Control of a Wing Type Flat-Plate for an Ornithopter Autonomous Robot With Differential Flatness

Control of a Wing Type Flat-Plate for an Ornithopter Autonomous Robot With Differential Flatness

Elkin Yesid Veslin Díaz (Universidade Federal do Rio de Janeiro, Brazil), Cesar Francisco Bogado-Martínez (Universidad Nacional de Asunción, Paraguay), Max Suell Dutra (Universidade Federal do Rio de Janeiro, Brazil) and Luciano Santos Constantin Raptopoulos (Centro Federal de Educação Tecnológica Celso Suckow da Fonseca, Brazil)
DOI: 10.4018/978-1-7998-0137-5.ch009

Abstract

In this chapter, a two-degree-of-freedom controller that exploits the flat properties of a three degree-of-freedom wing type flat-plate for an Ornithopter Autonomous robot is proposed. A set of kinematical patterns inspired by nature is used to simulate the wing's movement around two wingtip trajectories; also, the effects of the aerodynamical forces as a function of the wind velocity and the wing's angle of attack are considered. In order to control the system, the effects of these forces are viewed as disturbs that affect the wing's dynamics. The proposed control scheme drives the device through the desired path by generating a set of desired inputs which are compensated by a feedback loop when the aerodynamical forces actuate upon the system.
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Introduction

Mechatronic engineering contributions has been becoming a strong requirement to increase the performance of any device, as the addition of an intelligent processing block increments their capabilities to expand the solution margin. However, it is the synergy concept that turns strong the mechatronics design paradigm, as it is intended as a mechanical structure or any system, that can organize and process their proper information through an efficient architecture, that is able to deal with instruments (sensors and actuators), control system, diagnosis, and communication (Habib, 2008).

In the mechatronics engineer concept, the control system acts like the brain (Rahn, 2002), it becomes from a knowledge base, constructing from it a precise model of the system to be controlled through feedback and feedforward loops. To build a proper control algorithm, it is required to a system’s mathematical model, parameter identification and estimation, controller design methods and control performance criteria (Isermann, 2005). Being them, the research of control systems is an important requirement into the design of any mechatronic system, it is intended to deal with statics and dynamics behaviors, meaning that, it is able to compensate uncertainties generated by non-linear external or internal factors, who may cause instability when they are not properly faced.

In this chapter, the study and evaluation of a control scheme for an ornithopter wing is proposed. The control scheme will be able to deal with the proper system’s dynamics and the aerodynamic forces that continuously affect the wing’s stability. To guarantee the proper model design, biomimetic characteristics will be considered into the dynamic model study.

The design of an aircraft with biomimetic characteristics will lead to developing a device with the runway and reduced takeoffs, energy efficiency during flight, high maneuverability and low noise generation. Diverse academics works focused in this area should be found, some of them especially focused in military applications, others present a research emphasis on specific areas: as the wing design, aerodynamical studies, wing kinematics, drive mechanism design, mathematical modeling, control, and simulation.

For the development of this work, an ornithopter wing is considered as an open chain structure consisting of a flat-plate structure. This structure that constitutes the wing’s body is attached to the robot body through a spherical joint, named as the shoulder joint, which performs three movements during flying, they are the upstroke and downstroke movement; the rotation of the wing; and, the abduction and adduction movement.

The device’s parametric values are based in morphometric data of a pigeon, with this information, both the kinematical and dynamical model are determined. To model the flight dynamics and wing motion, the hypothesis that the bird is flying at a constant velocity in a horizontal rectilinear trajectory is considered.

This work introduces Differential Flatness as a control solution to obtain an appropriate set of joint's moments (inputs) required to perform the flight movement, for doing this, information based on natural wing movement parameterized as trigonometric functions are used. The results are introduced into a feedback control scheme to ensure path tracking during the flying in the presence or not of disturbs generated by aerodynamical forces. Two wingtip trajectories patterns are implemented in this study: the oval and shape-of-eight (infinite) trajectories, for both cases, the results prove that the Differential Flatness is profitable to determine the wing’s inputs to develop the flying movement and control them. A flowchart of the proposed work is presented below.

Figure 1.

Work Flowchart.

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Key Terms in this Chapter

Lagrangian Mechanics: The Lagrangian mechanics is a reformulation of the classical mechanical theory. In the Lagrangian mechanic the trajectory made by an object is obtained through the finding of the trajectory that minimizes the action, that is, the integral of the Lagrangian in time. The Lagrangian is obtained by the difference between kinetical energy and the potential energy.

Differential Flat Systems: A specific kind of system which structure of the trajectories of the dynamics can be characterized. A system is considered flat if their states and inputs could be determined by a set outputs and their derivatives.

Kinematic Patterns: A set of time course functions that describes the wing movements during flying in reference to a relative set of degree-of-freedom. Their objective is to replicate the kinematics of free flying in birds and insects.

Two Degree-Of-Freedom Controllers: A non-linear control technique composed by a feedforward compensator block that modifies the input of the feedback compensator block which is used to correct any errors due to the noise of uncertainties in the plant.

PD Control: A PD control stands for Proportional-Derivative control, it is a control loop feedback strategy used in industrial control to minimize the error over time by the adjust of a control variable or input, by means of calculating the error value as the difference between the desired setpoint and the measured state. The P term stands for the proportional part of the controller that generates a corrective input proportionally to the existing error. The D term acts on the derivative rate of change of the control error providing a fast response.

Aerodynamical Forces: The aerodynamical forces are a set of forces actuating on a body produced by the air or fluid that surrounds a body, it is generated by the relative motion between the body and the fluid.

Ornithopter: An ornithopter is defined as an aircraft that generates flies by the flapping of their wings. It structures and movement is inspired by the flight of birds and insects.

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