Flight Path Angle Research Articles

Reactive optimal UAV motion planning in a dynamic world

Navigation in a dynamic environment requires reactive actions to avoid collision and navigate safely. This paper deals with optimal and reactive motion planning for unmanned air vehicles in a dynamic world. A virtual space representation is used to formulate and solve the problem and derive real time optimal trajectories. This formulation allows for the construction of different control subspaces from which optimal control laws for the speed, the flight path angle, and the heading angle are derived. The safety margins are translated to the control subspaces as speed and orientation margins. Closed-form reactive optimal solutions are calculated to achieve reactive motion and avoid collision in each subspace. The dynamic and kinematic constraints are taken into account when planning motion in the control subspaces. Simulation results show the effectiveness of the proposed methods.

Modeling, Trimming and Simulation of a Full Scale Helicopter

The complex configuration of helicopter guarantees that the vehicle modeling, trim and simulation are significantly more difficult than fixed-wing aircrafts. In this paper, general expressions for aerodynamic forces and moments, acting on helicopter due to its main and tail rotors at any flight conditions, are derived by using momentum and blade element theories. These complex expressions are inserted in the rigid body equations of motion, derived from Newton second law, to build a generic nonlinear mathematical model for single main and tail rotors helicopters; in order to obtain their responses to arbitrary control inputs. This model can be used in pilot training, control system design, and studying the helicopter stability characteristics. Trimming problem is solved at general flight conditions; arbitrary turn rate, flight path and side slip angles. The power required to fly helicopter at forward flight with several flight path angles is determined. The flight path angle required for helicopter autorotation condition is calculated at any forward speed. The mathematical model is solved by numerical integration (Runge-Kutta method) in the simulation code. The resulting trim conditions are verified by supplying the trim control inputs to the simulation code and verifying that the helicopter is flying in steady-state.

Autonomous Landing Control of Fixed-wing UAVs: from Theory to Field Experiment

This paper describes our work on autonomous landing control of fixed-wing unmanned aerial vehicles (UAVs). A hierarchical control structure is developed for autonomous landing of fixed-wing UAVs. In the hierarchical control structure, active disturbance rejection controllers are designed for attitude control. A proportional guidance law is proposed for height tracking. Other controllers, such as flight path angle controller, heading angle controller and taxiing controller, are designed using proportion integration differentiation technique. A test system is developed to validate the hierarchical structure and narrow the gap between the theory and practice. The test system includes an X-Plane based hardware-in-the-loop(HIL) simulation subsystem and a flight test subsystem. The interface and protocol between the autopilot and X-plane are designed same with that of the flight test platform. Consequently, the autopilot passed the validation in the HIL simulation can be directly moved on to the flight test platform. Finally, results of the HIL simulation and field experiment are presented to demonstrate the performance of the proposed approach and the entire test system.

Robust adaptive gliding guidance for hypersonic vehicles

A novel robust adaptive gliding guidance strategy based on multi-constrained analytical optimal guidance and online identification of aerodynamic coefficients for hypersonic vehicles is proposed. The guidance models are constructed in both longitudinal and lateral directions and optimal guidance law, namely required load factor, is designed with minimum energy consumption to satisfy terminal position, altitude and flight-path angle constraints. Considering aerodynamic coefficients are the core factors in the angle-of-attack calculation, it constructs the aerodynamic models in the form of quadratic polynomial function and employs extended Kalman filter to estimate the unknown parameters. Using the optimal guidance law based on current flight states and terminal constraints and the identified outputs to calculate angle-of-attack, then the gliding guidance mission can be achieved adaptively and robustly. Finally, the simulation experiments of high performance of the common aerothermodynamics-shell vehicle (CAV-H) are carried out to validate the guidance performance.

