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Robust Attitude Control With Fixed Exponential Rate of Convergence and Consideration of Motor Dynamics for Tilt Quadrotor Using Quaternions
Abstract
In the existing literature on the robust control design of UAV systems, the controllers are designed without considering motor dynamics. Hence, if these controller gains are not correctly tuned, the system undergoes oscillation and may even go unstable. We have demonstrated this through an experiment in this work. Here, we propose a novel control strategy that considers actuator parameter uncertainties, including motor dynamics for a tilt quadrotor. This strategy is based on the traditional two-loop control scheme where the inner loop controls the angular velocity, and the outer loop controls the vehicle’s attitude based on quaternions. In the quaternion-based controller, usually, the convergence rate increases when the quaternion starts closer to its equilibrium point, thus making it challenging to design a linear controller for the inner loop. To overcome this, we propose a nonlinear control with a varying gain for the outer loop that ensures the quaternion has a fixed convergence rate. We propose the control design of the inner loop, which consists of a disturbance observer (DOB) and a linear controller. The DOB is optimally designed to minimize external disturbances in the presence of model uncertainties. With the DOB, a linear controller is designed for the inner loop, guaranteeing robust stability and performance against the model and actuator parameter uncertainties. The results of experimental flights are reported in this paper, and the corresponding videos are at https://youtu.be/dS9WUR0yLhA.
Note to Practitioners
—This paper was motivated by the potential application of the tilt quadrotors in industry, such as surveillance in confined spaces and landing on high-speed moving targets, due to their independent control of position and orientation. We demonstrate that a controller designed without consideration of motor dynamics can result in unwanted oscillatory or unstable behaviour in the case of a UAV. So, the proposed method considers these dynamics during the design. In most of the existing control designs based on quaternion, the convergence rate depends on the initial condition. This paper proposes a nonlinear control with a varying gain to achieve a faster response that ensures the quaternion has a fixed convergence rate. The stability and convergence of this nonlinear controller are analyzed mathematically and validated through experiments. In UAVs, the precise moment-of-inertia and motor parameters are difficult to estimate, and external disturbances such as wind gusts are always present in outdoor environments. Therefore, this paper designs a robust control scheme which guarantees robust stability and performance against inertia and motor parameter uncertainties. Secondly, a disturbance observer (DOB) whose filter coefficient is optimally tuned such that the effect of external disturbance is minimized in the presence of model uncertainties. The proposed approach is validated on a tilt quadrotor in an outdoor environment and has a faster response than the existing ones having same maximum convergence rate. Thus, this proposed approach has potential applications, like landing a tilt quadrotor on a ship while the ship is in motion under the influence of waves and winds.
This article presents a visual servoing strategy that integrates the capabilities of a physics-informed neural network (PINN) to estimate system uncertainties and inaccuracies with a dynamics-centered visual servoing technique for multirotors. The proposed method effectively combines these approaches, eliminating the need for inverse Jacobian calculations to determine multirotor motion by directly relating pixel variations to the multirotor’s torque and thrust inputs, while also strengthening the method’s robustness through the utilization of the PINN to model and address uncertainties in camera and multirotor parameters, as well as the modeling inaccuracies inherent in the dynamics-centered visual servoing technique. In contrast to existing state-of-the-art data-driven approaches, the proposed PINN approach requires, on average, 65% less labeled data to characterize uncertainties and inaccuracies. To ensure real-time implementation of the visual servoing model, the PINN-learned model is combined with an adaptive horizon monotonically weighted nonlinear model predictive controller (NMPC), capable of processing control efforts at rates 10 times faster than existing Tube MPC and Adaptive MPC strategies. These findings are validated through real-time trajectory tracking experiments, which not only highlight the effectiveness of the proposed approach in approximating modeling inaccuracies but also its capability in handling uncertainties upto 70% in camera parameters.
Abstract—This paper investigates the attitude tracking problem
for spacecraft with limited communication, network congestion,
unknown model parameters, actuator saturation, and
external disturbances. To alleviate communication load, a novel
sigmoid event-triggered mechanism is proposed with the special
ability to guarantee a high minimum inter-execution time to avoid
network congestion like package loss or time delay effectively. A
neural network-based adaptive control algorithm is designed to
deal with unknown model parameters. Besides, the problem of
actuator saturation is tackled by introducing a dynamic loop
gain function-based approach. System stability is proved by
Lyapunov stability analysis and the high minimum inter-event
time is substantiated by Zeno Behavior analysis with explanatory
remarks. Numerical simulation results also show that a high
minimum inter-event time and a high average inter-event time
can be realized on the premise of high attitude tracking accuracy.
Compared with all the previous studies, the ratio of the minimum
inter-execution time to the average minimum inter-execution
time has been improved by nearly 10 times with the proposed
approach.
