Stable Haptic Teleoperation of UAVs via Small $L_2$ Gain and Control Barrier Functions

We present a novel haptic teleoperation approach that considers not only the safety but also the stability of a teleoperation system. Specifically, we build upon previous work on haptic shared control, which uses control barrier functions (CBFs) to generate a reference haptic feedback that informs the human operator on the internal state of the system, helping them to safely navigate the robot without taking away their control authority. Crucially, in this approach the force rendered to the user is not directly reflected in the motion of the robot (which is still directly controlled by the user); however, previous work in the area neglected to consider the feedback loop through the user, possibly resulting in unstable closed trajectories. In this paper we introduce a differential constraint on the rendered force that makes the system finite-gain $L_2$ stable; the constraint results in a Quadratically Constrained Quadratic Program (QCQP), for which we provide a closed-form solution. Our constraint is related to but less restrictive than the typical passivity constraint used in previous literature. We conducted an experimental simulation in which a human operator flies a UAV near an obstacle to evaluate the proposed method.