## 1 Introduction
The objective is to maintain the equilibrium while the system performs some tasks such as contact inspection in sites inaccessible by conventional means such as oil and gas refineries (see Figure 2a). We consider the case of the robot with the body perched and the wings folded, which implies that the aerodynamic effects of the body vibration induced by the wing flapping do not need to be considered. To do that, it is very important to understand how birds maintain the equilibrium. Unlike standard manipulators, the most important requirement is being lightweight, which limits the frame size and torques and hence the use of micro motors. Under these hard constraints, their control becomes very challenging with two main objectives: to balance the body while the system is perched; to follow trajectories with the end effector of the manipulator in order to perform some kind of task. Figure 1: Phases of flapping wing aerial robots mission: sequence of the most relevant tasks. Moreover, in this work we focus on an underactuated manipulator prototype, i.e., fewer control inputs than degrees of freedom, because it is not actuated at the point of perching (passive joint). Underactuated mechanical systems are well known and their inherent difficulty of a lack of actuation have made them a challenge for the control community. In particular, the current system has a similar behavior to the acrobot [13]. This system is a two-link underactuated robot that mimics the human acrobat who hangs from a bar and tries to balance his/her body. The control of n-link underactuated robot with passive first joint has been studied recently as in e.g., [14; 15; 16; 17]. Moreover, very few researchers have addressed the control of n-link underactuated robot with the influence of a static friction on the unactuated passive joint [18; 19] due to the great difficulty of controlling these systems with a static friction in the passive joint. Two main control objectives have been studied with these kind of systems: (1) the stabilization of the system around an equilibrium point and (2) the swing-up problem. Unlike these standard underactuated manipulators, in this work we demonstrate that the use of a grabbing mechanism at its base imitating a bird's claw allows us to simplify the controller design by combining the friction exerted by the mechanism and an adequate control of the system posture, and, more importantly, it allows us to follow trajectories with the end effector of the manipulator while balancing the system, which will be necessary for performing manipulation tasks such as the contact inspection following trajectories with an ultrasonic sensor mounted in the end-effector. In this work, a simple mechanism was assembled to exert an equivalent friction torque at the base, which was used to verify the effectiveness of the proposed control methodology. In parallel, a bio-inspired claw was developed in our lab for the final prototype. The main contributions of this work are: the mechanical design of a manipulator imitating the skeleton of a bird with lightweight micro motors and, a novel bio-inspired control methodology that accounts for the static friction in the first passive joint (claw) for a precise control of the posture of the system. Moreover, this work addresses, for the first time, the control of an n-link manipulator with underactuation and static friction at its first passive joint in order to follow a path with the end-effector (beak). Both the design of the manipulator and the control approach are bio-inspired and based on the behaviors of bird species. Our results show that this framework opens the possibility to perform manipulation, such as performing contact inspection when the system is perched, and the early prototype developed successfully mimics the anatomy of birds and allows us to verify the efficiency of the proposed control strategy and, therefore, it is a good starting point for future developments.