Snake Aerial Manipulators: A Review <s> ,6,8. <s> In this paper a Lyapunov control algorithm for a tandem rotor helicopter is obtained using backstepping techniques. A simple model dynamics for a behavior of a helicopter close to hover is obtained. Some simulation results are presented to illustrate the performance of such controller. <s> BIB001 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> Preface. Acknowledgments. 1. Overview of Aerodynamics. 1.1. Introduction and Notation. 1.2. Fluid Statics and the Atmosphere. 1.3. The Boundary Layer Concept. 1.4. Inviscid Aerodynamics. 1.5. Review of Elementary Potential Flows. 1.6. Incompressible Flow over Airfoils. 1.7. Trailing-Edge Flaps and Section Flap Effectiveness. 1.8. Incompressible Flow over Finite Wings. 1.9. Flow over Multiple Lifting Surfaces. 1.10. Wing Stall and Maximum Lift Coefficient. 1.11. Wing Aerodynamic Center and Pitching Moment. 1.12. Inviscid Compressible Aerodynamics. 1.13. Compressible Subsonic Flow. 1.14. Supersonic Flow. 1.15. Problems. 2. Overview of Propulsion. 2.1. Introduction. 2.2. The Propeller. 2.3. Propeller Blade Theory. 2.4. Propeller Momentum Theory. 2.5. Off-Axis Forces and Moments Developed by a Propeller. 2.6. Turbojet Engines: The Thrust Equation. 2.7. Turbojet Engines: Cycle Analysis. 2.8. The Turbojet Engine with Afterburner. 2.9. Turbofan Engines. 2.10. Concluding Remarks. 2.11. Problems. 3. Aircraft Performance. 3.1. Introduction. 3.2. Thrust Required. 3.3. Power Required. 3.4. Rate of Climb and Power Available. 3.5. Fuel Consumption and Endurance. 3.6. Fuel Consumption and Range. 3.7. Power Failure and Gliding Flight. 3.8. Airspeed, Wing Loading, and Stall. 3.9. The Steady Coordinated Turn. 3.10. Takeoff and Landing Performance. 3.11. Accelerating Climb and Balanced Field Length. 3.12. Problems. 4. Longitudinal Static Stability and Trim. 4.1. Fundamentals of Static Equilibrium and Stability. 4.2. Pitch Stability of a Cambered Wing. 4.3. Simplified Pitch Stability Analysis for a Wing-Tail Combination. 4.4. Stick-Fixed Neutral Point and Static Margin. 4.5. Estimating the Downwash Angle on an Aft Tail. 4.6. Simplified Pitch Stability Analysis for a Wing-Canard Combination. 4.7. Effects of Drag and Vertical Offset. 4.8. Effects of Nonlinearities on the Aerodynamic Center. 4.9. Effect of the Fuselage, Nacelles, and External Stores. 4.10. Contribution of Running Propellers. 4.11. Contribution of Jet Engines. 4.12. Problems. 5. Lateral Static Stability and Trim. 5.1. Introduction. 5.2. Yaw Stability and Trim. 5.3. Estimating the Sidewash Gradient on a Vertical Tail. 5.4. Estimating the Lift Slope for a Vertical Tail. 5.5. Effects of Tail Dihedral on Yaw Stability. 5.6. Roll Stability and Dihedral Effect. 5.7. Roll Control and Trim Requirements. 5.8. The Generalized Small-Angle Lateral Trim Requirements. 5.9. Steady-Heading Sideslip. 5.10. Engine Failure and Minimum-Control Airspeed. 5.11. Longitudinal-Lateral Coupling. 5.12. Control Surface Sign Conventions. 5.13. Problems. 6. Aircraft Controls and Maneuverability. 6.1. Longitudinal Control and Maneuverability. 6.2. Effects of Structural Flexibility. 6.3. Control Force and Trim Tabs. 6.4. Stick-Free Neutral and Maneuver Points. 6.5. Ground Effect, Elevator Sizing, and CG Limits. 6.6. Stall Recovery. 6.7. Lateral Control and Maneuverability. 6.8. Aileron Reversal. 6.9. Other Control Surface Configurations. 6.10. Airplane Spin. 6.11. Problems. 7. Aircraft Equations of Motion. 7.1. Introduction. 7.2. Newton's Second Law for Rigid-Body Dynamics. 7.3. Position and Orientation: The Euler Angle Formulation. 7.4. Rigid-Body 6-DOF Equations of Motion. 7.5. Linearized Equations of Motion. 7.6. Force and Moment Derivatives. 7.7. Nondimensional Linearized Equations of Motion. 7.8. Transformation of Stability Axes. 7.9. Inertial and Gyroscopic Coupling. 7.10. Problems. 8. Linearized Longitudinal Dynamics. 8.1. Fundamentals of Dynamics: Eigenproblems. 8.2. Longitudinal Motion: The Linearized Coupled Equations. 8.3. Short-Period Approximation. 8.4. Long-Period Approximation. 8.5. Pure Pitching Motion. 8.6. Summary. 8.7. Problems. 9. Linearized Lateral Dynamics. 9.1. Introduction. 9.2. Lateral Motion: The Linearized Coupled Equations. 9.3. Roll Approximation. 9.4. Spiral Approximation. 9.5. Dutch Roll Approximation. 9.6. Pure Rolling Motion. 9.7. Pure Yawing Motion. 9.8. Longitudinal-Lateral Coupling. 9.9. Nonlinear Effects. 9.10. Summary. 9.11. Problems. 10. Aircraft Handling Qualities and Control Response. 10.1. Introduction. 10.2. Pilot Opinion. 