Nonlinear Dynamic Inversion Method Research Articles

Discrete-Time Incremental Backstepping Control with Extended Kalman Filter for UAVs

In this study, a discrete-time incremental backstepping (DTIBS) controller with an extended Kalman filter (EKF) is proposed for unmanned aerial vehicles (UAVs) with unknown actuator dynamics. The Taylor series and an approximate discrete method are employed, transforming the second-order continuous-time nonlinear system into a discrete-time nonlinear plant with an incremental input form. The incremental control laws are designed using the incremental nonlinear dynamic inversion (INDI) method and the time-delay control (TDC) method. The TDC is introduced to design the control law, eliminating the need for prior knowledge of the control effectiveness matrix involving some unknown aerodynamic coefficients. In addition, the airflow angle and body rotation rate are selected as key system states, and the EKF is used to design a state estimator to estimate the local state of the small unmanned aerial vehicle closed-loop flight control system under strong noise conditions. The effectiveness of the DTIBS control method with EKF is verified through numerical simulation. The results show that the proposed method can effectively estimate the state under the typical noise characteristics of low-cost sensors, and the closed-loop control systems has good tracking performance and can quickly and effectively track sudden commands.

Low-level control with actuator dynamics for multirotor UAVs

PurposeA low-level controller is critical to the overall performance of multirotor unmanned aerial vehicles. The purpose of this paper is to propose a nonlinear low-level angular velocity controller for multirotor unmanned aerial vehicles in various operating conditions (e.g. different speed and different mode).Design/methodology/approachTo tackle the above challenge, the authors have designed a nonlinear low-level controller taking the actuator dynamics into account. The authors first build the actuator subsystem by combining the actuator dynamics with the angular velocity dynamics model. Then, a recursive low-level controller is developed by designing a high-gain observer to estimate unmeasurable states. Furthermore, a detailed stability analysis is given with the Lyapunov theory.FindingsSimulation tests and real-world flying experiments are provided to validate the proposed approach. In particular, we illustrate the performance of the proposed controller using violent random command test, attitude mode flight and high-speed flight of up to 18.7 m/s in real world. Compared with the classical method used in PX4 autopilot and the estimation-based incremental nonlinear dynamic inversion method, experimental results show that the proposed method can further reduce the control error.Research limitations/implicationsLow-level control of multirotor UAVs is challenging due to the complex dynamic characteristics of UAVs and the diversity of tasks. Although some progress has been made, the performance of existing methods will deteriorate as operating conditions change due to the disregard for the electromechanical characteristics of the actuator.Originality/valueTo solve the low-level angular velocity control problem in various operating conditions of multirotor UAVs, this paper proposes a nonlinear low-level angular velocity controller which takes the actuator dynamics into account.

A Comparative Study of Nonlinear MPC and Differential-Flatness-Based Control for Quadrotor Agile Flight

Accurate trajectory-tracking control for quadrotors is essential for safe navigation in cluttered environments. However, this is challenging in agile flights due to nonlinear dynamics, complex aerodynamic effects, and actuation constraints. In this article, we empirically compare two state-of-the-art control frameworks: the nonlinear-model-predictive controller (NMPC) and the differential-flatness-based controller (DFBC), by tracking a wide variety of agile trajectories at speeds up to 20 m/s (i.e., 72 km/h). The comparisons are performed in both simulation and real-world environments to systematically evaluate both methods from the aspect of tracking accuracy, robustness, and computational efficiency. We show the superiority of the NMPC in tracking dynamically infeasible trajectories, at the cost of higher computation time and risk of numerical convergence issues. For both methods, we also quantitatively study the effect of adding an inner loop controller using the incremental nonlinear dynamic inversion method, and the effect of adding an aerodynamic drag model. Our real-world experiments, performed in one of the world’s largest motion capture systems, demonstrate more than 78% tracking error reduction of both NMPC and DFBC, indicating the necessity of using an inner loop controller and aerodynamic drag model for agile trajectory tracking.