Note to Practitioners—This paper was motivated by the problem
of spacecraft attitude takeover control, but it also applies
to other aperiodic discrete-time control systems. Existing event-triggered control methods have solved the problem of limited
communication for attitude takeover control of spacecraft by
reducing the number of times wireless communication is required.
This paper proposes a new method for realizing quasiperiodic
control with a large time gap between any two consistent
control impulses using a hyperbolic tangent function or another
sigmoid function in an event-triggered mechanism. The proposed
sigmoid event-triggered mechanism (ETM) can magnify the
event-triggered threshold dozens of times in a short time to avoid
unnecessary frequent triggering without decreasing the precision
of control. It’s feasible to employ the proposed sigmoid ETM
to deal with limited communication and network congestion in
other network control systems that are constructed with similar
dynamic structures. Furthermore, it would be marvelous if we
could transform this sigmoid ETM into a high-efficiency decision making mechanism in some control systems without using a
wireless network. Now we are studying how to realize orbital-attitude
(maneuver) control with a relatively average time interval
and fewer times of orbit transfer by using the proposed sigmoid
ETM. Besides, to further improve the system performance, we
are also seeking to further increase the ratio of the minimum
inter-execution time to the average inter-execution time. For the
purpose of a more even distribution of the triggering events on the
time axis, we may modify the proposed sigmoid event-triggered
method or associate it with other methods.
This paper addresses the landing problem of a quadrotor on an unpredictable moving vehicle, using a robust image-based visual servoing (IBVS) method. The circle-based image moments are defined to construct image dynamics, and the passivity-like property of the circle features is preserved by reprojecting to the virtual image plane. The landing control system is decoupled into translation and rotation modules due to the rotation invariance of the proposed circle features. First, by exploiting the error transformation in the image space, a robust IBVS controller can overcome the lack of both the desired depth information of target features and the velocity feedback of the target. Next, an adaptive geometric attitude controller is developed directly using rotation matrices to avoid the singularities of Euler-angles and the ambiguity of quaternions. One benefit of the proposed scheme is that it can potentially improve the camera visibility, guarantee the transient and steady-state behaviors in image space, and be efficiently implemented on the low-cost quadrotor. Finally, The stability analysis is presented using Lyapunov stability theory on cascaded systems, and the effectiveness of the proposed control strategy is demonstrated through simulations and experiments. Note to Practitioners —The motivation of this paper is to investigate a practical control strategy for the image-based landing control of underactuated quadrotors on an unpredictable moving vehicle. In most of the existing image-based landing control schemes for underactuated quadrotors, having the prior predictive model of the moving landing vehicle to provide a feed-forward compensation during the landing maneuver. However, due to the fact that the landing environment and vehicle are primarily stochastic, resulting in no predictive models are valid in practice. Therefore, this paper suggests a robust image-based landing control strategy without the model or state of the moving landing vehicle. In particular, a novel virtual circle feature, possessing the characteristic of rotation invariance, is designed for the landing of underactuated quadrotors, which decouples the landing system and simplifies the control design. Moreover, the image feature errors are directly retained within prescribed performance funnels in the image space. As a result, the transient and steady-state landing behaviors can be implicitly guaranteed in Cartesian space. The stability and convergence of the system are analyzed mathematically and the experiment using quadrotors provides promising results. In ongoing research, we are addressing the issues of collision avoidances and unknown disturbances to provide a more realistic setup for the autonomous deployment and recovery of underactuated quadrotors in GPS-denied environments.
In this paper, an inner-outer loop control structure with linear quadratic optimal controllers and integrative action is proposed for trajectory tracking of an Unmanned Aerial Vehicle. The dynamic model of the quadrotor is derived and linearized in preparation for the design of the controllers. The full state-feedback relies on measurements from motion sensors installed on-board and on on-flight estimates provided by Kalman filters and an attitude filter. The control system obtained is validated in simulation and implemented in a commercially available drone, equipped with an Inertial Measurement Unit, a compass and an altimeter. The inertial position of the drone is given by a motion capture system.
In this paper, we present a feed-forward control approach for complex trajectory tracking by a tilting-rotor quadcopter during autonomous flight. Tilting-rotor quadcopter is a more agile version of conventional quadcopter as the propeller motors are actuated to tilt about the quadcopter arm. The tilt-rotor quad-copter is capable of following complex trajectories with ease. In this paper, we employ differential flatness based feed-forward position control by utilizing a combination of propeller rotational speeds along with rotor tilts. The rotational motion of propellers work simultaneously in sync with propeller tilts to control the position and orientation of the UAV during autonomous flight. The results for tracking complex trajectories have been presented by performing numerical simulations and a comparison is shown with respect to conventional quadcopter for similar flight conditions. It has been found that the tilt-rotor quadcopter is more efficient than the conventional quadcopter during complex trajectory following maneuvers.
