This work studies a stabilization problem of flapping-wing flying robots (FWFRs) before a take-off phase while a robot is on a branch. The claw of the FWFR grasps the branch with enough friction to hold the system steady in a stationary condition. Before the take-off, the claw opens itself and the friction between the claw and branch vanishes. At that moment, the mechanical model turns into an under-actuated multi-link (serial configuration) robotic system where the first joint can rotate freely without any friction as opposed to rotation. The stabilization and balancing are the crucial tasks before take-off. This work explores a new methodology to control an under-actuated lightweight manipulator for its future adaptation to FWFR to improve the stabilization performance before take-off. The setup tries to mimic the birds with two-link legs, a body link, and 2-DoF (degrees of freedom) arms, being all active links except the first passive one. In contrast to common arms, the lightweight-design restriction limits the frame size and requires micromotors. With all of these constraints, control design is a challenge, hence, the system is categorized: a) the leg subsystem (under-actuated), including the two first links, and b) the body and arm subsystem (fully actuated) with the rest of links. The fully-actuated links are controlled by feedback linearization and the under-actuated part with active disturbance rejection control (ADRC) for estimation and rejection of the coupling between both subsystems. The mechanical design, modeling, and control of the proposed system are reported in this work. Experimental results have been also proposed to present a proof of concept for this modeling and control approach.

The authors acknowledge support from the European Project GRIFFIN ERC Advanced Grant 2017, Action 788247; and also partially support from "Sistema robótico híbrido aéreo-acuático para muestreo, monitorización e intervención (HAERA)" funded by the Spanish Ministry of Science and Innovation PID2020-119027RB-I00.