10.3. Dynamic Handling Quality Prediction. 10.4. Response to Control Inputs. 10.5. Nonlinear Effects and Longitudinal-Lateral Coupling. 10.6. Problems. 11. Aircraft Flight Simulation. 11.1. Introduction. 11.2. Euler Angle Formulations. 11.3. Direction-Cosine Formulation. 11.4. Euler Axis Formulation. 11.5. The Euler-Rodrigues Quaternion Formulation. 11.6. Quaternion Algebra. 11.7. Relations between the Quaternion and Other Attitude Descriptors. 11.8. Applying Rotational Constraints to the Quaternion Formulation. 11.9. Closed-Form Quaternion Solution for Constant Rotation. 11.10. Numerical Integration of the Quaternion Formulation. 11.11. Summary of the Flat-Earth Quaternion Formulation. 11.12. Aircraft Position in Geographic Coordinates. 11.13. Problems. Bibliography. Appendixes. A Standard Atmosphere, SI Units. B Standard Atmosphere, English Units. C Aircraft Moments of Inertia. Nomenclature. Index. <s> BIB002 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> The study of flight dynamics requires a thorough understanding of the theory of the stability and control of aircraft, an appreciation of flight control systems and a grounding in the theory of automatic control. Flight Dynamics Principles is a student focused text and provides easy access to all three topics in an integrated modern systems context. Written for those coming to the subject for the first time, the book provides a secure foundation from which to move on to more advanced topics such as, non-linear flight dynamics, flight simulation, handling qualities and advanced flight control. About the author: After graduating Michael Cook joined Elliott Flight Automation as a Systems Engineer and contributed flight control systems design to several major projects. Later he joined the College of Aeronautics to research and teach flight dynamics, experimental flight mechanics and flight control. Previously leader of the Dynamics, Simulation and Control Research Group he is now retired and continues to provide part time support. In 2003 the Group was recognised as the Preferred Academic Capability Partner for Flight Dynamics by BAE SYSTEMS and in 2007 he received a Chairman's Bronze award for his contribution to a joint UAV research programme. New to this edition: * Additional examples to illustrate the application of computational procedures using tools such as MATLAB , MathCad and Program CC . * Improved compatibility with, and more expansive coverage of the North American notational style. * Expanded coverage of lateral-directional static stability, manoeuvrability, command augmentation and flight in turbulence. * An additional coursework study on flight control design for an unmanned air vehicle (UAV). <s> BIB003 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> TABLE OF CONTENTS Preface to the Fifth Edition Part 1: Fundamental Principles 1. Aerodynamics: Some Introductory Thoughts 2. Aerodynamics: Some Fundamental Principles and Equations Part 2: Inviscid, Incompressible Flow 3. Fundamentals of Inviscid, Incompressible Flow 4. Incompressible Flow Over Airfoils 5. Incompressible Flow Over Finite Wings 6. Three-Dimensional Incompressible Flow Part 3: Inviscid, Compressible Flow 7. Compressible Flow: Some Preliminary Aspects 8. Normal Shock Waves and Related Topics 9. Oblique Shock and Expansion Waves 10. Compressible Flow Through Nozzles, Diffusers and Wind Tunnels 11. Subsonic Compressible Flow Over Airfoils: Linear Theory 12. Linearized Supersonic Flow 13. Introduction to Numerical Techniques for Nonlinear Supersonic Flow 14. Elements of Hypersonic Flow Part 4: Viscous Flow 15. Introduction to the Fundamental Principles and Equations of Viscous Flow 16. A Special Case: Couette Flow 17. Introduction to Boundary Layers 18. Laminar Boundary Layers 19. Turbulent Boundary Layers 20. Navier-Stokes Solutions: Some Examples Appendix A: Isentropic Flow Properties Appendix B: Normal Shock Properties Appendix C: Prandtl-Meyer Function and Mach Angle Appendix D: Standard Atmosphere Bibliography Index <s> BIB004 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> This paper describes the modeling, control and hardware implementation of an experimental tilt-rotor aircraft. This vehicle combines the high-speed cruise capabilities of a conventional airplane with the hovering capabilities of a helicopter by tilting their four rotors. Changing between cruise and hover flight modes in mid-air is referred to transition. Dynamic model of the vehicle is derived both for vertical and horizontal flight modes using