Anand Sanchez-Orta

• PhD
• Professor (Full) at Center for Research and Advanced Studies of the National Polytechnic Institute

In the last decade, unmanned aerial vehicles (UAVs), commonly known as drones, have been used for different purposes, including applications such as search and rescue, highway patrol, and infrastructure inspections for power lines, bridges, and factories. These applications require UAVs that can operate under specific conditions or complex environm...

Quadrotor navigation has been studied mainly in a free-flight regime, and a multitude of modeling and control schemes have been proposed, but fewer schemes have been proposed for engaging purposely contact. The flight regime of contact tasks is needed, for instance, to polish a surface or turn on a switch, where simultaneous force-position is requi...

On the one hand, a class of model-free integral sliding modes requires damping injection to stabilize the closed-loop system to a certain bound. This technique has been extended to a variety of robots, including quadrotors. However, the damping matrix K value is difficult to calculate precisely. Henceforth, it is customary to overestimate it in pra...

This paper presents the design of a new control scheme for a group of omnidirectional robots in a multi-robot system operating in an environment with obstacles. The control scheme uses a decision agent based on discrete-time Markov chains and takes into account the state of the system, obstacle positions, and geometries to manipulate targets, provi...

Accelerated advances in science and technology drive the need for professionals with flexible problem-solving abilities towards a collaborative working environment. The advances pose a challenge to educational institutions about how to develop learning environments that contribute to meeting the aforementioned necessity. Additionally, the fast pace...

Euler–Lagrange mechanical systems usually possess nonlinear models, which are subject to uncertainties and unknown disturbances. In this article, a robust but smooth controller is proposed, relying on a high-gain proportional–integral structure that renders an accurate tracking, even in the case of uncertain effects. The tracking performance can be...

An observed-based control strategy for position-yaw tracking of quadrotors is proposed. From a virtual controller for the position dynamics, attitude and angular velocity references are estimated with the aim of allowing the position-control components to enforce the tracking of a position reference. In addition, no measurement of the linear veloci...

Disturbance observer-based control allows to compensate unknown inputs, however, in most cases, requiring their integer-order differentiability. In this paper, a novel disturbance observer-based state feedback controller is proposed to compensate a more general class of fractional-, but not necessarily integer-order, differentiable unknown inputs....

A novel contour tracking scheme is proposed, which is based on a well-posed kinematic representation of differential-drive nonholonomic mobile robots. Firstly, a velocity field is designed to encode the desired velocity vector pointing to the target (the contour), using a fuzzy aggregation of spatial sets in cluttered environments. The resultant sm...

Surveillance is a major concern nowadays for the development of autonomous vehicles (AVs) technology, in particular during prototyping stage. However, it is unclear what an effective strategy is for aerial imagery with drones. On one hand, the dynamics of such autonomous vehicle is commonly subject to non-holonomic constraints, whose steering wheel...

The Super Twisting Control Algorithm (STA) constitutes a powerful and robust technique for control and observation problems. The structure of the STA allows inducing second-order sliding modes, such that the sliding variable and its derivative remain at zero after some finite time. However, the STA requires the strong differentiability of the slidi...

Wind energy constitutes an important renewable resource for environmentally safe production of electricity. To assure maximum energy capture, the turbine rotor tracks a nominal profile depending on the wind speed, requiring a fast and robust controller to overcome the presence of disturbances and abrupt wind speed changes. Besides, just a part of t...

In this paper, a robust geometric navigation algorithm, designed on the special Euclidean group SE(3), of a quadrotor is proposed. The equations of motion for the quadrotor are obtained using the Newton-Euler formulation. The geometric navigation considers a guidance frame which is designed to perform autonomous flights with a convergence to the co...

Dynamic models approximate physical phenomena to certain extent and ideal controllers are proposed. Nevertheless, when system specifications crave for better performance, additional robust controllers are considered. In this sense, a robust controller is proposed in this paper, which accounts for a general class of fractional-order systems, in orde...

This paper aims at designing a contour tracking scheme based on an adaptive velocity field formulation, for the case of uncertain non-holonomic (differential drive) mobile robots, with its dynamic controller. Firstly, in order to handle kinematic uncertainties that deviates the map of the velocity field into wheel velocities, a linear parameterisat...

