Guidance of Aircraft in Periodic Inspection Tasks

This is the author’s version of a work that was submitted/accepted for publication in the following source: Bruggemann, Troy S. & Ford, Jason J. (2011) Guidance of aircraft in periodic inspection tasks. In The Australian Control Conference (AUCC), 1011 November 2011, University of Melbourne, Melbourne, VIC. (In Press) This file was downloaded from: ❤tt♣✿✴✴❡♣r✐♥ts✳q✉t✳❡❞✉✳❛✉✴✹✻✺✹✶✴ c Copyright 2011 IEEE & IEAUS Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source: Guidance of Aircraft in Periodic Inspection Tasks Troy S. Bruggemann and Jason J. Ford Abstract— This paper presents a guidance approach for aircraft in periodic inspection tasks. The periodic inspection task involves flying to a series of desired fixed points of inspection with specified attitude requirements so that requirements for downward looking sensors, such as cameras, are achieved. We present a solution using a precision guidance law and a bank turn dynamics model. High fidelity simulation studies illustrate the effectiveness of this approach under both ideal (nil-wind) and non-ideal (wind) conditions. I. I NTRODUCTION The benefits of using manned or robotic airborne platforms for inspection of infrastructure assets such as powerlines has been argued since the mid-1990’s [1], [2], [3], [4], [5], [30]. Rotorcraft have traditionally been the platform of choice for sustained low-altitude flight above and near infrastructure for visual inspection or high resolution photography. However fixed-wing aircraft or UAV’s can often achieve longer sustained flight at lower cost per distance inspected. This is important for areas where thousands of kilometers of powerline need to be inspected and cost per asset inspected is a key factor. The requirement for low altitude fixed wing aircraft with downward-looking body-fixed cameras to capture the objects on the ground within their fixed and limited field-of-view is well acknowledged in the literature [6], [7], [8], [9], [10], [11], [12], [30]. In these applications, the aircraft itself must achieve a certain orientation, but only at the moment of inspection, so that a downward looking body-fixed camera attached to the aircraft is pointing towards the desired inspection point for images to be taken. Even if gimballed cameras are mounted, there still may be inspection attitude requirements that are not completely resolved by camera gimballing. Hence, control of both aircraft orientation and position relative to the infrastructure point under inspection must be considered. Certain features of the infrastructure (such as insulators near power poles) may need to be viewed at a certain angle using narrow field-of-view and high resolution cameras. We refer to this as the point inspection problem. With assets such as powerlines, often certain features of the assets spaced at regular intervals need to be inspected. We refer to this task as the periodic inspection problem and involves flight to and between a finite set of T.S. Bruggemann is with the Cooperative Research Centre for Spatial Information and Australian Research Centre for Aerospace Automation at Queensland University of Technology, 22-24 Boronia Rd, Eagle Farm, Brisbane, QLD, 4009 Australia [email protected] J.J. Ford is with the Cooperative Research Centre for Spatial Information and Australian Research Centre for Aerospace Automation at Queensland University of Technology, Brisbane, QLD, 4001 Australia [email protected] regular-spaced specific points of interest on the infrastructure to be inspected. Over the past decade, there has been a considerable amount of work on Unmanned Aerial Vehicle (UAV) automation that is relevant to our aircraft automation application. A control solution for the UAV loitering problem is given in [13], a geometrical guidance law solution that accounts for camera angles to observe a ground target from a UAV is presented in [14], use of a UAV to provide 3D coverage of urban environments is given in [15], and a control solution using cameras for quasi-stationary flight above features of interest in bridge inspection is given in [16]. There has been numerous other investigation of automated tracking of targets with body-fixed or gimbaled cameras from UAVs or aircraft, see [17], [18], [19], [20], [21], [22], [23], [24], [25], [30]. These mentioned approaches typically involve the aircraft orbiting around the target in an