Newtonian approach. Two nonlinear control strategies are presented and evaluated at simulation level to control, the vertical and horizontal flight dynamics of the vehicle in the longitudinal plane. An experimental prototype named Quad-plane was developed to perform the vertical flight. A low-cost DSP-based Embedded Flight Control System (EFCS) was designed and built to achieve autonomous attitude-stabilized flight. <s> BIB005 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> We propose a new aerial tool operation system consisting of multiple quadrotors connected to a tool by spherical joints to perform tool operation tasks. We model the system and show that the attitude dynamics of each quadrotor is decoupled from the tool dynamics, so that we can consider the quadrotors as thrusters and control the tool by adjusting the orientation and magnitude of these thrusters. We also show that the 6-DOF tool dynamics could be under-actuated or fullyactuated, depending on the number of quadrotors attached to the tool and the geometric configuration of their attachments. We then design control laws for the tool-tip position/orientation tracking of the (under-actuated) tool system with two quadrotors and the (fully-actuated) tool system with three quadrotors. We use Lyapunov approach to find the desired thrust command for each quadrotor while also taking into account the spherical joint limits in a form of constrained optimization. Simulation and implementation results are performed to support the theory. <s> BIB006 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> In this paper a novel aerial manipulation system is proposed. The mechanical structure of the system, the number of thrusters and their geometry will be derived from technical optimization problems. The aforementioned problems are defined by taking into consideration the desired actuation forces and torques applied to the end-effector of the system. The framework of the proposed system is designed in a CAD Package in order to evaluate the system parameter values. Following this, the kinematic and dynamic models are developed and an adaptive backstepping controller is designed aiming to control the exact position and orientation of the end-effector in the Cartesian space. Finally, the performance of the system is demonstrated through a simulation study, where a manipulation task scenario is investigated. <s> BIB007 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> We propose a novel multi-rotor flying platform, ODAR (omni-directional aerial robot), which is fully-actuated (i.e., can assume arbitrary motion in SE(3) or generate arbitrary control wrench in se(3)) by six opportunistically distributed rotors, each driven by reversible ESC (electronic speed controller) for bi-directional thrust generation. Due to this omni-directional wrench generation, the ODAR system can realize such powerful behaviors impossible with conventional multi-rotor flying platforms as: 360° photo/video shooting while holding its position for VR scene generation; or resisting sideway gust while keeping its attitude and exerting downward pushing force larger than its own weight for aerial manipulation applications. This paper presents optimal mechanical design, modeling and control, hardware and software implementation, and experimental verification of the ability of the ODAR system to attain those behaviors impossible with the conventional drones as stated above. <s> BIB008 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> In this study, we investigated a novel type of the multirotor aerial vehicle with two-dimensional multilinks to demonstrate stable aerial transformation for high mobility in three-dimensional environments. Our goal was to tackle the challenge of traversing narrow spaces or gaps, which is one of the difficulties for existing structure of multirotors, especially in the cluttered indoor environment of disaster sites. The research involved three steps. First, we developed the modeling of the link modules that compose a multirotor with two-dimensional multilinks and conducted a quadrotor prototype. Second, we derived a stable flight control method for aerial transformation on the basis of linear-quadratic-integral optimal control. Third, we investigated the motion planning for the aerial transformation using a state validation method and path optimization in the joint space to maintain the stability during transformation. Successful aerial transformation and the ability of the prototype to negotiate narrow