Flight Dynamics and Trajectory Modeling for a Strategic Long-Endurance Solar Unmanned Aircraft

Transcription

1 Flight Dynamics and Trajectory Modeling for a Strategic Long-Endurance Solar Unmanned Aircraft B. M. Albaker, Member, IEEE UMPEDAC Research Centre, University of Malaya Kuala Lumpur, Malaysia baraaalbaker@um.edu.my Abstract Recently, there has been great interest in the development of advanced strategic green unmanned aircraft capable of executing missions in complex dynamic environments. Among green Unmanned Aerial Vehicle (UAV), solar-powered unmanned aircraft have a bright future due to their longendurance missions. This paper presents the development of a three degree of freedom dynamics and path planning trajectory modeling for a solar-powered long-endurance UAV. The paper orbit around the development of UAV s longitudinal and lateral dynamics low-level abstraction modeling and UAV s trajectory modeling in the high-level intelligent control. Index Terms UAV, Modeling, Aircraft dynamics, UAV Trajectory. I. INTRODUCTION The absence of a human pilot in the UAV makes it highly suited to repetitive, dirty, and dangerous operations. The world of the future will be filled with intelligent unmanned aircraft employed to autonomously perform tasks and substituting human efforts in a wide variety of applications. The importance of UAVs in scientific applications has been thoroughly demonstrated in [1, 2]. The concentrated efforts and serious considerations paid them may make UAVs the next milestone in the evolution of aviation. In addition, for a greener society, there is a desire to use an alternative source of energy for UAVs. The deployment of intelligent green UAVs has been made possible through technological advances. A promising alternative green energy includes: fuel-cells, bio-fuel, and solar cells. Solar technology is considered as the cleanest and limitless energy source. This topic had been covered by the robotics community since the late 1970s [3]. Based on these efforts, various algorithms and implementations are currently available. Although short-endurance UAVs offer great benefits for tactical short range missions, they fall to accomplish long strategic missions due to their power source limitations. In this case, either UAVs land to recharge or use another UAV to complete designated mission [4]. Thus, it may result in an extremely costly mission or expose UAVs to dangerous physical damage in war situations. Even though the fuel-cell is an environment-friendly power supply, it is too heavy and produces limited power for UAV. Increasing the battery size or the number of batteries cannot solve this problem, due to the weight restrictions. Sun harnessing plays an important role in the humanities search for clean energy because of the growing electricity demands, serious environmental awareness, and limited energy resources. With the use of solar cells, the aircraft will be able to consume solar energy during the day and stores part of the energy in a battery to be used later to provide energy for night-time flight, and thereby solve the recharge problem. However, the design process for a solar-powered aircraft is more complex than that of a conventional aircraft because the solar cells are attached to the wing, which must be proportional to the generated power. Moreover, all aircraft subsystems must be lightweight and efficient enough to cope total weight of the UAV[5, 6] Extensive efforts by many international organizations are underway, investigating new green energy technologies that allow UAVs to operate for long-endurance. With programs such as FAA s NextGen [7], more funding of technology and automation is coming. For instance, at the Politecnico University, several researches are being carried out with the aim of designing a high altitude very-long endurance UAV [2]. The remaining of the paper is organized as follows. The abstraction layer of the solar-powered UAV system is first described, as the interaction of the UAV s hardware to other layers of the UAV system including high-level intelligent control, user interface, and air-to-air communication data-link. A description of the low-level-abstraction makes apparent the control vector and the aircraft performance limits. The proposed three-degree-of-freedom UAV longitudinal and lateral dynamics modeling is then presented with its constraints those form the feasible options to appear to the solar unmanned aircraft. Later, the intelligent control is presented with its functions. Finally, a path planning trajectory generation for the solar UAV in three dimensional spaces is proposed, modeled and presented.