ellipse, circle, or spiral manner whilst keeping the target in the camera field of view with possibly a desired look-angle [25]. To achieve the desired flight paths, typical approaches include waypoint placement design (e.g. [18]) or the use of commanded change of heading to track or result in a desired flight path about the ground feature to be kept within the sensor field of view (e.g. [21],[25]). In contrast to this previous work, in this paper we propose a guidance approach for controlling the lateral motion of an aircraft so that it achieves a desired orientation (or “look angle”) to a point to be inspected by body-fixed downward looking cameras at regular intervals. Our approach is based upon a simple bank turn dynamics model with an optimal precision guidance law. We aim for a solution to the periodic inspection problem which does not require special modifications to a standard autopilot, nor relies upon visual servoing. Our solution can be interfaced with existing commercially available autopilots that can accept roll or heading commands. Results from high fidelity simulations to study the effectiveness of the approach under both ideal and non-ideal (wind) conditions, are presented. This paper is structured as follows: Section II introduces our assumed dynamic model and the periodic inspection problem. Section III present our proposed inspection approach. Section IV provide a simulation study of our proposed periodic inspection solution. II. T HE P ERIODIC I NSPECTION P ROBLEM The goal of periodic inspection is to achieve controlled aircraft flight to and above the infrastructure features under inspection so that they can be seen by body-fixed downward pointing sensors mounted to the aircraft. In this section, we describe the dynamics involved, a control-loop architecture design, and then provide a formal definition of both the point inspection and periodic inspection problems. A. Aircraft Dynamics As shown in [30], if we assume the inspection aircraft is flying at constant speed, the aircraft’s translational dynamics can be represented by ẋ = V cos χ cos γ ẏ = V sin χ cos γ ż = V sin γ, (1) where x, y, z is aircraft position in a navigation frame, V is the magnitude speed of the aircraft, and χ and γ are the course and flight path angles, respectively. The evolution of χ, γ during a time period [tk , tk+1 ) can be described by the aircraft’s maneuver dynamics 1 [(L + T sin α) sin σ mV cos γ + (D − T cos α) cos σ sin β + Y cos σ cos β] 1 [(L + T sin α) cos σ(T cos α − D) sin σ sin β γ̇ = mV 1 −Y sin σ cos β] − g cos γ, (2) V where σ is bank angle (rotation about the velocity vector), α is angle of attack, β is angle of sideslip, L is the lift force, T is the thrust force, D is the drag force, Y is the side force and g is gravitational acceleration. Here, with pitch angle θ, the bank angle σ is related to roll angle φ through the expression cos σ cos γ = cos α cos θ cos φ + sin α sin θ [26, p. 55]. χ̇ = B. Inspection Problem Definitions We first describe the point inspection problem, before describing the periodic inspection problem. 1) The Point Inspection Problem: Let us consider a set of inspection points indexed by i = 1, . . . n. The ith point inspection problem is the problem of inspecting a point P i = [xiP , yPi , zPi ], from a specific look direction. Let the aircraft attitude in the navigation frame be denoted Θ = [σ, γ, χ]. For an aircraft at initial location Ai0 = [xi0 , y0i , z0i ] and attitude Θi0 = [σ0i , γ0i , χi0 ] the problem is to guide the aircraft to i i intercept an inspection waypoint W P i = [xiW P , yW P , zW P ] i i i i with altitude zW = h +z where h is commanded height P P d d above the inspection point, and aircraft attitude Θ with the   value Θid = φid , θdi , ψdi where φid , θdi , ψdi are desired Euler roll, pitch and yaw inspection angles (designed to ensure that appropriate inspection occurs). These aircraft position and attitude characteristics are desired at the inspection point, so that a body-fixed downward looking camera achieves inspection of fixed P i with pointing error angle η = 0, and line of sight range error ∆R = RLOS − Rcam = 0. This situation is shown in Fig. 1 where RLOS is the line of sight range from aircraft location Ai (at waypoint intercept W P i ) to P i , and Rcam is the range in the direction of the downward-looking body-fixed Fig. 1. Inspection geometry at inspection waypoint W P . camera boresight axis from aircraft location Ai (at waypoint intercept W P i ) to some point where it intersects the x − y plane created by z = zPi . Alternatively, we can say that the point inspection guidance task S(P i , Θid ) is to inspect fixed point P i from an aircraft with a specified desired attitude Θid (where P i and Θid together fix the inspection waypoint W P i ). 