Source-linked AI summary
Linear Twisting Sidewinding Gaits for Twistable Snake Robot Motion Planning on Complex Terrains
Qingling Fan, Zhongqiang Ren
TL;DR
Sidewinding can be slow or struggle on uneven terrain, while the rolling-vector approach concentrates twisting load on two joints. This paper introduces linear twisting sidewinding to spread that load across the body. In real-robot tests, it reduces peak twist-joint power and traverses terrain faster than conventional sidewinding.
Problem
Sidewinding can be slow on flat ground or get trapped on uneven terrain, and the rolling-vector approach concentrates twisting on two middle joints.
Source: §I · p. 1Method
The paper proposes linear twisting sidewinding, which varies twist linearly along the backbone to distribute twisting over the entire body.
Source: §I · p. 1Results
42% lower peak output power of a single twist joint under similar angular velocities and total output power, and traversal time reduced by up to 49% versus conventional sidewinding.
Source: §I · p. 2Takeaways & Limitations
Real-robot experiments demonstrate lower peak twist-joint load and faster traversal on various complex terrains.
Source: §V · p. 8
Abstract
from arXiv · showhide
Sidewinding is an efficient gait for snake robots to locomote on various terrains, by undulating the backbone curve and shifting the contact segments along it. However, relying solely on undulatory motion limits the locomotive capability of snake robots, and combining it with twisting motion can improve their speed and robustness. This hypothesis has recently been verified by the rolling vector approach, which locomotes the robot like a differential-drive car. Yet its twisting is concentrated in a short buffer segment, imposing most of the workload on the two twist joints in the middle, which can often overburden the motors and limit its locomotion. With that in mind, this paper develops a new family of twisting sidewinding gaits that distribute the workload over the entire body with our proposed linear twisting function. Under matched turning speed and total output power, our gaits reduce the peak output power of a single twist joint by 42%. Real-robot experiments show that, with the reduced workload, our new gaits can locomote the robot in various terrains that the existing rolling vector approach cannot. Besides, our new gaits can move up to 49% faster than conventional sidewinding without twisting.
I. INTRODUCTION
The paper addresses uneven twist-joint loading in twisting sidewinding by proposing gaits that distribute twist across the body. It situates this design within prior snake-robot gait work and develops it using backbone-curve methods.
I. INTRODUCTION
- Sidewinding is efficient and robust, but can be slow or get trapped on uneven terrain; the rolling-vector approach concentrates twist in a short buffer that burdens two middle joints.Linear twisting sidewinding varies twist linearly along the backbone; uniform twist produces rolling sidewinding, while varying twist produces turning, with the zero-rolling-speed point acting as a movable turning center.Source: §I · pp. 1–2
- 42% lower peak output power of a single twist joint under similar angular velocities and total output power, while traversal time falls by up to 49% versus conventional sidewinding.The real-robot comparison reports the load reduction during in-place turning and faster traversal across four outdoor terrain types.Source: Figure 1 · p. 1, §I · p. 2
II. RELATED WORKS
- Prior snake-robot gait design includes central pattern generators, reinforcement learning, parameterized gait equations, and backbone-curve methods, while sidewinding supports varied terrain and maneuvers.The paper also distinguishes twistable robot mechanisms and notes that T-Snake can twist its backbone without limit, meeting the proposed gaits’ mechanical requirement.Source: §II · p. 2
III. METHOD
- The method adopts a sidewinding backbone curve, applies linear twisting, and uses a piecewise-approximation integration method based on T-Snake’s joint arrangement to generate executable joint angles.The sidewinding backbone is represented as a time-varying elliptical helix.Source: §III · p. 2, Figure 2 · p. 2
A. Dorsal Reference Curves
Dorsal reference curves represent the robot’s shape and axial twist through frames and shape functions. The paper uses bellows and complete models to distinguish bending-only motion from motion that includes twisting.
1) Dorsal Reference Frames:
- Dorsal reference frames use orthonormal tangent, normal, and binormal vectors along a spatial curve to specify its shape and dorsal–ventral distinction.The two curvature functions describe curvature along axes perpendicular to the tangent, while τ describes torsion along the curve.Source: 1) Dorsal Reference Frames · p. 2
2) Torsion Description:
- The bellows model sets τ to zero and represents bending without twisting, whereas the complete model allows nonzero curvature and torsion to represent both bending and twisting.The paper uses bellows and complete frames to model rolling and twisting motion, respectively.Source: 2) Torsion Description · pp. 2–3
- The relative rotation angle from bellows frame B to complete frame C varies along the curve to describe torsion through the shape-function relationships.The paper uses these relationships to design the proposed gaits.Source: 2) Torsion Description · p. 3
B. Backbone Curve of Sidewinding
The method starts from a time-varying elliptical-helix backbone for sidewinding, then combines it with a linear twist function to construct a family of gaits.