This paper proposes an adaptive control method for the robust stabilization of a general class of fractional-order systems, which are subject to matched and mismatched disturbances. The control design is based on a nominal linear-time-invariant system, and the deviation from such a model is considered as the disturbance, which is decoupled as the s...

A robust attitude quadrotor control based on a novel differintegral PI nonlinear structure is proposed and experimentally validated. The proportional action depends on a nonlinear transformation of the sliding variable, while the integral action of fractional-order rejects non-differentiable disturbances, such as turbulent effects and gust winds, e...

In order to assure maximum energy capture, the angular velocity of the rotor of a wind turbine tracks a nominal profile depending on the wind speed. Thus, a fast and robust controller is required to induce such nominal regime for maximum energy capture. However, conventionally, wind flows present non-differentiable components due to turbulence and...

It is well known that a fractional-order system with a continuous right hand side does not have finite-time stable equilibria, but the discontinuous case has remained elusive in literature. Thus, based on novel mathematical tools, recently published in literature, it is demonstrated that, it is not possible for a fractional-order system to attain f...

A nonlinear PID controller for robust tracking of second-order nonlinear systems is proposed, which consists in a classical PD structure plus a fractional-order nonlinear integral action of control (FONLI). This Nonlinear Integral Action of Fractional-order induces robustness properties to the closed-loop system in order to withstand for a general...

Linear PID controller stands for the most widespread technique in industrial applications due to its simple structure and easy tuning rules. Recently, considering fractional orders λ and μ, there has been studied the fractional-order PI^λD^μ (FPID) controller to provide salient advantages in comparison to the conventional integer-order PID, such as...

Quadrotors are autonomous aerial vehicles widely developed in the last decade due to their small size, low weight and vertical take off and landing capabilities. Nowadays, some demanding applications involve the quadrotor interacting with rigid objects, requiring stable contact and force tracking. In this paper, an attitude control is proposed to h...

Based on proximal subdifferentials and subgradients, and instrumented with an extended Caputo differintegral operator, the stability analysis of a general class of fractional-order nonlinear systems is considered by means of non-smooth but convex Lyapunov functions. This facilitates to conclude Mittag--Leffler stability for fractional-order systems...

In this paper a model-free continuous nonlinear control law for the attitude of a quadrotor, based on the Attractive Ellipsoid Method and a saturation term, is proposed. This control law allows the vehicle to track aggressive maneuvers, such as multiple flips about the y axis of the body frame, with high angular velocities. The controller is design...

Quadrotors are highly maneuverable light weight drones, which are prone to aerodynamic disturbances, vibrations and uncertainties. These factors stand for a problem that demands robust control laws. For position tracking, the control problem is exacerbated because the plant is underactuated in the coordinates of interest, requiring a high performan...

The robust control for a class of disturbed fractional-order systems is presented in this paper. The proposed controller considers a dynamic observer to exactly compensate for matched disturbances in finite-time, and a procedure to compensate for unmatched disturbances is then derived. The proposed disturbance observer is build upon continuous frac...

The problem addressed in this paper is the on-line differentiation of a signal/function that possesses a continuous but not necessarily differentiable derivative. In the realm of (integer) high-order sliding modes, a continuous differentiator provides the exact estimation of the derivative D f(t), of f(t), by assuming the boundedness of its second-...

Solutions of fractional-order differintegral equations are generally not necessarily integer-order differentiable, neither in the strong nor in the weak sense, thus limiting the stability analysis in systems based on the most conventional fractional-order operators. In this paper, a consistent and well-posed definition for fractional-order systems...

When robots grasp a rigid object, homogeneous holonomic constraints give rise to a stiff nonlinear constrained dynamics, thereby, smooth motion is preferred to grasp tightly but gently the object, making it a difficult control problem that increases when there exist uncertainties and unmodelled dynamics. In this paper, a fuzzy design is proposed by...

Recently, a great effort has been devoted for designing robust control techniques that compensate for lumped disturbances in mechanical robots and general electro-mechanical systems through disturbance observers. In this paper, assuming the Hamiltonian structure of Euler-Lagrange systems subject to a wider class of disturbances, and by exploiting s...

The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fr...