2) The Periodic Inspection Problem: The guidance for periodic inspection problem is now described. A periodic inspection task SP is to achieve stable and controlled flight to inspect a set of n fixed inspection points, {P i }, in succession; each point with an associated aircraft attitude objective, {Θid }. That is, a periodic inspection task is defined as a control flight through the sequence of point inspection tasks described as SP = {S(P 1 , Θ1d ), S(P 2 , Θ2d ), S(P 3 , Θ3d ), . . . , S(P n , Θnd )}. III. P ROPOSED P ERIODIC I NSPECTION S OLUTION We will first propose a solution to the point inspection problem, and then will propose a solution to the periodic inspection problem. A. Aircraft Control Loop Design Fig. 2 shows our aircraft control loop design. The planning function determines placement of waypoints for the aircraft to commence, achieve and stop the control for inspection. The autopilot function must maintain aircraft body attitude so that infrastructure inspection can occur (this function is shown as the “dynamics with autopilot” block in the figure). We assume that the planning (waypoint design), and the autopilot block allows stable flight to meet the guidance objectives and this paper will not investigate either of these two functions. The guidance blocks (guidance and guidance logic, in the figure) of the control loop must determine acceleration commands that minimize both the position and velocity vector mismatch between the aircraft and the inspection Fig. 2. The waypoint planning, guidance (and guidance logic), and autopilot functions: this paper focuses on design of the guidance and guidance logic. point. In this paper we propose a new approach for these two blocks in following sections. B. Altitude Control We will assume that through-out the inspection task that i i i constant commanded altitude is achieved at zW P = h d + zP by the autopilot or by a human operator. This implies that the aircraft dynamics are described by (1) with γ = 0. C. Aircraft maneuvering restricted to bank-to-turn The usual manner that a fixed-wing aircraft achieves a change of heading, or achieves commanded lateral acceleration, is by banking (rolling) the airframe [27]. To achieve a commanded body-fixed frame lateral acceleration ac , the commanded roll angle φc is controlled to [6], [26], [30],   ac −1 . (3) φc = tan g We will assume that ua , ue , and ur are chosen so that β = 0, Y = 0 and also to ensure level flight in the sense that (L + T sin α) cos σ = g cos γ. Substitution in (2) shows that a BTT maneuver can be described by the dynamics [30] g tan σ χ̇ = V φ̇ = Proll (φc − φ) γ̇ = 0, (4) where Proll provides a first order approximation of the autopilot’s lower-level roll loop. D. Lateral Control for Point Inspection A lateral guidance solution that meets the Θid attitude objective is now presented. Our proposed guidance solution involves two stages, first the use of a precision guidance law to achieve control of heading to a preliminary waypoint W PPi G and secondly the activation of an open loop BTT at fixed bank angle to meet Θid attitude objectives at the desired inspection point. This situation is shown in Fig. 3 where the aircraft flies from some starting point Ai to capture W PPi G with intercept heading angle λiW P after which an open loop BTT is commanded over an arc distance dir (θri in radians) to achieve Θid at W P i . As shown on the figure the open loop BTT is assumed to travel the arc of a circle with turning radius rdi i and describing the angle θW P between the y-axis and the radial vector at commencement of the BTT. Our degrees of freedom are θdi , φid , ψdi and open loop BTT arc distance dir . Constant altitude of flight and a small angle of attack α assumption constrains the pitch angle of inspection to be small i.e. θdi ≈ 0. Hence, the remaining two degrees of freedom in our desired inspection attitude Θid can be described through the desired roll and yaw angles ψdi and φid , and dir is a design choice based upon prior knowledge of aircraft bank rate under autopilot control. We