion modes.Source: D. Kinematic Modeling · p. 6

IV. EXPERIMENTAL RESULTS

The experiments evaluate S-rolling on T-Snake hardware through motion demonstrations, a clearance test track, and tasks in two low-clearance environments.

IV. EXPERIMENTAL RESULTS

  • Real-robot experiments show T-Snake’s S-rolling gait generates various motion modes from different rolling-speed combinations, demonstrates maneuverability on a challenging test track, and accomplishes tasks designed for two real-world LCEs.Source: §IV · p. 6
  • The hardware’s twist joints have no torsional angle limits, allowing the head and tail segments to twist relative to each other without restriction.Source: §IV · p. 6
  • Across experiment groups, module count and head and tail rolling speeds vary; common settings include 0.2055 m modules, 50 Hz command updates, and 0.5 rad angular amplitude.Source: §IV · p. 6

A. Different Motion Modes

A three-module T-Snake experiment on a flat indoor surface tests S-rolling’s translation and turning capabilities.

A. Different Motion Modes

1) Translating:

Laboratory tests show S-rolling can translate, turn in place, and maneuver through low-clearance test-track passages. The model predicts translation more accurately than in-place turning, where ground slip is identified as the source of discrepancy.

1) Translating:

  • The model predicts 1.75 cm/s translation, while measured forward and backward averages are (1.86 ± 0.20) cm/s and (1.97±0.19) cm/s, with relative errors of 5.7% and 10.9%.Ten velocity measurements were performed for each motion.Source: 1) Translating · p. 6

2) In-place Turning:

  • In-place turning measures (8.03±0.72) °/s clockwise and (7.54±0.50) °/s counterclockwise, versus a 4.19 °/s model prediction; the authors attribute the discrepancy to ground slip.The model predicts zero linear velocity when head and tail rolling speeds are opposite; further analysis of slip is left for future work.Source: 2) In-place Turning · p. 6

B. Maneuverability in Low-Clearance Environments

  • Under a large workpiece, the rolling arc gait cannot reach the target exit, while S-rolling completes the task.The figure compares the two gaits and includes a bottom view of traversal beneath the workpiece.Source: Figure 7 · p. 7
  • On the 10 cm-clearance track, the robot moves forward, reverses, turns approximately 90°, and uses differential steering through a curved track.The track contains two low-clearance passages and measures 3 m×4 m.Source: B. Maneuverability in Low-Clearance… · p. 7

C. Real-world Scenario Experiments

Real-world tests compare S-rolling with rolling arc beneath a workpiece and car chassis, where the baseline cannot steer to complete the tasks. The conclusion identifies future work in autonomous navigation and onboard sensing.

1) Under a Large Workpiece:

  • At a 15 cm-clearance workpiece, S-rolling steers from one side to the orthogonal exit, whereas rolling arc cannot steer from its straight path.The workpiece test represents an LCE serving as the only passage between two spaces.Source: 1) Under a Large Workpiece · p. 7

2) Under a Car Chassis:

V. CONCLUSION AND FUTURE WORKS

  • S-rolling combines planar rolling’s low swept height with steering capability lacking in existing rolling gaits, as demonstrated in track and real-world tests.The gait uses a designed backbone curve, a joint-space equation with a central twist joint, and a quasi-static model relating segment rolling speeds to robot velocities.Source: §V · p. 7
  • Future work will extend S-rolling from teleoperation to closed-loop autonomous navigation and integrate onboard sensing for inspection and nondestructive testing.Source: §V · p. 7
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