2 II. UAV LOW-LEVEL ABSTRACTION The low-level abstraction for the solar UAV forms the low-level control and sense/actuation functions that interface the higher intelligent control and supervision layers to the hardware. The functions executed include flight path control, navigation-state information extraction, and threats surveillance. The output from the intelligent control layer specifies a sequence of objective waypoints converted to a flight trajectory. The commands, sent in a timely manner, include three-dimensional information about UAV position and orientation. The local collision-free flight trajectory from Collision Avoidance System (CAS) is then passed to the flight-path controller for issuance of the actuating signals necessary to the designated trajectory. The flight-path controller function (which represents the main function of the autopilot system) controls the UAV s actuators through the aircraft s state as obtained from navigation sensors and commanded trajectory variables of the CAS. Its design should consider airframe characteristics. In this paper, the flight characteristics of the airframe used in the solar-powered UAV was analyzed through a 3DOF point mass equation of motion. Navigation, another function executed by the UAV abstraction, is defined as the process of determining the state (position, orientation, velocity) of a moving UAV above Earth s surface [3, 8]. The sensed variables of interest to autonomous UAV control are altitude, position, velocity, acceleration, and orientation. The navigation processor implements the navigation system equations. Navigationaiding sensors can use satellite-based systems such as (for position and velocity) Global Positioning System (GPS) and wide-area augmentation, optical-vision-based, ground-based, or any combination at all. Other sensors include magnetometers (for orientation), dynamic pressure (airspeed), barometric air pressure (altitude), laser (altitude and range), radar (range, range rate, and bearing angles), etc.. A Kalman filter may be used to fuse data from multiple sensors to reduce information uncertainty and accordingly provide more robust and useful information on the state of a UAV. The noise property of multiple sensors is used to estimate the dependency weight of each sensor when combining the measurement. III. UAV MODELING The UAV model shows the nature of aircraft dynamics in three-dimensional space. In general, aircraft modeling requires the definition of forces and moments acting on the aircraft, as these are motion factors. The mathematical model of forces and moments include aerodynamics, propulsion system, gravity, and wind disturbance (if any). For equations of motion, the coordinate systems used as reference frames were first considered. The coordinate systems used here as the reference frame for three-dimensional motion of aircraft were Earth Centered Earth Fixed (ECEF), geodetic, Local (L), Body (B), and Velocity Vector (VV). Fig. 1 demonstrates some of these coordinate systems. Fig. 1. ECEF, geodetic and Local NED reference frames The kinematic equations relate the UAV s velocities (angular and linear) to the time derivatives of its position and orientation. Solutions to the complete equations of motion provide the characteristics of motion of any solid body in threedimensional space: three translational motions, and three angular motions. Let the a th UAV (A a ) be one of the aircraft operating in a shared airspace together with other aircraft (Ã). Development of the 3DOF flight simulator was based on 3DOF equations of motion, with velocity (V), air-relative flight path angle (γ), headings ( ) North and East, Down velocities (V NED ), and North, East, and Down positions (P NED ) being the state variables. Such that the state vector of the a th UAV (S a ) is defined by: (1) For the 3-DOF flight simulator prototype, this work used two primary frames: velocity vector frame and local frame. The velocity vector frame was attached to the aircraft center of gravity, referenced to the standard body frame. The state of the UAV was updated by the 3DOF equations of motion as of below: where m is the UAV s mass, g the gravitational acceleration, and the UAV s heading angle relative to the positive north axis clockwise. Assumed was that the applied forces acted at the body s center of gravity. Also assumed were the body s rigidity and constant mass. The assumptions eliminated the need to consider the forces acting on individual elements of the mass. The input control commands to the UAV dynamics were defined by: Angle of Attack command (U AoA ), throttle command (U th ), and bank angle command (U Φ ). The control vector for A a à was thus defined by the set (2) (3)

3 . The point-mass equations of motion were derived relative to the North, East, and Down (NED) local coordinate system from [3, 9, 10]. represents the direction transformation cosine matrix that transforms a vector expressed in local frame into a vector expressed in the aircraft s velocity vector frame; The physical aircraft s dynamic and kinematic constraints for the aircraft A a à were defined by the maximum velocity ( ) and the minimum velocity ( ), both as limited by the maximum and the minimum throttles; by the maximum angular turn-rate ( ), as limited by the minimum horizontal turn left/right radius ( ); by the maximum angular pitch rate ( ), as limited by the minimum vertical climb/dive radius ( ); and by the maximum climb/dive pitch angle ( ). The following constraints should be adhered to by the trajectory generation for feasible options to appear to an unmanned aircraft and so the flight controller can successfully track the commands issued by these systems. They also form the trajectory envelope boundaries that define the maximum maneuvering performance of the aircraft. IV. UAV HIGH LEVEL INTELLIGENT