In this paper, a design of a robust filter (state observer), which improves the state estimation of a quadrotor, is presented. It is considered that the available measurements, from low-cost sensors, have significant noise and uncertainties. Additionally, in some cases the aerial vehicle does not count with the instrumentation for the accurate esti...

A new fractional-order controller is proposed, whose novelty is twofold: i) it withstands a class of continuous but not necessarily differentiable disturbances as well as uncertainties and unmodeled dynamics, and ii) based on a “principle of dynamic memory resetting” of the differintegral operator, it is enforced an invariant sliding mode in finite...

Some hydrodynamic phenomena of an underwater Remotely Operated Vehicle (ROV), such as turbulence, cavitation, and multi-phase fluidic regimes, are associated to continuous but nowhere differentiable functions. These disturbances stand as complex forces potentially influencing the ROVs during typical navigation tasks. In this paper, the tracking con...

Aiming at designing a robust controller to withstand a class of continuous, but not necessarily differentiable, disturbances, such as Hölder type, a continuous and chattering-free sliding mode control is proposed. The key idea is a judicious synthesis of a resetting memory principle for the differintegral operators to show that a sliding mode is in...

Memory and heritage of differintegral operators require knowledge of the error manifold derivative at the initial time to sustain a sliding motion for any initial condition. Moreover, when the system is subject to (unknown) disturbances, such initial condition is unknown; thus, the enforcement of an integral sliding motion has been elusive with a c...

Quadrotors are Unmanned Aerial Systems (UAS), whose nonlinearities, uncertainties, and unavoidable aerodynamic disturbances stand for a difficult control problem. Additionally, the highly nonlinear coupling between the position and the orientation dynamics exacerbates the underactuation problem when the objective is the position tracking. In this p...

Light weight quadrotors are highly manoeuvrable autonomous aerial robots (UAV) that outperform most UAVs; however, quadrotors are prone to a wide class of aerodynamic disturbances, vibrations, and uncertainties that demand not only robust but fast attitude control structures. These arguments are compelling enough to motivate the design of a novel f...

An integral sliding mode controller based on fractional order differintegral operators is proposed. This controller generalizes the classical discontinuous (integer order) integral sliding mode scheme. By using differitegral operators, their topological properties lead to a uniformly continuous controller that enforces an integral sliding mode for...

Aiming at clarifying recent advances on disturbance rejection, we analyze a class of non-differentiable disturbances. We expose some subtle but fundamental differences between the fractional order (FO) and integer order (IO) integral sliding modes (ISM) to control a general class of nonlinear dynamical systems. This comparative study suggests that...

Exploiting algebraic and topological properties of differintegral operators as well as a proposed principle of dynamic memory resetting, a uniform continuous sliding mode controller for a general class of integer order affine non-linear systems is proposed. The controller rejects a wide class of disturbances, enforcing in finite-time a sliding regi...

This paper focuses on a convertible unmanned aerial vehicle (CUAV) whose main characteristics is to perform hover flight for launch or recovery, and horizontal mode during cruise. The dynamic model is obtained using the Newton-Euler approach and it considers the aerodynamic effects. An adaptive backstepping control, based on quaternions, is propose...

There exists a large class of physical systems modeled by differential equations subject to holonomic constraints, called DAE (Differential Algebraic Equations) systems, such as constrained robots. Several schemes have been successfully implemented by using integer order error manifolds, however no studies have been reported on fractional order man...

Brain Computer Interface (BCI) has emerged as a mechanism to communicate users with machines using simple high-level EEG commands by decoding brain rhythms. When a BCI is used for online command of a kinematic or dynamic external agent (either real or virtual ones), human perceives the task with different attributes, thus different brain regions ar...

This paper focuses on the aerodynamic design and performance of a mini airplane UAV. The mini aerial vehicle is based on a conceptual design considering a high aerodynamic finesse (a high ratio between lift and drag), flying and handling qualities in order to perform a reliable and stable flight. The equations of motion are described using the Newt...

A yaw angle, different from zero, introduces highly nonlinear couplings in the rotational and translational quadrotor dynamics, implying undesirable motions. This argument has motivated that the position control problem of quadrotors is studied generally regulating yaw at zero. However, zeroing yaw limits the maneuverability of underactuated quadro...

Abstract—The command of a dynamic entity with Brain-Computer Interfaces, based on a noninvasive low cost device that interprets EEG signals to infer commands, has been pursued with apparent success. However, little is understood on how to deal with the online dynamic response of the external robot. In this paper, sequences of neural activity during...

