cs.ROApr 13, 2026

Dynamic Modeling and Robust Gait Optimization of a Compliant Worm Robot

Authors: Xinyu Zhou, Yu Mei, Faith Thomson, Christian Luedtke, Xinda Qi, Xiaobo Tan

Organizations: Michigan State University, East Lansing, MI 48824 USA

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Abstract

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.

Figures & tables

Figure 1: Prototype of the compliant worm robot. The robot consists of a compliant bellows body and two end fin modules. The visual markers are attached for robot motion tracking and are not essential to the robot’s locomotion mechanism.
Figure 2: Illustration of the structure of a single fin and its interaction with the corrugated pipe. Each fin comprises an embedded gear driven by the servo inside the fin module and two compliant bars used for interaction with the corrugated pipe. During operation, one compliant bar interacts with the pipe wall and achieves anchoring engagement or anchoring disengagement depending on the locomotion direction.
Figure 3: System-level view of the problem formulation considered in this paper. A commanded gait, parameterized by stroke and frequency, is mapped by the actuation model to the realized body-length trajectory, which then drives the locomotion and energy models used for optimization.
Figure 4: A schematic diagram of the worm robot moving in a corrugated pipe. M1M_{1} and M2M_{2} are the designation of the two mass blocks, as well as their masses. F1F_{1} , F2F_{2} , FcF_{c} represent the forces acting on M1M_{1} and M2M_{2} through the fins, and the traction force of the cable, respectively. x1x_{1} and x2x_{2} are the positions of the two mass blocks, in more details, the positions of where the fins’ roots are located, while A1A_{1} and A2A_{2} are the anchoring positions between each pair of fins and the corrugated pipe.
ParameterSymbolValue
Robot Body Dynamics
Mass of the rear body segmentM1M_{1}0.429 kg
Mass of the front body segmentM2M_{2}0.429 kg
Unstressed length of robot bodyLfreeL_{\mathrm{free}}0.30 m
Stiffness coefficient of the bellowskbk_{\mathrm{b}}968.8 N/m
Damping coefficient of the bellowscbc_{\mathrm{b}}862.4 N ⋅\cdot s/m
Table 1: Parameters of the Worm Robot System
Figure 5: Bellows force–deformation test and linear fit used to identify the stiffness coefficient kbk_{\mathrm{b}} .
Figure 6: Identification of the clearance-aware fin–groove interaction model. (a) The experimental setup. (b) Experimental results and the identified parameters, δc\delta_{\mathrm{c}} , kengk_{\mathrm{eng}} , and kdisk_{\mathrm{dis}} .
Figure 7: Representative locomotion-model result for the gait with stroke S=0.07S=0.07 m and frequency f=0.2f=0.2 Hz. The figure compares the measured and predicted trajectories of x1(t)x_{1}(t) under the experimentally measured realized robot body length L(t)L(t) .
Figure 8: Representative actuation-model result for the gait with stroke S=0.07S=0.07 m and frequency f=0.2f=0.2 Hz. (a) Measured and predicted realized body-length change. (b) Commanded and effective inputs under the identified slack-aware actuation model.
Figure 9: Representative energy-model result for the gait with stroke S=0.07S=0.07 m and frequency f=0.2f=0.2 Hz. (a) Measured and predicted source-side power. (b) Measured and predicted accumulated energy over the five-ridge traversal.
Figure 10: Price-of-robustness analysis used for selecting the kinematic robustness margin. The imposed margin is chosen at the cliff point, where the optimal cost of transport begins to increase abruptly. In the present study, the selected value is δm=3.4\delta_{m}=3.4 mm.
Figure 11: Sim-to-real transferability of the selected robustly optimized gaits. The theoretical Pareto front is shown in the average speed–average power plane, together with the experimental results of the selected minimum-power, cruising, and maximum-speed gaits. The annotated experimental COT values are provided for reference.
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