Dynamic Modeling and Robust Gait Optimization of a Compliant Worm Robot

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.

Learning energy-efficient humanoid locomotion requires discovering mechanically economical gait coordination, not merely reducing actuator effort. Reinforcement learning promotes efficiency through effort-related reward penalties, which guide the step-to-step mechanics of walking only indirectly. This article proposes a framework inspired by passive dynamic walking (PDW) that temporarily creates slope-equivalent conditions favorable to economical gait discovery and removes all PDW-specific guidance before nominal-dynamics optimization. During early training, a tilted-gravity field assists sagittal progression on flat collision geometry, complemented by curriculum-coupled reward terms. The core framework requires no reference trajectories, gait phases, or contact schedules. In a five-seed forward-locomotion study on a 29-DoF Unitree G1, the framework reduces mechanical cost of transport by 6.8-15.2% over commanded speeds of 0.5-2.0m/s without degrading velocity tracking. Mechanical-work decomposition attributes the reduction to positive actuator work, and reward-matched comparisons separate the guided regime's faster gait acquisition from the tilt's additional benefit to converged economy. The framework extends to unassisted omnidirectional locomotion, where its benefit persists once a walking-specific motion prior supplies kinematic coordination, the combination reducing speed-matched cost of transport by 18.7%. On hardware, forward cost of transport falls by 16.3% with the motion prior and by 4.5% without it, the latter within the trial-to-trial spread.

While modular robots offer versatility, excessive joint torque during locomotion poses a significant risk of mechanical failure, especially for detachable joints. To address this, we propose an optimization framework using the NSGA-III algorithm. Unlike conventional approaches that prioritize mobility alone, our method derives Pareto optimal solutions to minimize joint load while maintaining necessary locomotion speed and stability. Simulations and physical experiments demonstrate that our approach successfully generates gait motions for diverse environments, such as slopes and steps, ensuring structural integrity without compromising overall mobility.