Euler-Lagrange systems, such as robots, exhibit benign structural properties, including passivity, which allow us to design robust and efficient energy-shaping controllers. In this paper, a fractional order absolutely continuous control scheme for Euler-Lagrange systems is proposed, without depending on the dynamic model, which enforces in finite-t...

In multi-rotor UAVs, a controlled Thrust is a main factor to achieve a safe and stable flight. Thrust is the result of a coordinated action of a set of symmetrically distributed thrusters whose single contribution is usually described as a square function of its rotor speed; however, aerodynamic forces induce a load torque on the rotor that disturb...

The model-free sliding mode control based on fractional order sliding surface is built upon: i) An absolutely continuous control structure that does not require the exact dynamic model to induce a fractional sliding motion in finite time, and ii) A methodology to design fractional references with a clear counterpart in the frequency domain is propo...

A flexible tool to dimensioning and optimizing the performance of a propeller-engine system for multi-rotor Unmanned Aerial Vehicles (UAVs) is proposed. The study is centered on an experimental platform designed to identify the dynamic behavior of the thruster which operates as main actuator in multi-rotor UAVs. The aim is to optimize the performan...

Velocity field (VF) control has proved effective for kinematic robots, aiming essentially at providing desired velocities for navigation along the field, and for obstacle avoidance in cluttered environments. When robot dynamics are involved, it is usually considered either that dynamics are known and that robot is fully actuated, thus it is not cle...

Modern non-inertial robots are usually underactuated, such as fix or rotary wing Unmanned Aerial Vehicles (UAVs), underwater or nautical robots, to name a few. Those systems are subject to complex aerodynamic or hydrodynamic forces which make the dynamic model more difficult, and typically are subject to bounded smooth time-varying disturbances. In...

Based on adaptive wavelet neural net-works, a PID discrete control scheme for induction motor drives is presented. An auto-tuning wavenet scheme is synthesized for the PID feedback gains by means of gradient-descendent algorithm through online plant identification. The latter uses input and output data for a radial basis neural network (RBNN) with...

In this paper we present a model of a Propeller-Engine system and a simulation analysis of its dynamics in order to estimate the total load torque produced by the aerodynamic effects of a spinning propeller attached to its rotor when it is used as a thruster in small scale Unmanned Aerial Vehicles. The contribution is twofold: first, we obtain the...

In this paper, we introduce the concept of time parametrization for Quadrotor flight maneuvers establishing a novel, robust and model free feedback controller based on a quaternion representation without singularities. Three prominent features are remarked: firstly, the control algorithm assures exponential stability of the full position/attitude d...

Passive Force Velocity Field Control (PFVFC) renders tracking along tangent of the contour, with low normal velocity regime, which is of particular interest for constrained tasks. Despite the evident advantageous characteristics of PFVFC, the original pioneering approach by Li&Horowitz has shown limitation for implementation. In this paper, a simpl...

Quadrotor are non-inertial systems with inherent nonlinear, very fast and very unstable dynamics where measurements of their state variables in an absolute frame of reference are very complex in GPS denied environments, such as indoors. In order to design control strategies for Quadrotors, we solve problems of imprecisely known models and noisily,...

Velocity field (VF) control has proved effective for mobile robots and robot arms, aiming essentially at navigation and obstacle avoidance under position and velocity control in cluttered environment, however additional features are required for quadrotors due to its underactuated flight dynamics. The design of a VF control then comprises of two as...

A simple, fast and robust Passive Velocity Field Control (PVFC) scheme for contour tracking in 2D and 3D is presented. A model-free and chattering-free second order sliding mode controller is proposed, which enforces an invariant manifold for all time such that the generalized velocity tracks the spatial velocity field. A constructive simple and in...

A backstepping-based controller that induces integral sliding modes for underactuated lightweight quadrotors is presented for the Newton-Euler dynamic model subject to smooth bounded disturbances, including wind gust and sideslip aerodynamics, as well as dissipative drag in position and orientation dynamics. The chattering-free sliding mode compens...