propose to use an open loop BTT to achieve inspection of point P i = [xiP , yPi , zPi ] with desired roll and heading angles φid and ψdi . From (4) and geometry the aircraft must i i intercept an inspection waypoint W P i = [xiW P , yW P , zW P ] given by xiW P i yW P i zW P = xiP + hid sin ψdi tan φid = yPi − hid cos ψdi tan φid = zPi . (5) φid The desired roll angle can be achieved by commanding an open loop BTT such that φc = φid for a chosen time period ∆tiBT T . This leaves the design choice ψdi as the remaining degree of freedom to be controlled. Since both roll and heading angles are coupled and the aircraft cannot achieve φid instantaneously (but is described by (4)), the aircraft must fly for some period of flight at roll angle φid . This period of flight at this roll angle is a design variable which we call the lead-in arc distance of inspection (shown in Figure 3) that is denoted dir or θri = dir /rdi in radians. To allow us to appropriately design the lead-in arc distance of inspection we first note that the turn radius of the aircraft in open loop BTT [26] i and the angle θW P are given by V2 g tan φid π i − ψdi + θri sign(φid ). (6) θW = P 2 To ensure turning fixed wing aircraft flight through the desired inspection point W P i with the desired body attitude, we need to determine an intermediate waypoint W PPi G = [xiP G , yPi G , zPi G ] (at some point prior to the inspection W P i as shown in Figure 3) that places the aircraft on the BTT flight path to the inspection waypoint W P i . The location of W PP G can be calculated from geometry consideration as rdi = xiP G i i = xiP + rdi (sin θW P − cos ψd ) yPi G i i = yPi + rdi (cos θW P − sin ψd ) zPi G = zPi . (7) Fig. 3. Geometric representation of proposed guidance solution. Superscript ”i” has been dropped from the symbols to avoid cluttering the diagram. A required intercept heading angle λiW P at W PPi G , defined clock-wise positive from the x-axis direction is π (8) λW P = − θri + ψdi sign(φid ). 2 Now that we have a solution to achieve φid and ψdi , the final problem is to find a way to intercept W PPi G with intercept angle λiW P . We propose to use an optimal precision guidance law which minimises the range to a waypoint and achieves desired heading at waypoint intercept [28]: ac,P G = V (4λ̇ + 2(λ − λiW P )/tgo ), (9) where ac,P G is the commanded acceleration, λ = tan−1 (ỹ/x̃) is the line-of-sight angle with x̃ = xiP G −x, ỹ = p i 2 yP G − y and tgo = (x̃) + (ỹ)2 /V is the time-to-go to W PPi G . Finally, guidance switching logic is required to determine when to switch from the precision guidance law to the open loop BTT. The switching can be achieved when a time to go threshold tr to W PPi G is crossed, and our complete guidance solution becomes  (  a G when tgo ≥ tr tan−1 c,P g (10) φc = φid for ∆tiBT T when tgo < tr E. Guidance for Periodic Inspection Stable and controlled flight through the sequence of point inspection tasks described by SP = {S(P 1 , Θ1d ), S(P 2 , Θ2d ), S(P 3 , Θ3d ), . . . , S(P n , Θnd )} is required to achieve the periodic inspection objective. The path of an aircraft is constrained due to the aircraft being an underactuated dynamical system with nonholonomic constraints. This suggests that a solution to the periodic inspection problem utilizing the guidance strategy for point inspection developed in the previous section, is in the form of a solution to a point inspection waypoint route planning problem. One solution is to order each point inspection task > dmin , where such that S(P i , Θid ) − S(P i+1 , Θi+1 d ) 1 ≤ i < n and dmin is a minimum distance between successive inspection points. The value of dmin will need to be determined by consideration of the initial starting location Ai to each point inspection task, the dynamic capabilities of the aircraft (such as maximum turn-rate) and the distance between successive inspection points. Assuming that the point inspection waypoint route planning problem is solved, the problem is reduced to flying from one point inspection task to the next until all point inspection tasks are completed. For this purpose a third switching logic stage in the form of a PN law with ac,P N = 3V λ̇ is introduced into the guidance logic (10) to provide direct flight from one point inspection task to the next. Then the guidance logic for periodic inspection involves flight in PN mode until a time to go threshold trP G to W PPi G