Nonlinear direct data-driven control for UAV formation flight system

This paper proposes the nonlinear direct data-driven control from theoretical analysis and practical engineering,i.e.,unmanned aerial vehicle(UAV)formation flight system.Firstly,from the theoretical point of view,consider one nonlinear closedloop system with a nonlinear plant and nonlinear feed-forward controller simultaneously.To avoid the complex identification process for that nonlinear plant,a nonlinear direct data-driven control strategy is proposed to design that nonlinear feed-forward controller only through the input-output measured data sequence directly,whose detailed explicit forms are model inverse method and approximated analysis method.Secondly,from the practical point of view,after reviewing the UAV formation flight system,nonlinear direct data-driven control is applied in designing the formation controller,so that the followers can track the leader’s desired trajectory during one small time instant only through solving one data fitting problem.Since most natural phenomena have nonlinear properties,the direct method must be the better one.Corresponding system identification and control algorithms are required to be proposed for those nonlinear systems,and the direct nonlinear controller design is the purpose of this paper.

An Optimization Method of Formation Flight for Minimizing Fuel Consumption

A method for formation flight trajectory optimization was established.This method aims at minimizing fuel consumption of a two-aircraft formation flight,without changing the original trajectory of the leader.Candidate flight pairs were selected from all international flights arriving at or departing from China in one day according to the requirement of the proposed method.Aircraft performance database Base of Aircraft Data(BADA)was employed in the trajectory computation.By assuming different fuel-saving percentages for the following aircraft,pre-flight plan trajectories of formation flight were optimized.The fuel consumption optimization effect under the influence of different trajectory optimization parameters was also analyzed.The results showed that the higher the fuel savings percentage,the longer the flight distance of formation flight,but the smaller the number of formation combinations that can be realized,which is limited by the aircraft performance.The following aircraft flying along the approximate actual flight trajectory can be benefited as well,and the optimal fuel-saving efficiency is related to the expected fuelsaving efficiency of formation flight.

IDENTIFYING THE NUMBER OF AIRCRAFT IN FORMATION FLIGHT USING ISAR TECHNIQUE

In this paper, an attempt at applying the cross range one dimensional ISAR processing for identifying the number of aircraft in formation flight is described. The procedure will succeed only if the translational motion of the target is compensated perfectly. The two dimensional ISAR motion compensation methods based on high resolution range profile, such as the scatter point referencing and the track the target centroid, can not be used here. The track fitting method, which can be used for one dimensional ISAR motion compensation, relies on a parametric model and suffers from a serious defect of large amount of computation. The authors proposed an iterative dominant scatterer method for one dimensional ISAR motion compensation. It is robust and nonparametric with low computational complexity. Live echo signals from two fighter planes in formation flight have been collected using an S band surveillance radar. The cross range one dimensional ISAR processing was done. Experimental results show that identifying the number of aircraft in formation flight via cross range one dimensional ISAR processing is feasible.

Relative navigation for satellite formation flight using a continuous-discrete converted measurement Kalman filter

The present paper develops an approach of relative orbit determination for satellite formation flight.Inter-satellite measurements by the onboard devices of the satellite were chosen to perform this relative navigation,and the equations of relative motion expressed in the Earth Centered Inertial frame were used to eliminate the assumption of the circular reference orbit.The relative orbit estimation was achieved through a continuous-discrete converted measurement Kalman filter design,in which the measurements were transformed to the inertial frame to avoid the linearization error of the observation equation.In addition,the situation of the coarse measurement period(only microwave radar measurements are available)existing was analyzed.The numerical simulation results verify the validity of the navigation approach,and it has been proved that this approach can be applied to the formation with an elliptical reference orbit.