Barrier Lyapunov function-based adaptive control for hypersonic flight vehicles

This paper presents an adaptive control strategy for hypersonic flight vehicles (HFVs) subject to parametric uncertainties, external disturbances and faulty actuators. Besides the guaranteed tracking performance, the main novelty of this study is to strictly constrain the flight states, which are crucial to hypersonic flights, such as the bounded angle of attack required by the scramjet. To achieve this, the disturbed control-oriented model of HFVs with uncertain parameters and faulty actuators is first rewritten into a parameterized form, based on which novel adaptive controllers are then designed for velocity and altitude subsystems. By introducing barrier Lyapunov functions to design procedures, specific tracking performances of velocity and altitude are guaranteed, while the other flight states of angle of attack, flight path angle, pitch angle and pitch angle rate can be kept within the prescribed ranges. Command filters are employed in the back-stepping design for altitude subsystem to limit the magnitudes of virtual controls and to avoid the complicated analytical calculations. In addition, an adaptive inverse is integrated into the adaptive control scheme to sufficiently compensate for the unknown dead-zone nonlinearity in elevator. It is shown that the developed control system regulates the tracking errors within some neighborhoods of zero, which become sufficiently small by proper adjustments on design parameters. Finally, the numerical simulation is provided for comparison and verification purposes.

Automatic Approach and Landing Trajectory Planner for Unpowered Reusable Launch Vehicle

A new guidance scheme for the approach and landing (A & L) phase of an unpowered reusable launch vehicle (RLV) has been developed. The main advantage of the new guidance is the use of glide-efficiency factor as the independent variable to compute the geometrical flare parameters by a set of analytical functions. The trajectory-planning algorithm generates its reference geometry based on the steep and shallow subphases, respectively. During the steep segment, the quasi-equilibrium glide (QEG) solution, which assumes a constant dynamic pressure and flight-path angle during the flight, is used to create the flight reference while the shallow segment is defined by polynomial functions for altitude and dynamic pressure profiles. Standard linearization methods are used to design a closed-loop command in order to track the QEG profile. Furthermore, proportion-derivative (PD) control is used to modulate the lift coefficient during the flare flight. Once the reference trajectory is created, a closed-loop simulation is obtained to track the reference. Off-nominal conditions, in terms of change in initial glide-efficiency factor, dynamic pressure, flight-path angle, and altitude are tested using a Monte-Carlo simulation. The simulated results demonstrate the effectiveness of the proposed algorithm to land the vehicle successfully under large dispersions of glide-efficiency factor.

Nonlinear modelling of leader-follower UAV close formation flight with dynamic inversion-based control

The nonlinear dynamic inversion (DI) control techniques are used in leader-follower unmanned aerial vehicle (UAV) dynamics modelling considering new input variables in the present paper. Three separate DI controllers are developed for holding the velocity, heading and flight path angles of both UAVs in a synchronous manner. A numerical simulation is performed at the end for validating this formation control mission of multiple UAVs. The quantitative estimation of reduction in follower drag while in close formation flight is also calculated along with the controller design.

Asteroid Apophis: Evaluating the impact hazards of such bodies

Soon after the discovery of asteroid 99942 Apophis, it was classified as a potentially hazardous object with a high probability of an impact on the Earth in 2029. Although subsequent observations have substantially reduced the probability of a collision, it has not been ruled out; moreover, similar-sized asteroids in orbits intersecting the Earth’s orbit may well be discovered in the near future. We conduct a numerical simulation of an atmospheric passage and an impact on the Earth’s surface of a stony cosmic body with a diameter of 300 m and kinetic energy of about 1000 Mt, which roughly corresponds to the parameters of the asteroid Apophis, at atmospheric entry angles of 90° (vertical stroke), 45°, and 30°. The simulation is performed by solving three-dimensional equations of hydrodynamics and radiative transfer equations in the approximations of radiative heat conduction and volume emission. The following hazards are considered: an air shock wave, ejecta from the crater, thermal radiation, and ionospheric disturbances. Our calculations of the overpressure and wind speed on the Earth’s surface show that the zone of destruction of the weakest structures can be as large as 700–1000 km in diameter; a decrease in the flight path angle to the surface leads to a marked increase in the area affected by the shock wave. The ionospheric disturbances are global in nature and continue for hours: at distances of several thousand kilometers at altitudes of more than 100 km, air density disturbances are tens of percent and the vertical and horizontal velocity components reach hundreds of meters per second. The impact of radiation on objects on the Earth’s surface is estimated by solving the equation of radiative transfer along rays passing through a luminous area. In clear weather, the size of the zone where thermal heating may ignite wood can be as large as 200 km, and the zone of individual fire outbreaks associated with the ignition of flammable materials can be twice as large. In the 100-km central area, which is characterized by very strong thermal damage, there is ignition of structures, roofs, clothes, etc. The human hazardous area increases with the decrease in the trajectory angle, and people may experience thermal effects at distances of up to 250–400 km from the crater.

