Vertical COM Motion Generation to Reduce Slipping and Mechanical Work during Walking

A robot foot can slip when the horizontal shear force acting on the foot exceeds the frictional force between the foot and the ground. In the linear inverted-pendulum (LIP) model, the vertical height of the center of mass (COM) is kept constant, and the vertical force is always equal to the gravitational force at any walking speed. However, the horizontal force increases upon increasing the walking speed. This restriction on the vertical force in the LIP model can cause the robot foot to slip at fast walking speeds, as the horizontal force can exceed the frictional force, which is proportional to the vertical force. In this study, we present an optimization method to generate vertical COM motion to maintain the utilized coefficient of friction (uCOF) less than the available coefficient of friction between the foot and the ground, and to minimize the mechanical work of the COM. Vertical motions at various speeds are generated using the proposed optimization method. Subsequently, the generated COM motion patterns are used as reference trajectories of the COM in robot simulation. Optimization and simulation results demonstrate that the mechanical work and uCOF decrease because of the vertical motion. This study suggests a way to generate slip-safe and energy-efficient COM patterns, which, in turn, overcome the limitations of the LIP model by adding vertical COM motion.