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 c(s) . (b) The relative rotation angle ϕBC between frames B and C . (c) The backbone curve of sidewinding is a time-varying elliptical helix.
Fig. 3: Local frame at snake head. z∥ is obtained by finding the component of zL within the normal plane at s=0 . The normal vector of the bellows frame on the snake head, e^aB(0,t) , is computed by normalizing z∥ . ϕoffset defines the angle from e^aF(0,t) to e^aB(0,t) . The twist function ϕBC defines the rotation angle from the bellows frame B to the complete frame C .
Fig. 4: Overview of rolling sidewinding and twisting sidewinding. For rolling sidewinding, ωr (a) is a non-zero constant, providing translating capability (b) for the T-Snake. For twisting sidewinding, ωr (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 ϕ~BC becomes a piecewise constant function. (c) The correspondence to the discrete T-Snake.
Parameter
Value
Description
n
6
Number of modules
ka
0.02 m
Vertical amplitude of ceh
kb
0.08 m
Horizontal amplitude of ceh
kθ
(1/2π) m
Pitch of ceh
L0
0.2055 m
Module length
Δt
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 creates feasible, task-directed trajectories for robots to move, manipulate objects, and interact with people and environments.
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∘ and 180∘ heading changes, whereas the baseline rolling arc gait cannot change the robot heading.
Qingling Fan, Zhongqiang Ren
Global College, Shanghai Jiao Tong University, China
Nature suggests that exploiting the elasticities and natural dynamics of robotic systems could increase their locomotion efficiency. Prior work on elastic snake robots supports this hypothesis, but has not fully exploited the nonlinear dynamic behavior of the systems. Recent advances in eigenmanifold theory enable a better characterization of the natural dynamics in complex nonlinear systems. This letter investigates if and how the nonlinear natural dynamics of a kinematic elastic snake robot can be used to design efficient gaits. Two types of gaits based on natural dynamics are presented and compared to a state-of-the-art approach using dynamics simulations. The results reveal that a gait generated by switching between two nonlinear normal modes does not improve the locomotion efficiency of the robot. In contrast, gaits based on non-brake periodic trajectories (non-brake orbits) are perfectly efficient in the energy-conservative case. Further simulations with friction reveal that, in a more realistic scenario, non-brake orbit gaits achieve higher efficiency compared to the baseline gait on the rigid system. Overall, the investigation offers promising insights into the design of gaits based on natural dynamics, fostering further research.
Tristan Ehlert, Arne Sachtler, Annika Schmidt +2
German Aerospace Center (DLR), Robotics and Mechatronics Center (RMC), Münchner Str. 20, 82234 Weßling, Germany · Technical University of Munich (TUM), Department of Computer Engineering; Boltzmannstraße 3, 85748 Garching, Germany
Worm-inspired robots provide an effective locomotion strategy for constrained environments by combining cyclic body deformation with alternating anchoring. For compliant robots, however, the interaction between deformable anchoring structures and the environment makes predictive modeling and deployable gait optimization challenging. This paper presents an experimentally grounded modeling and optimization framework for a compliant worm robot capable of traversing corrugated pipes. First, a hybrid dynamic locomotion model is derived, in which the robot motion is represented by continuous dynamics within a corrugation groove and discrete switching of anchoring positions between adjacent grooves. A slack-aware actuation model is further introduced to map the commanded gait input to the realized body-length change, and an energy model is developed based on physics and calibrated with empirical power measurement. Based on these models, a multi-objective gait optimization problem is formulated to maximize average speed while minimizing average power. To reduce the fragility of nominal boundary-seeking solutions, a kinematic robustness margin is introduced into the anchoring-transition conditions, leading to a margin-based robust gait optimization framework. Experimental results show that the proposed framework captures the dominant locomotion and energy-consumption behavior of the robot over the tested conditions, and enables robust gait optimization for achieving speed-power trade-off.
Xinyu Zhou, Yu Mei, Faith Thomson +3
Michigan State University, East Lansing, MI 48824 USA