Energy Efficient and Robust Balancing with Motion Primitive Switching

Balancing motions are usually designed using simplified models of the Center of Mass (CoM) and feedback control without accounting for energy efficiency. In order to tackle this shortcoming, we introduce a Motion Primitive switching methodology where samples of optimal motions (Motion Primitives) are chosen online based on a Euclidean distance metric. The chosen sample is used to provide reference trajectories, torques and ground reaction forces to be tracked. In order to satisfy all of the modeling assumptions while tracking the reference values, a Quadratic Program (QP) is solved online where the dynamics of the robot, friction, Center of Pressure and torque bounds are treated as constraints. Convergence to the desired trajectories is dictated by a Control Lyapunov Function constraint which is introduced in the QP. The methodology is evaluated on a four-link simulated robot where we show that switching between Motion Primitives provides energy efficient balancing motions for different disturbance situations. At the same time the methodology provides more efficient motions for different disturbance forces when compared to a nonswitching approach, where a Motion Primitive is chosen only once at the beginning.