Unified modeling of pelvic transverse rotations across walking,jogging,running,and sprinting using a single-sensor: Minimal limit cycle approach

Abstract

This study investigated transverse pelvis rotations across walking, jogging, running, and sprinting using minimal limit cycle (MLC) modeling. Ten soccer players performed four gaits while a sacrum-mounted inertial measurement unit (IMU) recorded kinematics. We hypothesized that one expression could capture control mechanisms across gaits. A unified MLC model described all gait types within a common dynamical structure, with differences explained by coefficient modulation rather than distinct control strategies. Nonlinearity decreased from walking to sprinting, consistent with energetic differences between pendulum-like walking and spring–mass running dynamics. Stiffness coefficients (linear and nonlinear) varied significantly: linear stiffness was higher in sprinting than walking and jogging, while nonlinear stiffness was reduced in sprinting compared to jogging. These adaptations suggest gait-specific modulation of pelvis rotational velocity within an overarching shared framework, consistent with (but not directly demonstrating) central pattern generator (CPG)-based control architecture. Damping coefficients showed less sensitivity across gaits. Nonlinear stiffness (Duffing) and damping (Van der Pol) coefficients were consistent with stabilization mechanisms related to momentum preservation and energy recycling. Model fit improved from ∼63% in walking to ∼93% in sprinting, without changing equation structure, highlighting parameter modulation as the key mechanism. Quantifying gait transitions with a single pelvis sensor supports field-based monitoring, rehabilitation, and movement-quality screening related to injury risk, while informing bipedal robotics and rehabilitation devices requiring unified control architectures. To our knowledge, this is the first study to report unified gait modeling across four gait types using MLC with a single sensor, underscoring translational value in biomechanics, clinical practice, and robotics.