Autonomous Formation Flight Control of Large-Sized Flapping-Wing Flying Robots Based on Leader–Follower Strategy

Birds in nature exhibit excellent long-distance flight capabilities through formation flight,which could reduce energy consumption and improve flight efficiency.Inspired by the biological habits of birds,this paper proposes an autonomous formation flight control method for Large-sized Flapping-Wing Flying Robots(LFWFRs),which can enhance their search range and flight efficiency.First,the kinematics model for LFWFRs is established.Then,an autonomous flight controller based on this model is designed,which has multiple flight control modes,including attitude stabilization,course keeping,hovering,and so on.Second,a formation flight control method is proposed based on the leader–follower strategy and periodic characteristics of flapping-wing flight.The up and down fluctuation of the fuselage of each LFWFR during wing flapping is considered in the control algorithm to keep the relative distance,which overcomes the trajectory divergence caused by sensor delay and fuselage fluctuation.Third,typical formation flight modes are realized,including straight formation,circular formation,and switching formation.Finally,the outdoor formation flight experiment is carried out,and the proposed autonomous formation flight control method is verified in real environment.

Formation Flight Control and Cooperative Obstacle Avoidance of Multiple UAVs

This paper primarily focuses on the obstacle avoidance issue of followers in unmanned aerial vehicle(UAV)formation flight while considering formation constraints.Based on consensus theory and the artificial potential field(APF)principle,a new fusion UAV formation control algorithm is proposed.The method employs a formation control strategy that combines the leader-following method and the virtual structure method,enabling the generation,maintenance and transformation of the formation through the utilization of a consensus controller.In response to the specific problem of the follower within the formation entering the no-fly zone and the self-collision among UAVs,APF-based formation path replanning and self-collision prevention algorithms are introduced.The simulation results demonstrate the effectiveness of the proposed algorithm.

Trophallaxis network control approach to formation flight of multiple unmanned aerial vehicles

A novel network control method based on trophaUaxis mechanism is applied to the formation flight problem for multiple un- manned aerial vehicles （UAVs）. Firstly, the multiple UAVs formation flight system based on trophallaxis network control is given. Then, the model of leader-follower formation flight with a virtual leader based on trophallaxis network control is pre- sented, and the influence of time delays on the network performance is analyzed. A particle swarm optimization （PSO）-based formation controller is proposed for solving the leader-follower formation flight system. The proposed method is applied to five UAVs for achieving a ＇V＇ formation, and a series of experimental results show its feasibility and validity. The proposed control algorithm is also a promising control strategy for formation flight of multiple unmanned underwater vehicles （UUVs）, unmanned ground vehicles （UGVs）, missiles and satellites.

Cooperative coalition for formation flight scheduling based on incomplete information

This study analyzes the cooperative coalition problem for formation scheduling based on incomplete information. A multi-agent cooperative coalition framework is developed to optimize the formation scheduling problem in a decentralized manner. The social class differentiation mech- anism and role-assuming mechanism are incorporated into the framework, which, in turn, ensures that the multi-agent system （MAS） evolves in the optimal direction. Moreover, a further differen- tiation pressure can be achieved to help MAS escape from local optima. A Bayesian coalition nego- tiation algorithm is constructed, within which the Harsanyi transformation is introduced to transform the coalition problem based on incomplete information to the Bayesian-equivalent coali- tion problem based on imperfect information. The simulation results suggest that the distribution of agents＇ expectations of other agents＇ unknown information approximates to the true distribution after a finite set of generations. The comparisons indicate that the MAS cooperative coalition algo- rithm produces a significantly better utility and possesses a more effective capability of escaping from local optima than the proposal-engaged marriage algorithm and the Simulated Annealing algorithm.