Trajectory optimization of unmanned aerial vehicle in dynamic soaring

An aircraft can extract energy from a gradient wind field by dynamic soaring. The paper presents trajectory optimization of an unmanned aerial vehicle for dynamic soaring by numerical analysis and validates the theoretical work through flight test. The collocation approach is used to convert the trajectory optimization problem into parameters optimization. The control and state parameters include lift coefficient, bank angle, positions, flight path angle, heading angle, and airspeed, which are obtained from the parameter optimization software. To validate the results of numerical simulation, the dynamic soaring experiment is also performed and experimental data are analyzed. This research work shows that the unmanned aerial vehicle can gain enough flight energy from the gradient wind field by following an optimal dynamic soaring trajectory. Meanwhile, the variation of flight path angle, heading angle, and airspeed has a significant influence on the energy transform. The solution can provide theoretical guide to unmanned aerial vehicles for extracting maximum energy from gradient wind fields.

Optimizing Steady Turns for Gliding Trajectories

Dubins planners provide minimum-length planar paths between waypoints for turning constrained vehicles. For a no-thrust or glider aircraft, Dubins paths have been extrapolated to three dimensions by augmenting the planar path with a constant flight-path angle in each path segment. Best-glide flight maximizes the horizontal distance traveled per unit altitude loss, but steeper flight-path angles result in a maximum heading change per unit altitude loss. This paper investigates combinations of bank and flight-path angles yielding maximum ranges for gliding Dubins trajectories. Starting from the extrema flight-path angles usually applied in the literature, it is shown that the maximum range along each flight radial from an initial point (that is, the footprint) is obtained at a maximum glidepath angle for a given turn radius. This result is applied in a novel three-dimensional maximum-range Dubins path. Three-dimensional Dubins examples with different heading constraints are presented. The impact of constraining solutions to a single pair of turning bank and flight-path angles is analyzed.

Extended Tsiolkovskii Equation and Its Application to Launch Vehicles

To estimate mass transported to an orbit by the rockets with better accuracy and to compare transport ability of a two-stage-to-orbit aerospace plane with that of conventional rockets, the Tsiolkovskii equation of the mass ratio is modified and extended by use of the fundamental equations of motion of a vehicle. The calculated mass ratios with the modified equations show reasonable agreement with the ratios of the actual flights of H-IIA and H-IIB rockets. From the modification of the equation, the extended effective specific impulse is derived. The impulse incorporates the effects of angle of attack, flight-path angle, lift, drag, and specific impulse and can evaluate vehicle transportation ability. Transport capability of a two-stage-to-orbit aerospace plane with rocket-based combined-cycle engine is examined with the impulse and the modified equations. When the plane flies with the ramjet mode in a small change of the flight-path angle and flies with the scramjet mode in a large change of the angle, the mass to an orbit becomes larger. A two-stage-to-orbit aerospace plane will transport a larger amount of mass to an orbit than conventional rockets.

Target tracking using multiple unmanned aerial vehicles: Graph theoretic nonlinear control approach

This paper develops a cooperative controller for multiple Unmanned Aerial Vehicles (UAVs) with application to target tracking. The cooperation between the UAVs is established based on an algebraic graph connection and the target information is provided externally by pinning it into a subset of the network. A backstepping-like technique is employed to design a consensus-based controller for each UAV in order to achieve target tracking in 3-D. The proposed controller computes commanded signals for the speed, flight path angle, and heading angle to track the target. The paper considers both the cases of fixed and dynamically changing communication topologies. It is shown that target tracking is achieved for fixed connection topology, if the graph has a directed spanning tree; and for the dynamically changing topology, if the union of the graphs over finite time intervals has a directed spanning tree. The system’s stability is shown using a Lyapunov function-based approach for these cases. All tracking errors are shown to be bounded as long as the target states and its derivatives up to second order are bounded. Detailed numerical simulations further illustrate the controller performance.

