The limits of using angular momentum to control center of mass position

Introduction: Maintaining an upright posture requires that averaged over time the center of mass stays within the base of support. When the base of support is fixed, one can still move the center of mass by changing whole-body angular momentum around the center of mass such that this coincides with a horizontal ground reaction force that accelerates the center of mass (Otten, 1999). Here, we asked what the maximum horizontal position change that can be achieved through this mechanism is.Methods and Results: Assuming the vertical component of the ground reaction force is negligible, we derived a simplified relationship between changes in center of mass displacement and changes in whole body orientation to answer the question: “how much center of mass displacement can reasonably be obtained by using the angular momentum mechanism?”. This relationship reads as;ΔCoMx= -(Δφ⋅ICoM)/(m⋅CoMz)with ΔCoMx being the center of mass displacement caused by a change in body orientation Δφ, given an inertia of the body around its own center of mass ICoM, and a body mass of m, total center of mass height of CoMz. Using realistic values for ICoM, m and CoMz, as well as an estimated maximum desirable angle change, we show that realistically, one cannot use changes in angular momentum to displace the center of mass by more than ~8 cm.To assess the validity of this result, we used a physics-based, simple mechanical model which consists of a stance leg, a swing leg, and a point mass trunk coinciding with the hip. The model has two degrees of freedom (the two leg angles) that are actuated with a hip joint torque. For increasing stance leg angles (initial center of mass displacements), we asked if the model could still recover by generating angular momentum with the swing leg. The results of this modelling also showed that the maximal contribution of angular momentum changes to center of mass displacement in upright postures is in the order of a few cm.Conclusions: Both our simplified relationship between changes in center of mass position and changes in whole body orientation and our physics-based modelling showed that the maximal contribution of angular momentum changes to center of mass displacement in upright postures is in the order of a few cm. Our analysis showed that this is due to the low ratio between whole body inertia and the product of mass and center of mass height. In addition, movement is limited by the constraint to keep a somewhat vertically oriented body, as well as limits to actuators and control.