The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as well as mathematical complications involved in using them. This technical note gives a brief overview and discusses the quaternions, which are fourth dimensional extended complex numbers and used to represent orientation. Their relationship to other modes of attitude representation such as Euler angles and Axis-Angle representation is also explored and conversion from one representation to another is explained. The conventions, intuitive understanding and formulas most frequently used and indispensable to any quaternion application are stated and wherever possible, derived.
This paper addresses the problem of designing and experimentally validating a nonlinear robust control to attitude and altitude of a quadrotor unmanned flying vehicle (UAV). First a disturbance observer is proposed, focus on the attitude regulation control problem of a quadrotor in presence of external disturbances based on the angular velocity measurements and the control inputs. The stability analysis of the nonlinear observer scheme is proven via the use of Lyapunov theory. Later, we focus on the altitude dynamics of a quadrotor in the presence of uncertainty like wind gust are presented. A sliding mode control was proposed, the gain of control can be decreased and, as a result, the chattering amplitude is reduced. The objective is to introduce an adaptation in the control law in order to decrease the gain to the minimal value preserving the sliding mode control and keeping his property of a finite-time convergence. Finally, simulation and experimental results in a quadrotor are presented to show the effectiveness of the proposed nonlinear algorithm in presence of external disturbances.
Quadrotors are well suited for executing fast maneuvers with high accelerations but they are still unable to follow a fast trajectory with centimeter accuracy without iteratively learning it beforehand. In this paper, we present a novel body-rate controller and an iterative thrust-mixing scheme, which improve the trajectory-tracking performance without requiring learning and reduce the yaw control error of a quadrotor, respectively. Furthermore, to the best of our knowledge, we present the first algorithm to cope with motor saturations smartly by prioritizing control inputs which are relevant for stabilization and trajectory tracking. The presented body-rate controller uses LQR-control methods to consider both the body rate and the single motor dynamics, which reduces the overall trajectory-tracking error while still rejecting external disturbances well. Our iterative thrust-mixing scheme computes the four rotor thrusts given the inputs from a position-control pipeline. Through the iterative computation, we are able to consider a varying ratio of thrust and drag torque of a single propeller over its input range, which allows applying the desired yaw torque more precisely and hence reduces the yaw-control error. Our prioritizing motor-saturation scheme improves stability and robustness of a quadrotor’s flight and may prevent unstable behavior in case of motor saturations. We demonstrate the improved trajectory tracking, yaw-control, and robustness in case of motor saturations in real-world experiments with a quadrotor.
This paper presents the methodology of design of a nonlinear robust controller for attitude regulation and its implementation in an experimental platform of an unmanned aerial vehicle (UAV) quadrotor. Details on the kinematic and dynamic modeling based on the Euler-Lagrange formalism are provided, as well as the particulars of the design of a nonlinear robust H-infinity PID controller to regulate the rotational moments. The performance and effectiveness of the proposed controller are tested in a simulation and an experimental platform. The performance of the proposed controller is compared with a conventional PID controller by using the integral square error (ISE) as performance parameter. Experimental results help to demonstrate the correct operation of the system for real-time applications in the presence of unmodeled dynamics and the uncertainties of the parameters.
This study proposes a novel nonlinear resilient trajectory control for a quadrotor unmanned aerial vehicle (UAV) using backstepping control and nonlinear disturbance observer. First, a nonlinear dynamic model for the quadrotor UAV that considers external disturbances from wind model uncertainties is developed. A nonlinear disturbance observer is then constructed separately from the controller to estimate the external disturbances and compensate for the negative effects of the disturbances. Based on the estimates from the given observer, a nominal nonlinear backstepping trajectory-tracking position controller is designed to stabilize the subsystems step by step until the ultimate control law is obtained. An extra term is added to the nominal controller to address the problem of actuator effectiveness loss and to ensure system resilience. The stability of the resilient controller is analyzed using Lyapunov stability theory. Simulation results are presented to demonstrate the effectiveness and robustness of the proposed nonlinear resilient controller.
The present work refers to the mathematical modeling, experimental identification and control
design of a small unmanned indoors quadrotor aircraft, at low translational speeds around the
hovering condition, where the aerodynamic forces on the airframe are disregarded. A Kalman
filter is implemented for state estimation and noise filtering. Linear control techniques such as
PID, LQ as well as modern robust mixed-sensitivity H-infinity and μ-synthesis with DK-iteration
are employed and compared with each other in terms of flight trajectory reference tracking
and parametric and model uncertainty.