Highly reliable relative navigation for multi-UAV formation flight in urban environments

Formation flight of multiple Unmanned Aerial Vehicles(UAVs)is expected to bring significant benefits to a wide range of applications.Accurate and reliable relative position information is a prerequisite to safely maintain a fairly close distance between UAVs and to achieve inner-system collision avoidance.However,Global Navigation Satellite System(GNSS)measurements are vulnerable to erroneous signals in urban canyons,which could potentially lead to catastrophic consequences.Accordingly,on the basis of performing relative positioning with double differenced pseudoranges,this paper develops an integrity monitoring framework to improve navigation integrity(a measure of reliability)in urban environments.On the one hand,this framework includes a fault detection and exclusion scheme to protect against measurement faults.To accommodate urban scenarios,spatial dependence in the faults are taken into consideration by this scheme.On the other hand,relative protection level is rigorously derived to describe the probabilistic error bound of the navigation output.This indicator can be used to evaluate collision risk and to warn collision danger in real time.The proposed algorithms are validated by both simulations and flight experiments.Simulation results quantitatively reveal the sensitivity of navigation performance to receiver configurations and environmental conditions.And experimental results suggest high efficiency and effectiveness of the new integrity monitoring framework.

An approach for formation design and flight performance prediction based on aerodynamic formation unit:Energy-saving considerations

The performance improvement of swarm drones through aerodynamic shape optimization may be challenging due to folded size constraints imposed by the specific launch approach.However,fixed-wing aircraft swarms can benefit from formation flight in terms of energy consumption.This study introduces the concept of the"aerodynamic formation unit",which consists of two or three aircraft that form an inseparable unit of the formation.Considering the Unmanned Aerial Vehicle(UAV)distribution and wingtip vortex interference in the formation,two typical aerodynamic formation units are optimized by the variable-fidelity aerodynamic optimization method based on space mapping.The aerodynamic characteristics of the formation UAVs that affect flight performance,such as lift-to-drag ratio(L/D ratio)and static stability are analyzed by Computational Fluid Dynamics(CFD)simulations.The L/D ratio(cruising condition)of the following aircraft can be increased by 22.8%and 57.5%in the optimal units that involve two and three aircraft respectively.Moreover,this study conducts several CFD simulations for multi-aircraft formations formed by the units,which show that the average L/D ratio of the formation can be improved by more than 19%.These results verify the feasibility and effectiveness of the"aerodynamic formation unit"concept and the optimization framework for formation parameters.

Adaptive distributed formation maintenance for multiple UAVs:Exploiting proximity behavior observations

The formation maintenance of multiple unmanned aerial vehicles(UAVs)based on proximity behavior is explored in this study.Individual decision-making is conducted according to the expected UAV formation structure and the position,velocity,and attitude information of other UAVs in the azimuth area.This resolves problems wherein nodes are necessarily strongly connected and communication is strictly consistent under the traditional distributed formation control method.An adaptive distributed formation flight strategy is established for multiple UAVs by exploiting proximity behavior observations,which remedies the poor flexibility in distributed formation.This technique ensures consistent position and attitude among UAVs.In the proposed method,the azimuth area relative to the UAV itself is established to capture the state information of proximal UAVs.The dependency degree factor is introduced to state update equation based on proximity behavior.Finally,the formation position,speed,and attitude errors are used to form an adaptive dynamic adjustment strategy.Simulations are conducted to demonstrate the effectiveness and robustness of the theoretical results,thus validating the effectiveness of the proposed method.

Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.

Second-order divided difference filter for vision-based relative navigation

A second-order divided difference filter (SDDF) is derived for integrating line of sight measurement from vision sensor with acceleration and angular rate measurements of the follower to estimate the precise relative position,velocity and attitude of two unmanned aerial vehicles (UAVs).The second-order divided difference filter which makes use of multidimensional interpolation formulations to approximate the nonlinear transformations could achieve more accurate estimation and faster convergence from inaccurate initial conditions than standard extended Kalman filter.The filter formulation is based on relative motion equations.The global attitude parameterization is given by quarternion,while a generalized three-dimensional attitude representation is used to define the local attitude error.Simulation results are shown to compare the performance of the second-order divided difference filter with a standard extended Kalman filter approach.

