Modeling, Analysis and Activation of Planar Viscoelastically-combined Rimless Wheels

Rimless wheels are known as the simplest model for passive dynamic walking. It is known that the passive gait generated only by gravity effect always becomes asymptotically stable and 1-period because a rimless wheel automatically achieves the two necessary conditions for guaranteeing the asymptotic stability; one is the constraint on impact posture and the other is the constraint on restored mechanical energy. The asymptotic stability is then easily shown by the recurrence formula of kinetic energy. There is room, however, for further research into the inherent stability principle. In this paper, we reconsider the stability of the stance phase based on the linearization of the equation of motion, and investigate the relation between the stability and energy conservation law. Through the mathematical analysis, we provide a greater understanding of the inherent stability principle.

This paper proposes an energy-recycling rimless wheel with spring-clutch legs. The proposed mechanism uses a lockable clutch to store part of the impact-induced elastic energy after foot contact and reinject it in the next gait cycle. First, we develop a hybrid dynamic model of the energy-recycling rimless wheel. Second, numerical simulations are used to examine the dynamics, local stability of periodic gaits, and the Cost of Transport (CoT) of the proposed mechanism. The simulation results show that the proposed mechanism reduces the CoT by up to 16.13% compared with a benchmark viscoelastic-legged rimless wheel with telescopic spring-damper legs. Compared with the rigid rimless wheel, the viscoelastic-legged and energy-recycling models reduce the CoT by more than 50%. The energy-recycling model also maintains locally stable periodic gaits over the tested slope and stiffness ranges. Finally, prototype experiments on an inclined plane are conducted to examine the feasibility of the proposed mechanism. The experimental results show that the proposed rimless wheel achieves passive walking on a shallow 1° slope, corresponding to a CoT of approximately 0.02. These results suggest that the proposed spring-clutch mechanism can improve the simulated walking efficiency of the energy-recycling rimless wheel, while the prototype experiments support the feasibility of passive walking with the mechanism.

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.