Incremental control system design and flight tests of a micro-coaxial rotor UAV

This paper applies the incremental nonlinear dynamic inversion (INDI) method to the control system design of coaxial rotor UAVs. The aerodynamic uncertainties and anti-disturbances problems are solved in the control system design. The designed controller gives the UAV excellent flight performance and control robustness. The incremental gain method (IGM) is adopted for the delay problem of the state derivatives. This method has the advantages of less calculation load and simple parameter adjustment, which provides excellent convenience for applying INDI controllers to coaxial rotor UAVs. The principle of IGM is further investigated by the discrete-time stability analysis methods, and the parameter selection strategy of the IGM is provided. The advantages of the controller design method are verified by comparative flight tests. The experimental results show that the average trajectory tracking error of INDI is only 58.3% of that of NDI under the same wind speed. When the angular acceleration delay is less than 0.06 s, IGM can easily keep the system stable. In addition, INDI has better robustness under obvious model errors and strong input disturbances.

Automated 3-D Electromagnetic Manipulation of Microrobot With a Path Planner and a Cascaded Controller

Manipulating microrobots to move in a 3-D space is a basic requirement for their in vivo medical applications. In this study, the automatic manipulation of a microrobot in a liquid 3-D space via an electromagnetic coil system is investigated. A path planner is designed to search an optimal path in a 3-D space with obstacles automatically, and a cascaded control algorithm is developed to control the microrobot’s movement along the planned path. The path is generated by combining the A-star and minimum jerk methods. The collision of the generated path with the obstacles is prevented and the hysteresis caused by the current change is minimized by reducing the jerk of the movement with a passable path from the starting point to the endpoint. In the cascaded control algorithm, the incremental nonlinear dynamic inversion (INDI) method and a proportional control are used as the inner and outer loops to guide the microrobot’s movement along the desired trajectory with an appropriate velocity while eliminating the influence of system uncertainty and external disturbances. Simulation and experiments are performed to verify the effectiveness of the proposed control strategy.

Control Design for a Marine Hydrokinetic Cycloturbine Vehicle

Abstract Marine Hydrokinetic (MHK) cycloturbines generate sustainable power by exploiting tidal currents. By powering the turbines and using pitching foils for control, a vehicle comprised of MHK cycloturbines also has the ability to station keep and maneuver. The vehicle consists of four counter-rotating cycloturbines, with hydrofoils oriented perpendicular to the flow in a paddlewheel configuration. Lift and drag generated from these foils sum together to produce thrust. An experimentally tuned simulation model that solves the six-degrees-of-freedom rigid body equations of motion for the MHK vehicle subject to hydrodynamic, hydrostatic, and propulsive forces is used to aid the design of vehicle controllers. Global feedback controllers are initially designed by applying classical control methods to an approximate linear model of the system dynamics. A higher performing nonlinear controller is designed using the nonlinear dynamic inversion (NDI) method. NDI accounts for the nonlinearities of the MHK system and therefore is suitable for a wide range of operating conditions. The response of the classical and NDI controllers to speed, depth, roll, pitch, and yaw commands are evaluated and compared in simulation. The classical controller outperforms the NDI controller for small amplitude maneuvers, although the degradation with NDI is minor. However, in the nonlinear operating regime the NDI controller outperforms the classical controller and the classical controller exhibits instability.

INDI-based aggressive quadrotor flight control with position and attitude constraints

Recent studies have significantly contributed to the extensive use of quadrotors for delivery, mapping, and inspection. To further increase the versatility of quadrotors under confined environments, we focus on the precise trajectory tracking problem with position and attitude constraints. In tightly constrained scenarios, any slight error will infect flight security, especially in a large attitude maneuver. We utilize the incremental nonlinear dynamic inversion (INDI) method to precisely linearize the nonlinearities in the system and generalize it to the entire rotation space to reach a globally expressed control law. Meanwhile, the thrust alignment is introduced to improve the robustness against the mismatch between actuator dynamics and rotational dynamics, guaranteeing higher tracking accuracy. Improvements over a conventional geometry tracking controller are demonstrated in experiments where the quadrotor flies through an inclined narrow gap with orientation up to 90°. Flight tests also indicate the high disturbance rejection capabilities with the thrust alignment in gap traverse flight.