CONTROL The intelligent control for the solar-powered UAV encapsulates mission management, strategic and tactical planning, guidance controller, internal mapping of the surrounding environment, and Collision Avoidance System (CAS). The knowledge-based internal mapping provides perception of the UAV flying region. It has for the planner, sufficient database that includes world features. A global map with cell values shows how certain the sensors are that threats exist. Threats are converted to a local map, providing the aircraft with routes towards gaps in the shared airspace. Mission management assigns required tasks to the UAV. Such tasks may include flying from an initial position to a final configuration, flying according to a specific formation, flying as part of search and rescue, etc. A task is converted to an objective waypoint that must be fulfilled. Path planning details task waypoints into motion paths. It produces a continuous motion that connects a start configuration with a goal configuration while avoiding No-Fly Zones (NFZs). The planning steps are begun by getting prior knowledge about surrounding environment, making an initial plan. Next is look-ahead-and-update the world model. New threats are (4) (5) (6) (7) (8) accounted for by re-planning. A trajectory planner designs a realizable trajectory for the UAV, basing the design on a detailed dynamic model of the aircraft and the set of waypoints given by the tactical planner. A guidance controller tracks the commanded trajectory and issues suitable desired states to be followed by the flight path controller. These tasks, however, are out of scope to this thesis. The path planning in the subsystem comprises two phases: 1. Strategic planning, which refers to the ability of the UAV to plan a path from initial configuration to goal. This phase is deterministic and computed off-line, considering prior knowledge of NFZs, pre-planned requests, and time constraints. 2. Tactical planning, whose function plans a path from present-state information in the aircraft s coordinate frame. It is usually implemented on-line and considers strategic planning commands, trajectory smoothing, detected threats, and gap visibility. The path planning, trajectory generation, and guidance controller were responsible for execution of the UAV mission tasks. The path planning problem is used to continually choose an appropriate shortest path from the current position of UAV, acquired from onboard navigation sensors, towards its final destination. Path planning and trajectory generation are usually represented as a three-dimensional optimization problem formulated with an objective function and a set of constraints in a Cartesian referential frame where is the position of the UAV in its center of gravity. Constraints to be adhered to in designing the path are: the aircraft s dynamics/ kinematics, environmental, and the reaching of target as specified to configured aims. The path-planning algorithm generated a series of waypoints that formed a flight path along which the UAV would be guided. The trajectory generation and the guidance controllers were used to generate commands for feasible speed, heading, and altitude for the aircraft to pursue its waypoints in an area with multiple sources of threats and NFZs. The commanded control was generated with considerations for the UAV s dynamical constraints. The guidance controller issued the desired turn command (Ψ d ), altitude (H d ), and velocity (V d ). These outputs were handled by the collision avoidance algorithm, which checked for potential collision along the commanded trajectory using current aircraft state vector as acquired from the onboard navigation sensors and registered encounters states as acquired from the surveillance sensors and/or air-to-air communication data-link. The CAS algorithms serve as a control command filter that searches for and generates modified collision-free optimal trajectory control commands. Accordingly, the CAS sends the modified commands to the flight controller. These commands are turn command (Ψ, climb/dive command ( ) and velocity command ( ). The flight-path-holding controller executes the modified commands by manipulating the control surfaces of the UAV.

4 The flight path controller starts with acquiring the state of the aircraft as received from the UAV s navigation sensors, and receiving the modified trajectory commands to follow. The data received by the sensors are position, airspeed, and attitude. The controller output controls the UAV actuators. In fixedwing solar UAV, the main actuators are ailerons, elevators, rudder, and thrust speed control. Ailerons actuators control the UAV s roll and thereby changes in heading, producing a rolling moment about the aircraft's longitudinal axis. Elevators control the UAV s pitch and thereby changes in movement of the aircraft about its lateral axis. Rudder controls the UAV s yaw and accordingly changes in movement of the aircraft about its vertical axis. Other secondary actuators that change flight lift/drag characteristics may include flaps, spoilers, and air breaks. In this work, the actuations signals are abstracted and defined by throttle, angle of attack, and bank-angle control input vector. V. MATHEMATICAL MODEL OF A UAV TRAJECTORY Three control commands are used by the high-level intelligent control algorithms, defined by turn (left/right), altitude (climb/dive) and velocity (speedup/slowdown) commands. Constant-turn trajectory is the path generated from an initial state S 0, by a constant-turn command, over a time segment t S. It comprises four segments: constant turn-rate and straight-ahead segments to direct the UAV towards the commanded heading angle, and reverse direction constant turnrate and straight-ahead segments to direct the UAV to fly in same direction parallel to