B. Backbone Curve of Sidewinding
- The sidewinding backbone is a time-varying elliptical helix, parameterized by θ and converted numerically to arc length s for the subsequent derivation.The paper identifies t as time, ωt as temporal wave frequency, kθ as pitch, and kb and ka as horizontal and vertical amplitudes.Source: B. Backbone Curve of Sidewinding · p. 3
C. Backbone Curve of Linear Twisting Sidewinding
- The gait family applies a linear twist function to the sidewinding backbone using the complete model, with specific parameter settings producing rolling sidewinding and twisting sidewinding.The method defines head orientation and derives bellows-frame shape functions before obtaining complete frames.Source: C. Backbone Curve of Linear Twisting… · p. 3, Figure 3 · p. 3
1) Orientation of Snake Head:
The head frame is anchored to the backbone tangent, with its remaining orientation set by projecting the world vertical into the tangent’s normal plane. The bellows-frame shape functions are derived through the Frenet-Serret frame and a torsion-free alignment.
1) Orientation of Snake Head:
- At the head, the first bellows-frame vector follows the backbone tangent; projecting world vertical onto the normal plane defines the remaining orientation.The projected vector is normalized to obtain the frame’s a-axis.Source: 1) Orientation of Snake Head · p. 3
2) Construction of the Bellows Frame Along the Curve:
- The construction first derives the Frenet-Serret frame’s curvature and torsion, then uses its relative rotation to obtain curvature in the bellows frame.The stated sequence is to construct the Frenet-Serret frame, derive the relative angle, and substitute these quantities into Eq. (2a).Source: 2) Construction of the Bellows Frame… · pp. 3–4
- The bellows frame is torsion-free, so its torsion is constrained to zero.The relative rotation from the Frenet-Serret frame is derived using this condition and the frame orientation.Source: 2) Construction of the Bellows Frame… · p. 4
- The integral term removes Frenet-Serret-frame torsion, while a spatially invariant offset aligns that frame with the bellows-frame orientation.The offset is determined from the frames’ orientations at the curve’s start.Source: 2) Construction of the Bellows Frame… · p. 4
3) Linear Twisting and Complete-Frame Shape Functions:
A linear twist maps the bellows frame to complete frames, which define the T-Snake’s shape and drive its motion. The map’s coefficients generate a family of linear twisting gaits.
3) Linear Twisting and Complete-Frame Shape Functions:
- The linear twist function maps the bellows frame to complete frames that define the T-Snake’s actual shape and drive its motion.The function varies linearly with arc-length and generates motion as time advances.Source: 3) Linear Twisting and Complete-Frame… · p. 4
- Fig. 4 contrasts constant rolling velocity for rolling sidewinding with arc-length-varying velocity for twisting sidewinding.The caption associates constant velocity with translation and linearly varying velocity with turning.Source: Figure 4 · p. 4
- The coefficients a1 and a0 are the twisting and rolling coefficients, and modulating them generates linear twisting gaits.The complete-frame shape functions are derived from the bellows-frame functions and the relationship between the two frames; numerical integration yields joint angles to execute the gait.Source: 3) Linear Twisting and Complete-Frame… · p. 4
4) Gait Specialization:
The rolling-velocity profile determines the gait: uniform velocity gives rolling sidewinding, while a linear spatial gradient gives twisting sidewinding. Its parameters can be used to locate the turning center.
4) Gait Specialization:
- When a1 = 0 and a0 ≠ 0, uniform rolling velocity produces rolling sidewinding; setting both coefficients to zero recovers conventional sidewinding.The body rotates about its backbone at spatially constant angular velocity in rolling sidewinding.Source: 4) Gait Specialization · p. 5
- When a1 ≠ 0, rolling velocity varies linearly along the backbone, producing twisting sidewinding with a turning center where local rolling velocity vanishes.The turning center is s0 = −a0/a1.Source: 4) Gait Specialization · p. 5
- Changing a1 and a0 allows the T-Snake’s turning behavior to be designed by locating the turning center.The twist function can potentially combine with arbitrary gait curves, though this paper focuses on sidewinding.Source: 4) Gait Specialization · pp. 4–5
D. From Curve to Gaits
The section reviews conventional curve-to-joint integration and introduces a piecewise-approximation method for the proposed linear twisting gaits.
D. From Curve to Gaits
- The curve-to-gait conversion reviews conventional integration and introduces piecewise-approximation integration for linear twisting sidewinding.Source: D. From Curve to Gaits · p. 5
1) Integration for T-Snake:
The T-Snake realizes a dorsal reference curve with discrete dorsal, lateral, and twist joints. Because the existing integration becomes unstable as torsion accumulates, the paper introduces a piecewise approximation aligned with the robot’s discrete mechanism.