Robust dynamic inversion control of flight control system based on L1 adaptive structure

Nonlinear Dynamic Inversion(NDI) control has excellent rapidity and decoupling ability, unfortunately it lacks the essential robustness to disturbance. From the perspective of enhancing the robustness, an adaptive NDI method based on L1 adaptive structure is proposed. The L1 adaptive structure is introduced into the NDI control to enhance its robustness, which also guarantees the stability and expected dynamic performance of the system suffering from the disturbance influence. Secondly, the flight control law of the advanced aircraft is designed based on the present method to improve the robustness and fault tolerance of the flight control system. Finally, the effectiveness of the flight control law based on the present approach is verified under the fault disturbance. The results showed that the flight control law based on L1 adaptive NDI has excellent dynamic performance and strong robustness to parameter uncertainties and disturbances.

A CFD-based numerical virtual flight simulator and its application in control law design of a maneuverable missile model

A CFD-based Numerical Virtual Flight (NVF) simulator is presented, which integrates an unsteady flow solver on moving hybrid grids, a Rigid-Body Dynamics (RBD) solver and a module of the Flight Control System (FCS). A technique of dynamic hybrid grids is developed to control the active control surfaces with body morphing, with a technique of parallel unstructured dynamic overlapping grids generating proper moving grids over the deflecting control surfaces (e.g. the afterbody rudders of a missile). For the flow/kinematic coupled problems, the 6 Degree-Of-Freedom (DOF) equations are solved by an explicit or implicit method coupled with the URANS CFD solver. The module of the control law is explicitly coupled into the NVF simulator and then improved by the simulation of the pitching maneuver process of a maneuverable missile model. A nonlinear dynamic inversion method is then implemented to design the control law for the pitching process of the maneuverable missile model. Simulations and analysis of the pitching maneuver process are carried out by the NVF simulator to improve the flight control law. Higher control response performance is obtained by adjusting the gain factors and adding an integrator into the control loop.

A Data-Driven Adaptive Method for Attitude Control of Fixed-Wing Unmanned Aerial Vehicles

In this paper, a real-time online data-driven adaptive method is developed to deal with uncertainties such as high nonlinearity, strong coupling, parameter perturbation and external disturbances in attitude control of fixed-wing unmanned aerial vehicles (UAVs). Firstly, a model-free adaptive control (MFAC) method requiring only input/output (I/O) data and no model information is adopted for control scheme design of angular velocity subsystem which contains all model information and up-mentioned uncertainties. Secondly, the internal model control (IMC) method featured with less tuning parameters and convenient tuning process is adopted for control scheme design of the certain Euler angle subsystem. Simulation results show that, the method developed is obviously superior to the cascade PID (CPID) method and the nonlinear dynamic inversion (NDI) method.

An Improved Nonlinear Dynamic Inversion Method for Altitude and Attitude Control of Nano Quad-Rotors under Persistent Uncertainties

Nonlinear dynamic inversion (NDI) has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning. However, the weakness of relying on accurate model greatly restrains its application on quad-rotors, especially nano quad-rotors (NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties (mainly from complicated aerodynamic interferences, strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors) and external uncertainties (mainly from winds or gusts), particularly persistent ones.Therefore, developing accurate model for altitude and attitude control of NQRs is difficult. To solve this problem, in this paper, an improved nonlinear dynamic inversion (INDI)method is developed, which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer (LESO). Comparison with the traditional NDI(TNDI) method was carried out numerically, and the results show that, in coping with persistent uncertainties, the INDI-based method presents significant superiority.

Modeling and control of a flapping wing robot

The dynamics and control of a flapping wing robot are studied in this paper which helps to develop a complete dynamic model for the robot consisting of tail effects and also enhance the path tracking control of the robot. In the first part of the paper, the aerodynamic model of the wings is presented, and an aerodynamic force model for the tail is introduced which includes the leading edge suction effects. An experiment is also carried out on a flapping wing robot in a laboratory environment to evaluate the forces on the tail and its result will be compared with the results of the model presented for the tail. In the second part, a controller is designed for the robot. This controller uses the nonlinear dynamic inversion method to solve the nonlinear equations of the control system. The experimental results of the tail forces agree well with the theoretical predictions and reveal that the tail aerodynamics are affected by leading edge suction. Also, simulation results show that the competence performance and convergence performance of the designed controller are obtained.

