Angular Momentum Regulation
in Human Walking

Angular momentum is a conserved physical quantity for isolated systems where no net external moment acts on a body, but in the case of human locomotion, where the body interacts with the environment, there is no a priori reason to expect angular momentum conservation. In this study we measure how closely the human body regulates angular momentum in walking. Using a 16-segment, morphologically realistic human model and kinetic and kinematic gait data, we compute body angular momentum for one test subject walking at self-selected speed. We find that dimensionless spin angular momentum remains small ( (Spin) / Velocity Height Mass < 0.02) throughout the gait cycle, and maximum whole body angular excursions within sagittal (<1^o), coronal (<0.2^o), and transverse (<2^o) planes are negligible. Assuming zero net torque about the body center of mass, we derive a nonlinear relationship between ground reaction force, center of mass, and center of pressure location. These model forces closely match experimental forces (R²x = 0.94; R²y =0.91). We employ this relationship to rapidly generate biologically realistic center-of-pressure and center-of-mass reference trajectories. Using an open-loop optimization strategy, we show that biologically realistic leg-joint kinematics emerge through the minimization of spin angular momentum and the total sum of joint torque squared (energy criteria). Principal component analysis reveals how angular momentum is distributed throughout the body as a function of walking phase. In this study, a motor primitives approach is used for the first time to analyze whole body movements. We find that only three principle components are required to explain 99% of the walking data for sagittal plane-body rotations. In addition, our analysis shows that the angular momentum primitives are invariant with walking speed. Using these biomechanical results, we dynamically simulate human walking during the single-support phase using a morphologically realistic humanoid model. With only the model's walking speed and stride length as desired gait motion targets, our real-time controller gives resulting model joint kinematics that are in qualitative agreement with human gait data. Besides providing a model of human walking biomechanics, the regulation of spin angular momentum is useful as a high-level control objective for humanoid robots and "smart" assistive devices.