This paper proposes a method for designing disturbance observer (DOB) in vibration suppression control of two-inertia system. The key to a vibration suppression control of two-inertia system is eliminating the effect of vibration modes of the plant. For this purpose, feedback controller is designed to cancel the stable vibration modes of plant. However, this cancellation fails due to model error from parameter variations. In this paper, the DOB is employed to compensate for the effect of parameter variations. The Q-filter of DOB is designed with the following specifications: optimal disturbance suppression performance with restricted cutoff frequency; robust stability of closed-loop system against modeling error between the plant and its nominal model; structural restriction of Q-filter itself such as relative order and internal model order. This paper proposes a systematic and straightforward method to attain the above design specifications using standard H∞ control framework. Experimental results verify that the proposed DOB can improve the transient response and effectively suppress the vibration and improve external disturbance removing performance as well.
The development of miniature flying robots has become a reachable dream, thanks to the new sensing and actuating technologies. Micro VTOL systems represent a useful class of flying robots because of their strong abilities for small-area monitoring and building exploration. In this paper, we present the results of two model-based control techniques applied to an autonomous four-rotor micro helicopter called quadrotor. A classical approach (PID) assumed a simplified dynamics and a modern technique (LQ) based on a more complete model. Various simulations were performed and several tests on the bench validate the control laws. Finally, we present the results of the first test in flight with the helicopter released. These developments are part of the OS4 project in our lab.
In this paper, we propose a new quaternion-based feedback control scheme for exponential attitude stabilization of a four-rotor vertical takeoff and landing aerial robot known as a quadrotor aircraft. The proposed controller is based upon the compensation of the Coriolis and gyroscopic torques and the use of a PD2 feedback structure, where the proportional action is in terms of the vector quaternion and the two derivative actions are in terms of the airframe angular velocity and the vector quaternion velocity. We also show that the model-independent PD controller, where the proportional action is in terms of the vector-quaternion and the derivative action is in terms of the airframe angular velocity, without compensation of the Coriolis and gyroscopic torques, provides asymptotic stability for our problem. The proposed controller as well as some other controllers have been tested experimentally on a small-scale quadrotor aircraft.
In this paper, we present a controller design and its implementation on a mini rotorcraft having four rotors. The dynamic model of the four-rotor rotorcraft is obtained via a Lagrange approach. The proposed controller is based on Lyapunov analysis using a nested saturation algorithm. The global stability analysis of the closed-loop system is presented. Real-time experiments show that the controller is able to perform autonomously the tasks of taking off, hovering, and landing.
This paper presents a singularity free fast terminal sliding mode control (SFFTSMC) for position and attitude tracking of a quadrotor with unknown dynamics. The contribution of this work is threefold, namely: devising an SFFTSMC strategy using an auxiliary function to eliminate the singularity in the control law, a cost-saving minimum parameter update scheme using a fully connected recurrent neural network (FCRNN) to handle the unknown dynamics of quadrotor and development of an adaptive control law to compensate for the loss of effectiveness of the actuator and saturation effects, considered explicitly, without the requirement of any fault detection and diagnosis (FDD) unit. The proposed approach offers a direct singularity free control action in the presence of unknown dynamics, actuator faults, and saturation. Overall closed-loop stability is guaranteed in finite-time using Lyapunov stability theory and update laws for minimum parameters of FCRNN and fault compensator are derived using the same. Extensive simulations are presented for the trajectory tracking tasks using the proposed method and compared with the existing piece-wise fast terminal sliding mode controller (PFTSMC) and Radial basis function network (RBFN) based fault compensation approach. The proposed method is also validated in the Gazebo simulator via Pixhawk autopilot to demonstrate the feasibility in real-time.
Note to Practitioners
—This research is motivated by a cost-effective control scheme for quadrotors in cases of unknown/uncertain dynamics, external disturbances, actuator faults, and saturation. Precise quadrotor dynamics are difficult to obtain in real time. Also, there may be parametric uncertainties in quadrotor parameters like mass, inertia, and aerodynamic coefficients. External disturbances like wind gusts are always present in outdoor environments, and it may be the case that quadrotor motors lose their effectiveness due to defective motors or propeller damage while flying. To address these issues, first, it requires a precise control scheme to control the quadrotor while guaranteeing stability to ensure the safety of the quadrotor itself and people in the surrounding environment. Second, the approach should not be computationally heavy, which may sluggish the overall response of the quadrotor. Thus, we propose a control scheme to address these two issues simultaneously using a new fast terminal sliding mode control scheme augmented with FCRNN by updating minimum parameters instead of all the weight parameters of FCRNN. A compensator is introduced to mitigate the effect of unexpected actuator fault and saturation. The proposed approach can be helpful in various quadrotor applications, like pesticide spraying in agriculture, payload transportation, search and rescue, construction, etc., where unknown quadrotor dynamics and unknown payload situations occur.