Dynamic Inversion Control of Quadrotor with a Suspended Load

In this paper, I have tackled the problem of a quadrotor with a suspended load using nonlinear dynamic inversion method. The main purpose of this paper is to present a new dynamics of the UAV-load system using Newton’s law. I applied dynamic inversion control for directing the UAV to the desired coordinates and simultaneously minimizing the sway angle of the suspended mass. I have carried the entire simulation in the inertial frame. My approach is to use an outer loop controller for maintaining the position and an inner loop controller for the desired roll, pitch and yaw rate. I have performed the simulations on MATLAB.

Nonlinear control of the dissolved oxygen concentration integrated with a biomass estimator for production of Bacillus thuringiensis δ-endotoxins

Bacillus thuringiensis is a microorganism that allows the biosynthesis of δ-endotoxins with toxic properties against some insect larvae, being often used for the production of biological insecticides. A key issue for the bioprocess design consists in adequately tracking a pre-specified optimal profile of the dissolved oxygen concentration. To this effect, this paper aims at developing a novel control law based on a nonlinear dynamic inversion method. The closed-loop strategy includes an observer based on a Bayesian Regression with Gaussian Process, which is used for on-line estimating the biomass present in the bioreactor. Unlike other approaches, the proposed controller leads to an improved response time with effective disturbance rejection properties, while simultaneously prevents undesired oscillations of the dissolved oxygen concentration. Simulation results based on available experimental data were used to show the effectiveness of the proposal.

Diagonally dominant backstepping autopilot for aircraft with unknown actuator failures and severe winds

AbstractA novel formulation of the flight dynamic equations is presented that permits a rapid solution for the design of trajectory following autopilots for nonlinear aircraft dynamic models. A robust autopilot control structure is developed based on the combination of the good features of the nonlinear dynamic inversion (NDI) method, integrator backstepping method, time scale separation and control allocation methods. The aircraft equations of motion are formulated in suitable variables so that the matrices involved in the block backstepping control design method are diagonally dominant. This allows us to use a linear controller structure for a trajectory following autopilot for the nonlinear aircraft model using the well known loop by loop controller design approach. The resulting autopilot for the fixed-wing rigid-body aircraft with a cascaded structure is referred to as the diagonally dominant backstepping (DDBS) controller. The method is illustrated here for an aircraft auto-landing problem under unknown actuator failures and severe winds. The requirement of state and control surface limiting is also addressed in the context of the design of the DDBS controller.

Reconfigurable flight control based on nonlinear dynamic inversion and dynamic control allocation

Based on nonlinear dynamic inversion (NDI) and dynamic control allocation, a new reconfigurable flight control scheme is proposed for multi effector aircraft. Firstly, basic flight control law is designed by NDI method to produce desired moment command according to the given attitude angle command. Then, the moment command is optimally distributed into individual control surfaces with position and rate constraints by dynamic control allocation (DCA) algorithm. In the face of control surface faults, control reallocation is performed in the remained control surfaces to fulfil flight reconfiguration, and the basic flight control law need not to be redesigned. The reconfigurable flight control scheme is evaluated by a nonlinear six degree–of–freedom (DoF) aircraft model under jammed case and damaged case, respectively. Effectiveness of the reconfigurable flight control method is demonstrated by simulation results.

Design of Non-Linear Dynamic Inversion UAV with QFT

Flight control system of UAV (Unmanned Aerial Vehicle) has limitations with non-linear dynamic inversion method. This paper introduces QFT based on non-linear dynamic inversion method, for avoiding model errors during existing non-linear function offset, QFT theory is presented firstly, then UAV model is established using non-linear dynamic inversion method, definituding the range of errors and system performance requirements, flight control system of UAV is designed with QFT, the simulating curves show that system has robustness stability.

