Cross-coupling stiffness for natural goal-directed robot motion

The capability of humans to use their natural dynamics for generating explosive motions in a highly-coordinated sequence is a feat that has yet to be reached in robotics. With the introduction of intrinsically elastic joints, great progress towards this goal has been made. However, there are still some challenges associated with this type of actuation, which limits its application. Generating goal-directed sequences has proven difficult as optimal control solutions tend to result in uncoordinated swing-up motions. This can be explained when viewing the structure of the stiffness matrix: If the elastic elements are placed in series with the motor, a diagonal stiffness matrix is generated. This in turn leads to a multitude of frequencies at which the system can oscillate. By adding off-diagonal elements, a dominant primary resonance behaviour can be achieved. Leveraging this cross-coupling stiffness, we show that robots can produce natural goal-directed oscillatory and explosive movements that closely resemble human throwing.