In this paper, a multiple UAVs control scheme is developed considering the full nonlinear position/orientation model of a j-Quadrotor system. A novel second order sliding mode controller is presented which guarantees exponential and robust tracking of admissible time-varying pose. The harmful chattering is not involved and no dynamic model is requi...

Two novel model-free second order sliding mode controllers are proposed for the constrained underactuated position and orientation dynamic model of the quadrotor, i.e., considering contact wrench, based on spring-like contact force model. The main theorem establishes conditions for the closed-loop system to guarantee semi-global exponential and rob...

Motivated by the fact that regulating yaw at zero avoids complex second order aerodynamical terms coming from cross build up of thrust vector, which looses lift and increases drag, the position control problem of quadrotors has been studied generally regulating desired yaw, which limits the scope of underactuated quadrotors because yaw is a degree...

In this paper, a multiple UAVs control scheme is developed considering the full non-linear position/orientation model of a j-Quadrotor system. A novel second order sliding mode controller is presented which guarantees exponential and robust tracking of admissible time-varying pose. The harmful chattering is not involved and no dynamic model is requ...

A new control scheme for position-orientation tracking of underactuated quadrotor robotic vehicle is proposed. A quaternion-based sliding surface parametrizes the open-loop error equation of orientation dynamics, then a second order sliding mode (SOSM) is synthesized for global exponential stabilization of attitude coordinates along an orientation...

In this paper, we present the design of an autopilot embedded system applied to control a four rotor mini helicopter, called X4-flyer. The main goal is to achieve a stable flight, controlling the vehicle attitude; this is done using two control strategies: a linear PD control and nonlinear nested saturations control. The onboard system uses a simpl...

This paper present the design of a novel embedded control system for improving attitude stabilization of a quad-rotor mini UAV. The control strategy uses low cost components and includes an extra control loop based on motor armature current feedback. This additional control loop significantly improves the performance of the quad-rotor attitude stab...

We propose a vision-based position control method, with the purpose of providing some level of autonomy to a quad-rotor unmanned aerial vehicle. Our approach estimates the helicopter X-Y-Z position with respect to a landing pad on the ground. This technique allows us to measure the position variables that are difficult to compute when using convent...

In this paper, we present a comparison of three control techniques: Nested Saturations, Backstepping and Sliding Modes. The control objective consists of obtaining the best control strategy to stabilize the position of a quad-rotor when using visual feedback. We propose a method to measure translational speed as well as the UAV 3D position in a loc...

We present a vision system that deals with the problem of local estimation of the position and velocity of a UAV quad-rotor indoor. Our approach is based in the estimation of homographies from a visual landmark. Stabilizing the UAV locally, real time experiments demonstrate the effectiveness of our method.

We propose a vision based position estimation algorithm to provide some level of autonomy for a quadrotor unmanned aerial vehicle (UAV). Our approach estimates the helicopter X-Y-Z position with respect to a ground landmark. This technique allows us to measure the position variables that are difficult to compute when using conventional navigation s...

This paper present the design of a novel embedded control system for improving attitude stabilization of a quad-rotor mini UAV. The control strategy uses low cost components and includes an extra control loop based on motor armature current feedback. This additional control loop significantly improves the performance of the quad-rotor attitude stab...

Introduction Two-rotor UAV Control algorithm design Experimental platform Conclusion Bibliography

Introduction Dynamic model of a flying VTOL vehicle Attitude control of a flying VTOL vehicle Triple tilting rotor rotorcraft: Delta Single tilting rotor rotorcraft: T-Plane Concluding remarks Bibliography

Introduction Brushless DC motor and speed controller Quad-rotor Control strategy System configuration Experimental results Concluding remarks Bibliography

In this paper we present new results to compute the robustness margin of an attitude control algorithm for a quad-rotor mini-rotorcraft known as X4-flyer. The maximum parametric uncertainty is calculated when multivariable PD controller is used to stabilize the attitude of the aerial vehicle. This work is based on the value set characterization app...

Autonomous navigation of an unmanned aerial vehicle (UAV) can be achieved with a reactive system which allows the robot to overcome all the unexpected changes in its environment. In this article, we propose a new approach to avoid frontal obstacles using known properties of the optical flow and by taking advantage of the capability of stationary fl...