In this work we propose and demonstrate a method for increasing the frequency response bandwidth of actuator dynamics in a multi-rotor vehicle through open-loop compensation. The limitations of such method due to non-linearities in the dynamics are discussed. This method retains the existing electromechanical architecture as no additional sensing is required. The compensator design is based on the identified dynamics considering the non-linear phenomena. This ensures the compensator's performance within the operating range of system. The actuator dynamics are identified experimentally and the effectiveness of the compensation is demonstrated using the same hardware setup.
This article proposes a novel asymptotic robust control approach for rotorcraft unmanned aerial vehicles (UAVs), which can effectively eliminate the impact of external disturbances and the model uncertainties. Different from existing works, the proposed method alleviates the assumption that disturbances should have no variations in the existing observers for uncertainties. In addition, the equilibrium point of the entire observer-controller system is asymptotically stable without the assumption of the boundness of the outer-loop signals or the time-scale separation assumption. Specifically, two observer-based estimators are designed to estimate the model uncertainty and the external disturbance for the force and torque, respectively. On this basis, a nonlinear hierarchical tracking controller is then proposed with the feedforward compensated disturbance term. Despite the nonlinear coupled dynamics and the disturbances, a generic framework for the stability analysis is proposed to yield the asymptotic stability of the equilibrium point of the entire controller-observer system. Comparative experiments are conducted to show the superior performance of the proposed approach in terms of higher tracking accuracy and stronger robustness.
Note to Practitioners
—Most of the existing observer-based control approaches can only govern the rotorcraft closed-loop system to be ultimately uniformly bounded. The highly coupled dynamics and mismatched uncertainties in practice make the effective asymptotic robust control of rotorcrafts very challenging. A novel robust control approach for rotorcraft UAVs is proposed to yield the asymptotic stability of the equilibrium point despite the nonlinear coupled dynamics and the disturbances. The key insight of this work to guarantee the asymptotic stability of the system is that the nominal signals (i.e., the output of the nominal auxiliary dynamics) are fed back to the controller. In addition, the attitude error signal is proved to be exponentially convergent, which can further help prove the asymptotic stability of the entire controller-observer system. Comparative experiments are conducted to show the applicability of the proposed approach.
In this paper, a fast non-singular terminal sliding mode combined with angular velocity planning (FNTSMAVP) controller is developed to achieve high-speed, accurate and robust attitude tracking performance for a quadrotor. The proposed controller employs a sliding surface function with a continuous arctangent function, which can effectively eliminate chattering behavior on the quadrotor whilst retaining the speed and accuracy of attitude tracking. Unlike conventional methods, the proposed controller preferentially recovers the roll and pitch angles at desired attitude by planning the shortest arrival path, which is effective to improve the tracking performance. Finally, the finite time convergence and zero tracking error properties of the closed-loop control system under the proposed FNTSMAVP are analyzed and proved. The aggressive flight experiments demonstrate the advantage of faster convergence and fewer chattering behavior of the proposed method compared to the existing fast non-singular terminal sliding mode (FNTSM) controller.
The In-pipe Inspections robot (IPIR) are robots that run inside of pipelines and carry out the inspection work there. The pipelines develop certain anomalies like corrosion, cracks, dents, misalignments, etc. during their work cycle that needs to be rectified. Using IPIR eases the process of inspection that is difficult with the manual procedure that includes visual and some external non-destructive testings (NDTs). There are various types of robots in these fields including wheel-driven, track-driven, Pipe inspection gauge (PIG), walking type, and inchworm type. This paper will provide the specifications and design specialties of each type of robot. Each robot is designed considering certain parameters like maneuverability, pipeline diameter, adaptability, design structure, and more, and hence these are specific. There are certain limitations to each design at the end. Finally, this paper will help to select a specific robot for a particular requirement based on the comparison.
In this article, a novel robust observer-based nonlin-ear control approach is proposed for quadrotors with unmodeled dynamics and external disturbances, wherein the tracking errors are restricted effectively. Two nonlinear disturbance observers are proposed to deal with uncertainties in the inner and outer loops, respectively. On this basis, a robust observer-based non-linear control approach is put forward for quadrotor systems. Specifically, in the outer loop subsystem, a robust observer-based control scheme is proposed, which can reduce unexpected tracking errors for quadrotors effectively. Subsequently, based upon the geometric methods, the coordinate-free attitude controller and the nonlinear disturbance observer are integrated as a robust controller in the inner loop subsystem. Based upon full nonlinear dynamics, the solutions of the closed-loop system are proven to be uniformly ultimately bounded by means of rigorous Lyapunov analysis. A series of comparative experiments consisting of the implementation of a nonlinear proportional-integral-derivative (PID)-type controller, an observer-based sliding mode controller, and the proposed controller are conducted to demonstrate the remarkable performance of the proposed method in terms of higher tracking accuracy and stronger robustness.