New multi-UAV formation keeping method based on improved artificial potential field

Formation keeping is important for multiple Unmanned Aerial Vehicles(multi-UAV)to fully play their roles in cooperative combats and improve their mission success rate.However,in practical applications,it is difficult to achieve formation keeping precisely and obstacle avoidance autonomously at the same time.This paper proposes a joint control method based on robust H∞ controller and improved Artificial Potential Field(APF)method.Firstly,we build a formation flight model based on the “Leader-Follower”structure and design a robust H∞ controller with three channels X,Y and Z to eliminate dynamic uncertainties,so as to realize high-precision formation keeping.Secondly,to fulfill obstacle avoidance efficiently in complex situations where UAVs fly at high speed with high inertia,this paper comes up with the improved APF method with deformation factor considered.The judgment criterion is proposed and applied to ensure flight safety.In the end,the simulation results show that the designed controller is effective with the formation keeping a high accuracy and in the meantime,it enables UAVs to avoid obstacles autonomously and recover the formation rapidly when coming close to obstacles.Therefore,the method proposed here boasts good engineering application prospect.

Design and implementation of a leader-follower cooperative control system for unmanned helicopters

In this paper, we present a full scheme for the cooperative control of multiple unmanned aerial vehicle （UAV） helicopters. We adopt the leader-follower pattern to maintain a fixed geometrical formation while navigating the UAVs following certain trajectories. More specifically, the leader is commanded to fly on some predefined trajectories, and each follower is controlled to maintain its position in formation using the measurement of its inertial position and the information of the leader position and velocity, obtained through a wireless modem. More specifications are made for multiple UAV formation flight. In order to avoid possible collisions of UAV helicopters in the actual formation flight test, a collision avoidance scheme based on some predefined alert zones and protected zones is employed. Simulations and experimental results are presented to verify our design.

An Unmanned Aerial Vehicle Flight Formation for Enhanced Emergency Communication Based on Conformal Antenna Design

Benefiting from the inherent superiorities in flexibility and mobility,the use of unmanned aerial vehicles(UAVs)as flying base stations for wireless coverage has been of significant interest,especially for rescue services.This work concerns the reliable emergency communication based on commercial micro-sized UAVs due to their high availability and low cost.To decrease the weight overloads and to improve the power efficiency,a UAV body conformal and omnidirectional antenna is first presented based on the characteristic mode analysis.To extend the wireless coverage and to improve the communication quality of the UAV network,a UAV flight formation is then proposed and analyzed.In addition,the propagation analyses for the proposed UAV transmitter designs are performed in a realistic hilly canyon region.Simulations and comparisons are presented to demonstrate the effectiveness of the proposed designs in emergency communications and performance enhancement through the UAV flight formation.

Control of orientation for spacecraft formations in the vicinity of the Sun-Earth L2 libration point

Formation flying in the vicinity of the libration point is an important concept for space exploration and demands reliable and accurate techniques for the control of a spacecraft.On the basis of previous works,this paper addresses the problem of relative orientation control of spacecraft formation flying utilizing the framework of the circular restricted three-body problem(CR3BP)with the Sun and Earth as the primary gravitational bodies.Two specific tasks are accomplished in this study.First,the tangent targeting method(TTM),an efficient two-level differential correction algorithm,is exploited to control the Chief/Deputy architecture to maintain a prespecified orientation.The time spent within the orientation error corridor between successive maneuvers is maximized while the relative separation between the vehicles is held constant at each target point.The second task is to further optimize the maneuver intervals by dropping the constraint imposed on the relative vehicle separation.Numerical investigation indicates that the number of maneuvers can be significantly reduced and the length of time between successive maneuvers can be greatly increased by utilizing the TTM.