Comparison of Fuel Consumption of Descent Trajectories Under Arrival Metering

This paper compares fuel consumption of descent trajectories from cruise altitude to meter fix when the required time of arrival is later than the nominal time of arrival at the meter fix. The required delay, which is the difference between the nominal and the required times of arrival, is achieved by either slowing down the aircraft in the cruise and descent phases or flying a longer route at a constant altitude. Performance models of 10 different Boeing and Airbus aircraft, obtained from the Base of Aircraft Data, are employed for generating the results. It is demonstrated that the most fuel-efficient speed-control strategy for absorbing delay is first reducing descent speed as much as possible and then reducing cruise speed. This is a common finding for all 10 aircraft considered. For some aircraft, flying at a fixed flight-path angle and constant Mach number/calibrated airspeed results in lower fuel consumption compared to standard descent at idle thrust and constant Mach number/calibrated airspeed. Finally, for the cases examined, it is shown that executing a path-stretch maneuver at cruise altitude and descent at a reduced speed is more fuel efficient than inserting an intermediate-altitude cruise segment.

Development of Return to Base Flight Trajectory Generator Based on Dubins Path - Vector Field Method

In a Return to Base (RTB) situation, aircraft needs to immediately fly back to its origin airport. Since there is no published flight procedure for an RTB, an Air Traffic Controller (ATC) will assist the pilot for the flight procedure to fly. The objective of this work is to generate a flight trajectory in RTB situation based on the available airport flight procedures (departure and arrival) in Kertajati airport. The Dubins Path was used as a method to generate the flight trajectory and supported by the Vector-Field Methodology. The Python programming simulation was used to simulate the flight trajectory generation in the normal condition, second closest waypoint condition, and different parameters value condition. The trajectory was simulated based on flight characteristic of a single engine aircraft (Cesna 172) and multi-engine aircrafts (Boeing 737-800NG). The simulation results show that the Dubins Path and Vector-Field methodology success to generate the flight trajectory in different types of condition and parameters. The increase in aircraft velocity and the decrease in aircraft bank angle caused an increase in the aircraft turning radius. While, the decrease in aircraft flight path angle caused increase in the length of Dubins Path line.

Improved Perturbative Solution of Yaroshevskii's Planetary Entry Equation

An improved approximate analytical solution is developed for Yaroshevskii's classical planetary entry equation for the ballistic entry of a spacecraft into planetary atmospheres at circular speed. Poincaré's method of small parameters is used to solve for the altitude and flight path angle as a function of the spacecraft's speed. From this solution, other important expressions are developed including deceleration, stagnation-point heat rate, and stagnation-point integrated heat load. The accuracy of the solution is assessed via numerical integration of the exact equations of motion. The solution is also compared to the classical solutions of Yaroshevskii and Allen and Eggers. The new second-order analytical solution is more accurate than Yaroshevskii's fifth-order solution for a range of shallow (−3 deg) to steep (up to −90 deg) entry flight path angles, thereby extending the range of applicability of the solution as compared to the classical Yaroshevskii solution, which is restricted to an entry flight path of approximately −40 deg.

Robust estimation-free prescribed performance back-stepping control of air-breathing hypersonic vehicles without affine models

ABSTRACTThis paper investigates the design of a novel estimation-free prescribed performance non-affine control strategy for the longitudinal dynamics of an air-breathing hypersonic vehicle (AHV) via back-stepping. The proposed control scheme is capable of guaranteeing tracking errors of velocity, altitude, flight-path angle, pitch angle and pitch rate with prescribed performance. By prescribed performance, we mean that the tracking error is limited to a predefined arbitrarily small residual set, with convergence rate no less than a certain constant, exhibiting maximum overshoot less than a given value. Unlike traditional back-stepping designs, there is no need of an affine model in this paper. Moreover, both the tedious analytic and numerical computations of time derivatives of virtual control laws are completely avoided. In contrast to estimation-based strategies, the presented estimation-free controller possesses much lower computational costs, while successfully eliminating the potential problem of parameter drifting. Owing to its independence on an accurate AHV model, the studied methodology exhibits excellent robustness against system uncertainties. Finally, simulation results from a fully nonlinear model clarify and verify the design.