Unmanned surface vessels (USVs) are supposed to be able to adapt unstructured environments by means of multi-sensor active perception without any human interference, and high-accuracy path following is achieved for USVs by effective control strategies and intelligent devices of e-navigation. This paper proposes a finite-time predictor line-of-sight (LOS)-based integral sliding-mode adaptive neural (FPISAN) scheme for the path following of USVs in the presence of unknown dynamics and external disturbances, which copies with the problem of merging with the kinematic level and the kinetic level of USVs. From the point of view of USVs’ practical engineering, the inertia matrix of USVs maintains nonzero off-diagonal. In order to ensure that USVs can converge to and follow a defined path, a novel LOS-based guidance law that can acquire sideslip angles by error predictors within a finite time is presented, called finite-time predictor-based LOS (FPLOS). Then, the path-following control laws are designed by combining the neural network (NN) technique with the integral sliding-mode method, where radial basis function NN (RBFNN) is applied to approximate lumped unknown dynamics induced by nonparametric uncertainties and external disturbances. The theoretical analysis verifies that the path-following guidance-control system of USVs is semiglobally uniformly ultimately bounded (SGUUB) with the aid of Lyapunov stability theory. The effectiveness and performance of this presented scheme are illustrated by simulation experiments with the comparison.
Note to Practitioners
—The design of heading guidance laws and path-following control laws for path following of USVs subject to unknown dynamics and external disturbances is a critical problem, which affects the development of USVs. This problem associated with practical engineering of USVs due to the actual navigation environment that is complex, diversified, and highly unstructured. This paper presents a wholly tight strategy to compensate for unknown sideslip angles and approximate lumped unknown dynamics. Hence, an effective scheme being denoted FPISAN mentioned above is developed for path following of USVs.
In this article, we introduce a translational force control method with disturbance observer (DOB)-based force disturbance cancellation for precise 3-D acceleration control of a multi-rotor unmanned aerial vehicle (UAV). The acceleration control of the multi-rotor requires conversion of the desired acceleration signal to the desired roll, pitch, and total thrust. However, because the attitude dynamics and the thrust dynamics are different, simple kinematic signal conversion without consideration of those difference can cause serious performance degradation in acceleration tracking. Unlike most existing translational force control techniques that are based on such simple inversion, our new method allows controlling the acceleration of the multi-rotor more precisely by considering the dynamics of the multi-rotor during the kinematic inversion. By combining the DOB with the translational force system that includes the improved conversion technique, we achieve robustness with respect to the external force disturbances that hinder the accurate acceleration control. μ-analysis is performed to ensure the robust stability of the overall closed-loop system, considering the combined effect of various possible model uncertainties. Both simulation and experiment are conducted to validate the proposed technique, which confirms the satisfactory performance to track the desired acceleration of the multi-rotor.
Autonomous landing is a challenging phase of flight for an aerial vehicle, especially when attempting to land on a moving target. This paper presents vision-based tracking and landing of a fully-actuated tilt-augmented quadrotor on a moving target. A fully-actuated vehicle allows higher freedom in terms of control design and a larger flight envelope since the position and attitude states are decoupled. An adaptive control law is designed to track a moving target with only relative position information from a camera. Low-cost hardware is used, and experiments are carried out to validate the proposed methodology for targets moving at realistic speeds.
This review concentrates on three main challenges of controlling a quadrotor unmanned aerial vehicle (UAV) as an underactuated mechanical system (UMS). The challenges include underactuation, model uncertainty, and actuator failure. The review also illustrates the state of the quadrotor control research in an attempt to find practical solutions for those challenges. By definition, a UMS has less number of control actions than the number of degrees of freedom to be controlled. Hence, traditional control strategies developed for fully actuated systems are not directly applicable to UMS. Research on UMS is one of the most interesting topics in the robotics and control community because of its relevance to a variety of applications. Examples include humanoid robots and most aerial and underwater vehicles. However similar to any other nonlinear systems, the stability and control of quadrotors suffer from intrinsic complexities exasperated by underactuation, model uncertainties and actuator failure. In this review article, we are going to address these problems and discuss the solutions mostly concerning the application of different control strategies presented in recent literature. We also present the frontiers and research directions towards improving performance of quadrotors for emerging and complex applications.
This paper addresses a difficult problem of high-accuracy control for quadrotor unmanned aerial vehicles subject to external disturbance force and unknown disturbance torque. An observer-based full control scheme is presented. In the strategy, two observer-based estimators are firstly designed to estimate external disturbance force and torque, respectively. With the application of the precise estimation value, a nonlinear tracking controller is then proposed with disturbance compensated. It is shown by the Lyapunov stability analysis that the entire controller-observer system is asymptotically stable. The key feature of the scheme is that it not only has the superior capability to attenuate unknown external disturbance torque and external force generated by the wind, but also able to achieve full control (i.e., six-degree-of-freedom) of quadrotor UAVs with position and attitude successfully controlled. The effectiveness of the approach is verified on a quadrotor UAV example.