1) Integration for T-Snake:
- The T-Snake has n modules with three 1-DoF joints each, giving 3n DoFs and discrete representations of curvature and torsion.Lateral and dorsal rotations represent accumulated curvatures; twist rotations represent accumulated torsion.Source: 1) Integration for T-Snake · p. 5
- As torsional deformation increases, the existing integration makes dorsal and lateral joint angles numerically unstable, distorting motion and producing unexpected trajectories.The paper leaves the cause of this numerical problem for future work.Source: 1) Integration for T-Snake · p. 5
2) Piecewise-Approximation Integration Method:
- The proposed piecewise-approximation integration aligns with the T-Snake’s discrete mechanism, where rigid links are torsion-free and twist joints realize torsion.It approximates the twist angle as a piecewise-constant function of arc length; the method also handles dorsal joints similarly to lateral joints.Source: 2) Piecewise-Approximation Integration… · p. 5
IV. EXPERIMENTAL RESULTS
The experiments evaluate the piecewise-approximation method in simulation and outline further hardware tests of load distribution, locomotion modes, and terrain traversal. In simulation, the new method yields stable periodic joint angles and a clear circular head path, unlike the existing method.
IV. EXPERIMENTAL RESULTS
- The experimental program includes simulation validation, hardware load-distribution comparisons, locomotion-mode demonstrations, and rolling-sidewinding traversal tests on complex terrains.The passage lists these experiments but does not provide results for the latter hardware tests here.Source: §IV · pp. 5–6
A. Validation of the Proposed Integration Method
- After 200 seconds of simulated twisting sidewinding, the existing integration produces numerically unstable lateral angles and unexpected motion, while the new method yields stable periodic angles and a clear circular head path.The simulation uses ωt = 0, a1 = 1.5 rad/(m·s), and a0 = −1 rad/s.Source: A. Validation of the Proposed… · p. 6, Figure 6 · p. 6
B. Twist-Joint Load Distribution
On the T-Snake, the proposed gait distributes twist-joint power more evenly than the rolling vector approach under a comparison with similar turning speeds and total output power. The experiments also test locomotion modes on hard, flat laboratory ground.
B. Twist-Joint Load Distribution
- The load comparison uses in-place turns with similar angular velocities and total twist-joint output power for the proposed gait and rolling vector approach.The measured angular velocities are 2.36±0.05 °/s and 2.33±0.13 °/s, with total output powers of 6.8 W and 6.3 W, respectively.Source: B. Twist-Joint Load Distribution · pp. 6–7, 2) Results · p. 7
2) Results:
- The proposed gait reduces the peak twist-joint output power from 9.89 W to 5.76 W while spreading load across all six joints; the baseline places 96.8% of power on joints 3 and 4, versus 45.1% on the two most-loaded proposed-gait joints.The instantaneous power curves show the same distribution trend over time.Source: 2) Results · p. 7
C. Different Locomotion Modes
- The proposed gaits’ translating and steering capabilities are tested under laboratory conditions on hard, flat ground.The supplied passage states the test setting, not its outcomes.Source: C. Different Locomotion Modes · p. 7
1) Baseline:
Real-robot tests establish translating and steering with the proposed sidewinding variants, while rolling sidewinding reduces arrival times across four terrains. The conclusion reports a joint-angle integration method and identifies current scope limits.
1) Baseline:
- Rolling sidewinding (a1 = 0) is used for translation, while twisting sidewinding (a1 ≠ 0) is used for steering.Source: 1) Baseline · p. 7
1) Translating:
- With ωt = 0.5 rad/s, a1 = 0, and a0 = 0.8 rad/s, the proposed gait demonstrated translating locomotion on the real robot.Source: 1) Translating · p. 7
2) Steering:
- Varying a1 relative to a0 sets the turning center, and tests demonstrated tail-anchored, in-place, and head-anchored steering.The reported settings were a0 = 0.4 rad/s and a1 = −a0/L; a0 = −0.4 rad/s and a1 = −2a0/L; and a0 = 0 rad/s and a1 = −0.8/L, respectively.Source: 2) Steering · p. 7
D. Traversal Speed on Complex Terrains
- 45.1% on flagstone, 41.0% on grass, 47.1% on pebble, and 49.2% on the slope: rolling sidewinding reduced arrival time versus conventional sidewinding.The comparison used a 2 m track on each terrain, with five trials per gait on each terrain.Source: D. Traversal Speed on Complex Terrains · p. 7, Figure 9 · p. 7
V. CONCLUSION AND FUTURE WORKS
- The conclusion reports a piecewise-approximation integration method based on the discrete T-Snake mechanism to accurately generate joint angles, alongside lower peak twist-joint load and faster traversal.Source: §V · pp. 7–8
- The study only integrates twist into sidewinding, and the cause of the numerical problem in the existing integration method remains underexplored.Future work includes fusing twist motion with other gaits.Source: §V · p. 8