편대 유도 법칙 및 초소형 비행체의 자동 편대 비행 구현

본 논문에서는 초소형 비행체의 자동 편대 비행을 위한 유도 법칙과 비행 시험 결과를 기술하였다. 초소형 비행체는 탑재 중량과 비행시간 등의 제한으로 인해 짧은 시간 안에 복수의 비행체가 임무를 분담하거나 협력하여 동시에 수행하는 것이 효율적이며 편대 비행은 이러한 임무 하중을 효과적으로 감소시킬 수 있다. 제안된 편대 유도 법칙은 Leader-Follower 편대 비행의 기하학적 관계 기반으로 비선형 모델 역변환 기법을 이용하여 설계하였다. 편대 유도 법칙에 필요한 비행체의 상태 정보는 비행체 간 고속의 데이터 통신 시스템을 구성하고 지상국을 통해 송수신하도록 하였다. 본 연구에서 제안된 비행체간 통신 기반의 편대 유도 기법은 센서의 측정 잡음에 대한 강건한 성능을 확인하기 위해 실제 비행 데이터 기반 시뮬레이션을 수행하였고 다수의 초소형 비행체를 이용한 편대 비행 시험을 통해 유도 법칙의 타당성을 검증하고 확인하였다. This paper presents an autonomous formation flight algorithm for micro aerial vehicles (MAVs) and its flight test results. Since MAVs have severe limits on the payload and flight time, formation of MAVs can help alleviate the mission load of each MAV by sharing the tasks or coverage areas. The proposed formation guidance law is designed using nonlinear dynamic inversion method based on 'Leader-Follower' formation geometric relationship. The sensing of other vehicles in a formation is achieved by sharing the vehicles' states using a high-speed radio data link. the designed formation law was simulated with flight data of MAV to verify its robustness against sensor noises. A series of test flights were performed to validate the proposed formation guidance law. The test result shows that the proposed formation flight algorithm with inter-communication is feasible and yields satisfactory results.

Control and Robustness Analysis for a High-Infinity Maneuverable Thrust-Vectoring Aircraft

This study focuses on designing a nonlinear controller for high-α maneuvers of a fighter aircraft with a thrust-vectoring control ability and checking the robustness of the designed controller using the structured singular-value μ-based robustness analysis. The controller is designed using the nonlinear dynamic inversion method. It is designed to engage either the aerodynamic control surfaces or the thrust-vectoring control paddles of the engines, depending on the flight conditions. The necessary mathematical models are built to describe the nonlinear flight dynamics, the nonlinear aerodynamics, the engine with thrust-vectoring paddles, and the aircraft sensors. The robustness analysis is especially needed when thrust-vectoring control is engaged in a challenging high-α maneuver. This is necessary to analyze the effect of increasing uncertainty in the aerodynamic parameters in such a flight condition. In a flight with thrust-vectoring control, the effect of the aerodynamic uncertainties on the robustness is investigated for two different cases. In the first case, the aerodynamic forces and moments are treated as if they are completely unknown. This unusual uncertainty assumption is proposed and investigated for the first time in this paper. In the second case, the aerodynamic forces and moments are assumed to be known but only with a limited degree of confidence (e.g., 70%). The results of the robustness analysis for each case show that it is impossible to achieve a satisfactory robustness if the aerodynamic forces and moments are treated as completely unknown disturbances, whereas robustness can be achieved rather easily if they are known even with only 70 % confidence. These conclusions are also verified with numerical flight simulations.

유도탄의 유도명령 추종을 위한 혼합제어기 설계: 공력 및 측추력제어

This paper is concerned with a mixed control with aerodynamic fin and side thrust control applied to an agile missile using a dynamic inversion and a time-varying control technique. The nonlinear dynamic inversion method with the weighting function allocates the desired control inputs(aerodynamic fin and side thrust control) to achieve a reference command, and the time-varying control technique plays the role to guarantee the robustness for the uncertainties. The proposed schemes are validated by nonlinear simulations with aerodynamic data.