Dispersion reduction of artillery rockets guided by flight path steering method

ABSTRACTArtillery rockets are sensitive to disturbances (total impulse variation, wind, thrust misalignment, etc.). As the range of ground-to-ground rockets increases, the accuracy of free flight rockets decreases. Requirements for the increase of the range and minimisation of the impact point dispersions can be solved by adding guidance and control systems to rockets. Based on the differences between the measured flight parameters and the calculated parameters for the nominal trajectory, the flight path angle correction algorithm is obtained by adding the correction to the nominal value. The flight path steering guidance system with lateral acceleration autopilot in the inner loop, is used for the guidance of hypothetical artillery rockets. The guidance algorithm given in this paper eliminates the time correction due to rocket velocity variations. Efficiency of the proposed algorithm is illustrated by numerical simulation. There is no practical influence of the external disturbances on impact point dispersion. It is also shown that the measurement errors of the inertial measurement unit are the dominant factor affecting impact point dispersion of artillery rockets modified by adding a guidance system based on the flight path steering method.

Optimal Guidance Law to Maximize Terminal Velocity for Missiles with Impact Angle Constraint

In this paper, an optimal guidance law for missiles with impact angle and miss distance constraints is proposed to achieve the maximal terminal velocity. The normal acceleration command that includes the time-varying coefficients is introduced to satisfy the desired impact angle as well as zero miss distance according to the geometric relation and relative motion parameters between missile and target. The problem is formulated as an optimal control problem by defining the angle of velocity error and flight-path angle as state variables and maximizing a performance index of the terminal velocity. The analytical form of the proposed guidance law is obtained as the solution of the optimal control problem combining optimal control theory and numerical value computation method. Nonlinear simulations of various situations demonstrate the performance and feasibility of the proposed optimal guidance law.

Analytic Approach and Landing Guidance through a Novel Time-Varying Sliding Mode Control Method

AbstractIn this paper, a nonlinear guidance law is developed for the approach and landing (A&L) phase of a reusable launch vehicle (RLV). First, a novel time-varying sliding mode control (TVSMC) technique is introduced. The main feature of this technique is that it enables the system states to converge to zero at the desired finite time. Then, the developed technique is applied to the A&L guidance law design. The guidance law possesses the capability of generating trajectories online according to the current system states and the terminal constraints. Therefore, there is no need to design any reference trajectories in advance. In addition, the analytic solutions of the altitude and flight path angle can be obtained in advance by solving a first-order linear differential equation. These analytic solutions can also be used to estimate the boundary of the normal load factor of the RLV. The effectiveness of the proposed guidance strategy and the accuracy of the analytic solutions are demonstrated through nume...

Steady Glide Dynamic Modeling and Trajectory Optimization for High Lift-to-Drag Ratio Reentry Vehicle

Steady glide trajectory optimization for high lift-to-drag ratio reentry vehicle is a challenge because of weakly damped trajectory oscillation. This paper aims at providing a steady glide trajectory using numerical optimal method. A new steady glide dynamic modeling is formulated via extending a trajectory-oscillation suppressing scheme into the three-dimensional reentry dynamics with a spherical and rotating Earth. This scheme comprehensively considers all factors acting on the flight path angle and suppresses the trajectory oscillation by regulating the vertical acceleration in negative feedback form and keeping the lateral acceleration invariant. Then, a study on steady glide trajectory optimization is carried out based on this modeling and pseudospectral method. Two examples with and without bank reversal are taken to evaluate the performance and applicability of the new method. A comparison with the traditional method is also provided to demonstrate its superior performance. Finally, the feasibility of the pseudospectral solution is verified by comparing the optimal trajectory with integral trajectory. The results show that this method not only is capable of addressing the case which the traditional method cannot solve but also significantly improves the computational efficiency. More importantly, it provides more stable and safe optimal steady glide trajectory with high precision.