direction of nominal flight-trajectory over a specified time. This is to make suitable deviation to left or right away from the intended nominal flight-trajectory. The amount of turn deviation is a function of commanded heading angle value and duration at which the heading angle is applied (i.e., pulse width). For instance, a heading command of 30 and pulse width duration of 100s, yields 1.25km deviation than its nominal flight-trajectory when the UAV speed is 25m/s. For computation and implementation, the Turn Command (TC) is digitized into set of N T equally spaced values in the interval, limited by. The set also includes the control command associated with straight-line trajectory. This implies that N T should be an odd number. Hence, Ψ Ψ Ψ (9) Similarly, a constant climb/dive trajectory is the path generated from an initial state S 0, by a constant altitude command over a time segment t S. If the value of the altitude command is negative, the aircraft dives, and if positive, the aircraft climbs. Again, Altitude Command (AC) set consists of N C equally spaced values in the interval, based on the values of. The set also includes the altitude command for a constantly zero-altitudechange flight. The resultant digitized set is thus: Where,, and (10) A speedup/slowdown trajectory is next defined as the path generated by a straight acceleration/deceleration command from an initial state over a time segment t S. The Velocity Command set (VC) is digitized into N S equal values between the interval. The set also includes the control command associated with non-accelerating trajectory. The velocity command set is defined by: Where, and (11) For each there is an associated unique trajectory. The set of turn/climb and constant turn trajectories for each UAV therefore comprise N T -1 turn deviation paths with Nc-1 level altitude paths and one straight path. This leads to TC and AC being partitioned into three sets each, respectively: TC L, TC R and TC 0, and AC U, AC D, and AC 0. TC L thus contains the left-negative turning command, TC R the right-positive turning command, and TC 0 the single straightahead or zero-heading-change command, whereas AC U contains the climb-up command, AC D the dive-down command, and AC 0 the single straight zero-altitude-change command. For each, there is accelerating, non-accelerating, or decelerating straight trajectory. Similarly, VC is partitioned into three sets including accelerating straight trajectory (VC U ), non-accelerating constant velocity (VC 0 ), and decelerating straight trajectory (VC D ). Aircraft position in a given time (t [0, t H ]) (where t H is the horizon time) is mapped by. A given aircraft state and turn, altitude, and velocity commands, thus create heading, altitude, or straight trajectory in local coordinated frame. Let designate the trajectory of the a th UAV (A a Ã) associated with the turn command, climb command, and velocity command, such that: where the velocity command is applied only to a straight trajectory. Other turn or/and climb trajectories are considered as having constant velocity. Thus, the complete set of all possible trajectories of the a th UAV is formulated by the following equation: A trajectory is thus a geometric object representing turn, climb, and/or velocity commands. Fig. 2 exemplifies with two-

5 dimensional trajectories generated through the application of constant turn-rate commands at constant velocity and altitude. A trajectory s risk assessment can be determined by comparing a UAV s trajectory with the trajectories of other UAVs in the vicinity. Fig. 2. Constant turn-rate trajectories at constant speed and altitude VI. CONCLUSION As technology enhancement and lack of energy resources, next-generation automated solar powered supply UAV with more effective systems and algorithms will continue to develop, supporting green society demand. This paper focuses on two key issues to green UAV modeling. The issues are: longitudinal and lateral UAV dynamics, and UAV trajectory generated in three dimensional space. The modeling is based on the point-mass 3DOF longitudinal and lateral dynamics that includes the aircraft s response along the roll and pitch axes. The assumptions made in the developed solar UAV model, applied forces on the body s center of gravity; body s rigidity; and constant mass, eliminate the need to consider the forces acting on individual elements of mass. REFERENCES [1] Do D, U.S. Army Unmanned Aircraft Systems Roadmap US Fort Rucker, Alabama: Office of the Secretary of Defense, [2] E. Cestino, G. Frulla, and G. Romeo, "Design of a High- Altitude Long-Endurance Solar-Powered Unmanned Air Vehicle for Multi-Payload and Operations," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 221, pp , [3] B. L. Stevens and F. L. Lewis, Aircraft control and simulation: Wiley-Interscience, [4] G. Wilkins, D. Fourie, and J. Meyer, "Critical design parameters for a low altitude long endurance solar powered UAV," in AFRICON, AFRICON '09., 2009, pp [5] M. R. Bhatt, "Solar Power Unmanned Aerial Vehicle: High Altitude Long Endurance Applications (HALE-SPUAV)," M.Sc., Mechanical and Aerospace Engineering, San Jose State University, [6] F. Fazelpour, M. Vafaeipour, O. Rahbari, and R. Shirmohammadi, "Considerable parameters of using PV cells for solar-powered aircrafts," Renewable and Sustainable Energy Reviews, vol. 22, pp , [7] S. Darr, W. Ricks, and K. A. Lemos, "Safer systems: A NextGen Aviation Safety Strategic goal," IEEE Aerospace and Electronic Systems Magazine, vol. 25, pp. 9-14, [8] D. H. Titterton and J. L. Weston, Strapdown inertial navigation technology: Peter Peregrinus Ltd, [9] P. H. Zipfel, Modeling and Simulation of Aerospace Vehicle Dynamics, 2nd Edition: American Institute of Aeronautics & Astronautics (AIAA), [10] D. Allerton, Principles of flight simulation: Wiley, 2009.