This brief presents the design, analysis, and implementation of a nonlinear robust adaptive fault-tolerant altitude and attitude tracking method for accommodating actuator faults in quadrotor unmanned aerial vehicles without the need of a fault diagnosis mechanism. Actuator faults are modeled as a constant loss of effectiveness in the thrust generated by the rotors. The fault-tolerant control (FTC) algorithm guarantees asymptotic convergence of the altitude and attitude tracking error even in the presence of possible multiple actuator faults and modeling uncertainties. The FTC method is implemented using a real-time indoor quadrotor test environment. Experimental results are shown to illustrate the effectiveness of the algorithm.
This paper investigates the global tracking control of underactuated aerial vehicles. In particular, the globally exponentially stable attitude tracking controller serving as the inner loop of the overall controller is investigated. It can avoid the common problems that may be accompanied by other attitude controllers, such as singularity and unwinding. In order to overcome the topological obstacles of global control on SO(3), rotational motion of a rigid body is expressed in the exponential coordinate restricted in a compact domain. We then construct a hybrid tracking error dynamics whose states are all represented in Euclidean space. The geometric properties of the state space are mathematically analyzed. The tracking controller of underactuated aerial vehicles is, thus, designed based on the hybrid tracking error dynamics. The global exponential stability of the closed-loop attitude subsystem, as well as the global asymptotical stability of the closed-loop overall system under assumptions, is analyzed using Lyapunov's method strictly. These properties are demonstrated by simulation results. The proposed controller is also implemented and tested on our self-developed quadrotor, showing the feasibility of the controller in realtime applications.
In this paper a robust PID control strategy via affine parametrization is designed for an multivariable nonlinear unmanned aerial vehicle. The robustness of the controlled system is assured by using the H∞ norm of the weighted complementary sensitivity function. Simulation results carried out using a complete nonlinear model are shown, wherein the performance achieved with this control strategy is shown.
We present a novel, deeply embedded robotics middleware and programming environment. It uses a multithreaded, publish-subscribe design pattern and provides a Unix-like software interface for micro controller applications. We improve over the state of the art in deeply embedded open source systems by providing a modular and standards-oriented platform. Our system architecture is centered around a publish-subscribe object request broker on top of a POSIX application programming interface. This allows to reuse common Unix knowledge and experience, including a bash-like shell. We demonstrate with a vertical takeoff and landing (VTOL) use case that the system modularity is well suited for novel and experimental vehicle platforms. We also show how the system architecture allows a direct interface to ROS and to run individual processes either as native ROS nodes on Linux or nodes on the micro controller, maximizing interoperability. Our microcontroller-based execution environment has substantially lower latency and better hardware connectivity than a typical Robotics Linux system and is therefore well suited for fast, high rate control tasks.
This brief proposes a disturbance rejection control strategy for attitude tracking of an aircraft with both internal uncertainties and external disturbances. The proposed control strategy consists of a robust disturbance observer (DOB) and a nonlinear feedback controller. Specifically, a robust DOB is proposed to compensate the uncertain rotational dynamics into a nominal plant, based on which a nonlinear feedback controller is implemented for desired tracking performance. We first divide the practical rotational dynamics into the nominal part, external disturbances, and equivalent internal disturbances. Then, property of equivalent internal disturbances is explored for stability analysis. A robust DOB is optimized based on theory to guarantee disturbance rejection performance and robustness against system uncertainties. A practical nonlinear feedback controller is hence applied to stabilize the compensated system based on backstepping approach. Experiments on a quadrotor testbed show that the proposed robust DOB can suppress the external disturbances and measurement noise, with the robustness against system uncertainties.
Standard quadrotor unmanned aerial vehicles (UAVs) possess a limited mobility because of their inherent underactuation, that is, availability of four independent control inputs (the four propeller spinning velocities) versus the 6 degrees of freedom parameterizing the quadrotor position/orientation in space. Thus, the quadrotor pose cannot track arbitrary trajectories in space (e.g., it can hover on the spot only when horizontal). Because UAVs are more and more employed as service robots for interaction with the environment, this loss of mobility due to their underactuation can constitute a limiting factor. In this paper, we present a novel design for a quadrotor UAV with tilting propellers which is able to overcome these limitations. Indeed, the additional set of four control inputs actuating the propeller tilting angles is shown to yield full actuation to the quadrotor position/orientation in space, thus allowing it to behave as a fully actuated flying vehicle. We then develop a comprehensive modeling and control framework for the proposed quadrotor, and subsequently illustrate the hardware and software specifications of an experimental prototype. Finally, the results of several simulations and real experiments are reported to illustrate the capabilities of the proposed novel UAV design.
