High-Performance Six-DOF Flight Control of the Bee$^{++}$: An Inclined-Stroke-Plane Approach

We present a new method for synthesizing and implementing high-performance
six-degree-of-freedom
(
$\boldsymbol{6}$
-DOF) flight controllers for the Bee
$^{++}$
, an insect-scale flying robot driven by four independently-actuated flapping wings. Each wing of the Bee
$^{++}$
is installed with a preset orientation such that the stroke plane generated during flight is inclined, thus enabling reliable roll, pitch, and yaw torque generation. Leveraging this capability, we propose a Lyapunov-based nonlinear control architecture that enables closed-loop position and attitude regulation and tracking. The control algorithms presented in this article simultaneously stabilize position and attitude by independently varying the wingstroke amplitudes of the four flapping wings of the Bee
$^{++}$
. We use this particular control architecture to exemplify the process of controller synthesis and real-time implementation; however, the aerodynamic design of the Bee
$^{++}$
is compatible with a great variety of control structures and performance objectives. As a main result, we present the first set of experimental data demonstrating sustained and robust high-performance tracking of a
$\boldsymbol{6}$
-DOF reference signal during flight at the insect scale, which has been a long-standing control problem in the field of flapping-wing microrobotics. Furthermore, using data obtained through a series of systematic flight tests, we show that the Bee
$^{++}$
can achieve the highest
$\boldsymbol{6}$
-DOF performance ever recorded for an insect-scale flapping-wing flying robot during sustained flight.