  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.