Close relative motion on distant retrograde orbits

Distant Retrograde Orbits(DROs)in the Earth-Moon system have great potential to support varieties of missions due to the favorable stability and orbital positions.Thus,the close relative motion on DROs should be analyzed to design formations to assist or extend the DRO missions.However,as the reference DROs are obtained through numerical methods,the close relative motions on DROs are non-analytical,which severely limits the design of relative trajectories.In this paper,a novel approach is proposed to construct the analytical solution of bounded close relative motion on DROs.The linear dynamics of relative motion on DRO is established at first.The preliminary forms of the general solutions are obtained based on the Floquet theory.And the general solutions are classified as different modes depending on their periodic components.A new parameterization is applied to each mode,which allows us to explore the geometries of quasi-periodic modes in detail.In each mode,the solutions are integrated as a uniform expression and their periodic components are expanded as truncated Fourier series.In this way,the analytical bounded relative motion on DRO is obtained.Based on the analytical expression,the characteristics of different modes are comprehensively analyzed.The natural periodic mode is always located on the single side of the target spacecraft on DRO and is appropriate to be the parking orbits of the rendezvous and docking.On the basis of quasi-periodic modes,quasi-elliptical fly-around relative trajectories are designed with the assistance of only two impulses per period.The fly-around formation can support observations to targets on DRO from multiple viewing angles.And the fly-around formation is validated in a more practical ephemeris model.

Experimental and computational investigation of transonic speed

The influence of the wing-tip vortex of leading aircraft on energy savings,quantified by formation aerodynamic force fraction of the following aircraft,is studied at transonic speed for a matrix of leading aircraft’s vortex locations.The research model adopts the hybrid formation of medium and large aircraft.The leading aircraft is scaled by 2.1%,and the following aircraft is scaled by 1.4%.An aerodynamic benefit "map"is developed to determine the optimum location of the following aircraft relative to the leading aircraft wake and to compare with experimental results,thus validating the use of CFD for the formation flight at cruising speed.The response surface model of aerodynamic gain effect relative to formation parameters is established via numerical calculation and wind tunnel test.The optimal formation parameters and the setting criteria of the study model are optimized.Results show that the wing-tip vortex of large aircraft significantly increases lift and reduces drag on the medium-sized aircraft following it.Reduced drag slightly increases with the flow direction position.With the increase of flow direction distance,the peak area moves from 15%of wing-tip overlap to 20%of overlap.In addition,the maximum drag decreases about 16%,and the maximum lift increases about 12%.The lift drag ratio of the optimal position is increased by 27%,which is twice as large as that of the same scale ratio aircraft formation.Results show that the increase of lift is mainly caused by the increase of suction peak and suction range.

Pattern control for large-scale spacecraft swarms in elliptic orbits via density fields

Space swarms,enabled by the miniaturization of spacecraft,have the potential capability to lower costs,increase efficiencies,and broaden the horizons of space missions.The formation control problem of large-scale spacecraft swarms flying around an elliptic orbit is considered.The objective is to drive the entire formation to produce a specified spatial pattern.The relative motion between agents becomes complicated as the number of agents increases.Hence,a density-based method is adopted,which concerns the density evolution of the entire swarm instead of the trajectories of individuals.The density-based method manipulates the density evolution with Partial Differential Equations(PDEs).This density-based control in this work has two aspects,global pattern control of the whole swarm and local collision-avoidance between nearby agents.The global behavior of the swarm is driven via designing velocity fields.For each spacecraft,the Q-guidance steering law is adopted to track the desired velocity with accelerations in a distributed manner.However,the final stable velocity field is required to be zero in the classical density-based approach,which appears as an obstacle from the viewpoint of astrodynamics since the periodic relative motion is always time-varying.To solve this issue,a novel transformation is constructed based on the periodic solutions of Tschauner-Hempel(TH)equations.The relative motion in Cartesian coordinates is then transformed into a new coordinate system,which permits zero-velocity in a stable configuration.The local behavior of the swarm,such as achieving collision avoidance,is achieved via a carefully-designed local density estimation algorithm.Numerical simulations are provided to demonstrate the performance of this approach.