Geometric Mechanics and Stokes’ Theorem in Robotic Locomotion

<p dir="ltr">This research develops a rigorous mathematical framework for analyzing and predicting robotic locomotion using the principles of geometric mechanics. The robot’s configuration is modeled as a principal fiber bundle, separating body motion from internal shape changes, and a local connection maps shape velocities to body velocities, enabling precise computation of net movement. Stokes’ theorem and the associated curvature 2-form are employed to quantify the net displacement resulting from cyclic gaits, while convergence conditions ensure that displacement remains finite, even for large or high-frequency motions.</p><p dir="ltr">The methodology integrates analytical derivations with numerical simulations, including Python-based visualization of vector fields, local connections, curvature distributions, and gait paths. No human or animal subjects were involved, so no ethical approval was required. The framework is fully reproducible and provides a robust, quantitative tool for designing, analyzing, and optimizing locomotion in robotic systems.</p><p><br></p>