A New Power Law Linking the Speed to the Geometry of Tool-Tip Orientation in Teleoperation of a Robot Assisted Surgical System

Fine manipulation is important in dexterous tasks executed via teleoperation, including in robot-assisted surgery. Discovering fundamental laws of human movement can benefit the design and control of teleoperated systems, and the training of their users. These laws are formulated as motor invariants, such as the well-studied speed-curvature power law. However, while the majority of these laws characterize translational movements, fine manipulation requires controlling the orientation of objects as well. This subject has received little attention in human motor control studies. Here, we report a new power law linking the speed to the geometry in orientation control - humans rotate their hands with an angular speed that is exponentially related to the local change in the direction of rotation. We demonstrate this law in teleoperated tasks performed by surgeons using surgical robotics research platforms. Additionally, we show that the laws parameters change slowly with the surgeons training, and are robust within participants across task segments and repetitions. The fact that this power law is a robust motor invariant suggests that it may be an outcome of sensorimotor control. It also opens questions about the nature of this control and how it can be harnessed for better control of human-teleoperated robotic systems.