gap... <s> BIB009 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> In this article a Tilt-Wing Unmanned Aerial Vehicle (TW-UAV) and the preliminary evaluation of its hovering characteristics in extended simulation studies are presented. In the beginning, an overview of the TW-UAV's design properties are established, highlighting the novelties of the proposed structure and the overall merits. The TW-UAV's design and structural properties are mathematically modeled and utilized for the synthesis of a cascaded P-PI and PID based control structure for the regulation of its hovering performance. In addition, extensive simulation trials are performed in order to evaluate the structure's efficiency in controlling the TW-UAV's attitude and position under various noise and disturbance scenarios. <s> BIB010 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> This paper describes the Transformable HOvering Rotorcraft (THOR), a prototype Unmanned Aerial Vehicle (UAV) that explores a novel approach in combining the range and speed of a horizontal flying platform with the hovering and maneuverability of a rotor-wing. This is achieved by integrating a tailless flying wing configuration with a single-axis rotor, or monocopter. By maintaining full utilization of all aerodynamic surfaces and propulsion sources in both flight modes, this method represents the most structurally efficient approach to achieving a cruising mode and a hovering mode on the same frame. Using a dual servo and motor configuration, we propose an under-actuated system that is able to achieve controllability in 4 degrees of freedom while in its horizontal cruising mode and in 5 degrees of freedom while in its hovering mode. In both indoor and outdoor experiments, the UAV is able to transition between either flight modes seamlessly and repeatedly without the need for any additional mechanisms and actuators. <s> BIB011 </s> Snake Aerial Manipulators: A Review <s> ,6,8. <s> This paper presents a theoretical study on omni-directional aerial vehicles with body-frame fixed unidirectional thrusters. Omniplus multi-rotor designs are defined as the ones that allow to exert a total wrench in any direction using positive-only lift force and drag moment (i.e., positive rotational speed) for each rotor blade. Algebraic conditions for a design to be omniplus are derived, a simple necessary condition being the fact that at least seven propellers have to be used. An energy optimal design strategy is then defined as the one minimizing the maximum norm of the input set needed to span a certain wrench ellipsoid for the adopted input allocation strategy. Two corresponding major design criteria are then introduced: firstly, a minimum allocation-matrix condition number aims at an equal sharing of the effort needed to generate wrenches in any direction; secondly, imposing a balanced design guarantees an equal sharing of the extra effort needed to keep the input in the non-negative orthant. We propose a numerical algorithm to solve such optimal design problem and a control algorithm to control any omnidirectional platform. The work is concluded with informative simulation results in non-ideal conditions. <s> BIB012
Another challenge here is that, as it is presented in  , BIB006 , BIB007 , BIB008 , BIB009 , the dynamic and kinematic equations between the propellers and some center of reference, that is usually placed in the center of mass or gravity, now is fixed to a movable point. This way, some considerations such as lever arms, moments of inertia and the control design by itself, are related intrinsically to the shape of the system and not only to the tasks. Discussion: This section has discussed a preliminary classification based on the aircraft or propeller interconnection. A flexible configuration was shown, and also two rigid configurations, the serial and the parallel approaches. The known details above these configurations was already indicated, but it is convenient to investigate: The rigidity usually implies density and this consequently entails weight, although there are widely used materials such as carbon fiber, it would be convenient to use designs whose 3D-printing layers are by defect shock resistant, very hard (through high porosity, but high density) and over all ultra-light  . Other option is to take up the use of inflatable structures with highly resistant coatings. Based on the above, it would be appropriate not only to do research on fully rigid designs or fully flexible ones, but on intermediate or variable