Linear Twisting Sidewinding Gaits for Twistable Snake Robot Motion Planning on Complex Terrains

Qingling Fan; Zhongqiang Ren

cs.ROOct 21, 2026

Linear Twisting Sidewinding Gaits for Twistable Snake Robot Motion Planning on Complex Terrains

Authors: Qingling Fan, Zhongqiang Ren

Organizations: Global College, Shanghai Jiao Tong University, China

Abstract

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.

Figures & tables

Fig. 1: Twist-joint load distribution of the two gaits. The proposed LTS spreads the twisting over the entire body, whereas the rolling vector approach [ 8 ] concentrates it in a narrow buffer segment. (a) Rolling vector: $96.8\%$ of the total output power is carried by the two twist joints inside the buffer segment. (b) LTS: the twisting is uniform along the body, so all six twist joints share the load; the color bar gives the mean output power of each joint. (c) In-place turning on the T-Snake hardware: compared with the rolling vector approach, the peak output power of a single joint drops from $9.9$ to $3.0$ W at joint 3 and from $9.1$ to $5.8$ W at joint 4. (d) The LTS traverses four types of terrain $41$ – $49\%$ faster than conventional sidewinding.

Fig. 2: Overview of the dorsal reference curve and the backbone curve of sidewinding. (a) The dorsal reference frames along the curve $\mathbf{c}(s)$ . (b) The relative rotation angle $\phi^{\mathcal{C}}_{\mathcal{B}}$ between frames $\mathcal{B}$ and $\mathcal{C}$ . (c) The backbone curve of sidewinding is a time-varying elliptical helix.

Fig. 3: Local frame at snake head. $\mathbf{z}_{\parallel}$ is obtained by finding the component of $\mathbf{z}^{\mathcal{L}}$ within the normal plane at $s=0$ . The normal vector of the bellows frame on the snake head, $\mathbf{\hat{e}}^{\mathcal{B}}_{a}(0,t)$ , is computed by normalizing $\mathbf{z}_{\parallel}$ . $\phi_{\text{offset}}$ defines the angle from $\mathbf{\hat{e}}^{\mathcal{F}}_{a}(0,t)$ to $\mathbf{\hat{e}}^{\mathcal{B}}_{a}(0,t)$ . The twist function $\phi^{\mathcal{C}}_{\mathcal{B}}$ defines the rotation angle from the bellows frame $\mathcal{B}$ to the complete frame $\mathcal{C}$ .

Fig. 4: Overview of rolling sidewinding and twisting sidewinding. For rolling sidewinding, $\omega_{\text{r}}$ (a) is a non-zero constant, providing translating capability (b) for the T-Snake. For twisting sidewinding, $\omega_{\text{r}}$ (c) varies with arc-length linearly, inducing turning motions (d) for the T-Snake.

Fig. 5: Analysis of the piecewise approximation solution. (a) Illustration of the discrete mechanism of the T-Snake. (b) After the piecewise approximation, the relative rotation angle $\tilde{\phi}_{\mathcal{B}}^{\mathcal{C}}$ becomes a piecewise constant function. (c) The correspondence to the discrete T-Snake.

Parameter	Value	Description
$n$	$6$	Number of modules
$k_{a}$	$0.02$ m	Vertical amplitude of $\mathbf{c}^{\text{eh}}$
$k_{b}$	$0.08$ m	Horizontal amplitude of $\mathbf{c}^{\text{eh}}$
$k_{\theta}$	$(1/2\pi)$ m	Pitch of $\mathbf{c}^{\text{eh}}$
$L_{0}$	$0.2055$ m	Module length
$\Delta t$	$0.02$ s	Time step of joint command

TABLE I: Common Experiment Parameters

Fig. 6: Simulation of the twisting sidewinding. The lateral joint angles computed by the existing method (a) and our method (c). (b) and (d): corresponding snapshots from the simulation experiments.

Fig. 7: Analysis of twist-joint load distribution. (a) Mean output power of each twist joint. (b) Peak output power of each twist joint. (c) and (d) Instantaneous output power of the six twist joints for the proposed gait and the rolling vector approach, respectively.

Fig. 8: Different locomotion modes of the proposed gaits on the T-Snake.

Fig. 9: Comparative experiments of traversal speed on four different terrains: (a) flagstone, (b) grass, (c) pebble, (d) slope. The bar chart (e) verifies the proposed gait significantly reduces the arrival time compared to the conventional sidewinding.

Robot Motion Generation

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Oct 21, 2026J/K move · Enter open · S save

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

Qingling Fan, Zhongqiang Ren

Global College, Shanghai Jiao Tong University, China

Robot Locomotion Robot Motion Generation Robot Kinematics

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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.

Abstract

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