1 Reference Frames This section describes the various reference frames and coordinate systems that are used to describe the position of orientation of aircraft, and the transformation between these coordinate systems. It is necessary to use several different coordi-nate systems for the following reasons: • Newton's equations of motion are given the coordinate frame attached to the quadrotor. • Aerodynamics forces and torques are applied in the body frame. • On-board sensors like accelerometers and rate gyros measure information with respect to the body frame. Alternatively, GPS measures position, ground speed, and course angle with respect to the inertial frame. • Most mission requirements like loiter points and flight trajectories, are spec-ified in the inertial frame. In addition, map information is also given in an inertial frame. One coordinate frame is transformed into another through two basic opera-tions: rotations and translations. Section 1.1 develops describes rotation matrices and their use in transforming between coordinate frames. Section 1.2 describes the specific coordinate frames used for micro air vehicle systems. In Section 1.3 we derive the Coriolis formula which is the basis for transformations between between between translating and rotating frames.
Standard quadrotor UAVs possess a limited mobility because of their inherent underactuation, i.e., availability of 4 independent control inputs (the 4 propeller spinning velocities) vs. the 6 dofs parameterizing the quadrotor position/ orientation in space. As a consequence, the quadrotor pose cannot track an arbitrary trajectory over time (e.g., it can hover on the spot only when horizontal). In this paper, we propose a novel actuation concept in which the quadrotor propellers are allowed to tilt about their axes w.r.t. the main quadrotor body. This introduces an additional set of 4 control inputs which provides full actuation to the quadrotor position/orientation. After deriving the dynamical model of the proposed quadrotor, we formally discuss its controllability properties and propose a nonlinear trajectory tracking controller based on dynamic feedback linearization techniques. The soundness of our approach is validated by means of simulation results.
This brief describes the application of direct and indirect model reference adaptive control to a lightweight low-cost quadrotor unmanned aerial vehicle platform. A baseline trajectory tracking controller is augmented by an adaptive controller. The approach is validated using simulations and flight tested in an indoor test facility. The adaptive controller is found to offer increased robustness to parametric uncertainties. In particular, it is found to be effective in mitigating the effects of a loss-of-thrust anomaly, which may occur due to component failure or physical damage. The design of the adaptive controller is presented, followed by a comparison of flight test results using the existing linear and augmented adaptive controllers.
This work presents a direct approximate-adaptive control, using CMAC nonlinear approximators, for an experimental prototype quadrotor helicopter. The method updates adaptive parameters, the CMAC weights, as to achieve both adaptation to unknown payloads and robustness to disturbances. Previously proposed weight-update methods, such as e-modification, provide robustness by simply limiting weight growth. In order to let the weights grow large enough to compensate unknown payloads, the proposed method relies on a set of alternate weights to guide the training. The alternate weights produce nearly the same output, but with values clustered closer to the average weight so that the output remains relatively smooth. This paper describes the design of a prototype helicopter suitable for testing the control method. In the experiment the new method stops weight drift during a shake test and adapts on-line to a significant added payload, whereas e-modification cannot do both.
It is well known that controlling the attitude of a rigid body is subject to topological constraints. We illustrate, with examples, the problems that arise when using continuous and (memoryless) discontinuous quaternion-based state-feedback control laws for global attitude stabilization. We propose a quaternion-based hybrid feedback scheme that solves the global attitude tracking problem in three scenarios: full state measurements, only measurements of attitude, and measurements of attitude with angular velocity measurements corrupted by a constant bias. In each case, the hybrid feedback is dynamic and incorporates hysteresis-based switching using a single binary logic variable for each quaternion error state. When only attitude measurements are available or the angular rate is corrupted by a constant bias, the proposed controller is observer-based and incorporates an additional quaternion filter and bias observer. The hysteresis mechanism enables the proposed scheme to simultaneously avoid the “unwinding phenomenon” and sensitivity to arbitrarily small measurement noise that is present in discontinuous feedbacks. These properties are shown using a general framework for hybrid systems, and the results are demonstrated by simulation.
We show that a continuous dynamical system on a state space that
has the structure of a vector bundle on a compact manifold possesses no
globally asymptotically stable equilibrium. This result is directly
applicable to mechanical systems having rotational degrees of freedom.
In particular, the result applies to the attitude motion of a rigid
body. In light of this result, we explain how attitude stabilizing
controllers appearing in the literature lead to unwinding instead of
global asymptotic stability
Euler and roll-pitch-yaw angles are routinely used to represent the orientation of rigid bodies in aerospace, navigation, and robotics because they minimize the dimensionality of the control problem.Both representations, however, introduce unwarranted mathematical singularities which are identified in this paper.Trajectory-tracking algorithms break down at singularities and cause loss of control. Since mathematical singularities do not reflect physical limitations of orientation, remedial measures can beimplemented in the controller.
A tutorial on SE(3) transformation parameterizations and on-manifold optimization
- Blanco-Claraco