hardness designs, considering aerodynamical effects. The previous point would also implies an additional application to aerial robotic manipulators: physical systems test-benchs for mathematics and control on continuous, discrete and hybrid systems. This also implies the design of new centralized and decentralized cooperative control schemes, including new optimization problems. As it will be seen later, these problems are based on the fact that it is not very convenient to allow the reversibility of a propeller (because is not an instantaneous action and also it implies destructive inertial effects), examples of this, were highlighted and addressed by Nikou [], Tognon and Franchi BIB012 C. DESIGN CONSIDERATIONS OF AERODYNAMICS Concerning to aerodynamics, design is divided into three groups: On the flight: this is a dynamic operation, requires standard aerodynamic design, which corresponds to wind interaction, vortex effects, and other common phenomena acting on regular aircraft BIB004  BIB003  [92] BIB002 . It's convenient to transform the aerial manipulator into a tandem helicopter, a counterrotating one or an airplane and to develop ways for keeping the frame rigid, the task is devoted just to translate the full aerial robot to a distant workplace. As it can be noticed, this is a full structure task, and it is also useful for transporting objects  , BIB009 . In situ: this is a quasi-static operation, because is required a hoovering base in order to manipulate objects or to do miscellaneous robotic manipulator-like tasks, also if the aerial robot is in movement the velocities are expected to change slowly or in a constant manner for considering a kinodynamic model and control  ,  , where the dynamic control is just for translation and the kinematic like-manipulator control is concerned to orientations. The in situ tasks are related to hovering power consumption, distance among propellers, distance among manipulated and interacting objects and distance with respect to the floor [95]- BIB001 . Transformation: is needed to apply methods and algorithms in order to change between on the flight and in situ modes BIB010  BIB005 BIB011 (also see helibot throughout this text). This change also needs to do be done in a smooth way in cases of interacting with fragil materials or living beings. In the case of massive or volumetric aircrafts the transformation phase is by itself a challenge (e.g. V-22 Osprey)  ,  . Discussion: This section has remarked the three main flight operations of snake aerial manipulators and their inherent aerodynamic design considerations. Among the described, the most complex aerodynamic problems occur in the stages of transformation, manipulation and dexterity, especially if they are open kinematic chains, and it is convenient to analyze the turbulence and vortexes induced by arm-movements (as when swimming), and indicate how they affect both the hovering and the execution of the task to be performed. For this, even in an indoor test where the air flow is usually laminar, arm-movements can lead to chaotic effects and disturbances (it should be mentioned that the existing demonstrations of snake aerial manipulators have been conducted at low speeds). Here the point also implies a more specialized design of the linkages which at present are just solid and tubular assemblies, perhaps it is even advisable to think on like fish-scaled surface patterns to counteract the effect of such vortexes and turbulence. On the other hand, just as in the standard robotics of manipulators there are inoperability or redundant conditions known as singularities, it is also convenient to investigate for the these aerial manipulators if there are aerodynamic singularities, that is to say, configurations beyond the limits of mobility and force where the flight flows are canceled or become too much chaotic to allow the correct operation of the system, remembering that in this type of aircraft the interaction is not only mechanical but also fluidic. With the above it is also feasible to determine the previous question on which is more stable and efficient: an snake aerial robot based on aircraft interaction or the versions based on propellers or valves. Finally, as already noted, many types of stability and efficiency have been mentioned: aerodynamics, power consumption, task efficiency, control efficiency, etc., the next question is: How to rank these efficiencies and determine which of them is more relevant in these morphing-shape systems and their variable operating modes?