The purpose of this paper is to present a new configuration of a vectored-thrust coaxial UAV(V-co-aX). The main characteristic of this vehicle is that it uses thrust vectoring for control in hover mode. A functional description of this mechanism is given and the Newton-Euler approach is applied to obtain the dynamic model of the flight platform. A...

This paper presents a global stabilization of a chain of n integrators in cascade. The control strategy is obtained using the Lyapunov approach and separated saturation functions. Moreover, the stability analysis is obtained using the recurrence theorem. This generalized control law is designed in order to quickly implement it on a system, as choos...

In this paper, we describe the dynamic model of a four-rotor mini rotorcraft, and present the hardware design of real-time embedded control system for small Unmanned Aerial Vehicles (SUAV). We improve the driver performance for Brushless Direct Current (BLDC) motor. In addition, the modular programming method is adopted in software design to carry...

The real-time embedded control system for the quad-rotor helicopter is designed by using commercially available components which are inexpensive with the driver modified of BLDC (Brushless Direct Current) motor. These components are integrated into the electric PCB (Printed Circuit Board) meanwhile the corresponding embedded multitasking software i...

In this paper, the real-time embedded control system for quad-rotor helicopter is designed, while its flight mode is analyzed. The driver for brushLess direct current (BLDC) is improved. In addition, the multi-tasks programming method is adopted in software design to carry out the computation of control law, data processing and correction output to...

The aim of this paper is to present a configuration for a Convertible Unmanned Aerial Vehicle, which incorporates the advantages of the coaxial rotorcraft for hover flight and the efficiencies of a fixed-wing for forward flight. A detailed dynamical model, including the aerodynamics, is obtained via the Newton-Euler formulation. It is proposed a no...

The aim of this paper is to present a configuration for a Convertible Unmanned Aerial Vehicle, which incorporates the advantages of the coaxial rotorcraft for hover flight and the efficiencies of a fixed-wing for forward flight. A detailed dynamical model, including the aerodynamics, is obtained via the Newton-Euler formulation. It is proposed a no...

The goal of this paper is to present a novel configuration for a three-rotor mini unmanned aerial vehicle (UAV). The proposed design incorporates advantageous structural features which enhance the maneuverability of the rotorcraft. The detailed mathematical model of the vehicle's attitude is obtained through the Newton-Euler formulation. In terms o...

In this paper we address the development of a single-rotor tail-sitter Unmanned Aerial Vehicle (UAV), whose configuration provides structural benefits for flight stabilization. The mathematical model of the vertical take-off landing (VTOL) aircraft is obtained through the Newton-Euler approach. In order to stabilize the vehicle we employ a control...

The aim of this paper is to present a mini tilt-rotor unmanned aerial vehicle which is capable to perform hover flight. Unlike conventional full-scale tiltrotors, in our design we avoid the use of swashplate and we propose a simpler mechanical design which use only the tilting rotors to stabilize the vehicle dynamics. A detailed mathematical model...

The aim of this paper is to present a mini tilt-rotor unmanned aerial vehicle which is capable to perform hover flight. Unlike conventional full-scale tiltrotors, in our design we avoid the use of swashplate and we propose a simpler mechanical design which use only the tilting rotors to stabilize the vehicle dynamics. A detailed mathematical model...

A simple real-time stabilization of a vertical takeoff and landing (VTOL) aircraft based on Lyapunov analysis and saturation functions is presented. The proposed controller is studied in simulation and in real-time experiments in two prototypes of quad-rotor helicopters. The controller is applied to control the altitude of a radio-controlled electr...

The aim of this paper is to present a configuration for a Convertible Unmanned Aerial Vehicle (CUAV), which incorporates the advantages of the coaxial rotorcraft for hover flight and the efficiencies of a fixed-wing for forward flight. A detailed dynamical model, including the aerodynamics, is obtained via the Newton-Euler formulation. It is propos...

This paper deals with the problem of stabilizing n integrators in cascade with bounded input using a discrete-time controller. We propose here a control algorithm using saturation functions for the case of 3 integrators and then we extend the development to the case of n integrators. The control methodology developed is simple and is explicitly giv...

In this paper we present an original configuration of a small aerial vehicle having eight rotors, four of them are devoted to stabilize the helicopter and the rest are used to drive the lateral displacements. The dynamical model is obtained using Euler-Lagrange approach, the attitude dynamics (roll, pitch and yaw) are practically independent of the...