is reached, at which point flight in PG mode and then BTT mode commences in same manner as for the point inspection task (10). This logic sequence is repeated for each ith inspection point in succession. The guidance logic repeated to each point inspection task is    −1 ac,P N  when tgo ≥ trP G tan    g  a G (11) φc = when trP G > tgo ≥ tr tan−1 c,P g    i i r φd for ∆tBT T when tgo < t with tr < trP G . IV. S IMULATION S TUDIES To study the performance of the proposed guidance approach, the complete control architecture shown in Fig. 1 was implemented with full six degree-of-freedom nonlinear semicoupled equations of motion with rigid-body, fixed mass and uniform gravity assumptions for a Navion aircraft [29]. We highlight that the aircraft dynamics used in simulations had higher fidelity than those used in developing the guidance solution thus the simulation results include effects due to cross coupling between lateral and longitudinal dynamics including variations in airspeed and altitude. The autopilot loops, which included standard PID control, were tuned for aircraft stability and unchanged for all simulations. The autopilot was restricted to rate-1 (3 deg/sec) turns, to reflect roll limitations that are similar to an realistic aircraft autopilot. Airspeed of 30 m/s and inspection height hd of 133 m was commanded. The inspection point P was set to be 5 km north of initial aircraft location (x0 , y0 , z0 ) = (0, 0, 0). In this study we assume a constant lead-in arc, that is dir = dr (for all i). The design choice of dr was found to be important for good performance and must be established through experimentation. In our simulations, a dr value of 50 m was found to give good performance in terms of roll, heading and range errors at the point. If dr was larger, performance noticeably degraded since the aircraft flew in open loop BTT for a longer time period and this Fig. 4. Achieved roll errors for desired roll angles. Fig. 5. Achieved heading errors for desired roll angles. was sensitive to airspeed errors at the waypoint. If dr was smaller however, the aircraft (depending upon aircraft bank rate under autopilot control) intercepted W P i during the roll before the desired φid was achieved, causing increased roll error at the inspection point. A. Point Inspection Studies 1) Variation of Desired Roll Angles: This study examined the performance of the proposed control solution by a simulated flight from an initial location to a fixed inspection point directly 5 km north of the initial location, in nil-wind conditions. By keeping ψdi fixed at −10◦ the simulated flight was repeated a number of times for different φid = φd values ranging from 0 to 25◦ . The results for all tests are summarised in Figs. 4 to 7 which plot the roll error, heading error, angular pointing error, and range error, respectively, against the respective φd . The roll and heading errors are the difference between desired and achieved values at W P i interception. Minimum angular pointing error η and minimum range error is as defined in Fig. 1. In Fig. 4 the roll error is near 0◦ until after φd = 10◦ where it increases due to unfulfilled roll command due to the maximum roll constraint from the autopilot rate-1 turn limitation. Similar behaviour occurs as shown in Fig. 5, 6, and 7 where it is seen that the heading angles varies to about only 2◦ , minimum point error angle η less than 5◦ and minimum range error less than 1 m for φd between 0◦ and 10◦ . A tradeoff exists between the sensor field of view requirements and the autopilot’s ability to achieve desired attitude at the inspection point. For example, assuming a minimum sensor field-of-view requirement of 2η, Fig. 6 suggests that for desired roll 0 ≤ φd ≤ 20 at least a 22◦ field-of-view sensor is required for the inspection point P i to be captured. 2) Variation of Desired Heading Angles: The heading error at the inspection point is directly related to the heading error at the W PPi G which depends upon the heading error Fig. 6. Minimum angular pointing errors achieved for desired roll angles Fig. 7. Minimum range error achieved for desired roll angles Fig. 8. PG law heading errors in nil wind and wind-present conditions. performance of the PG law. The aim of this test was to study the heading error performance of the PG Law in both constant wind and nil wind conditions. The test setup is the same as for the previous variation of desired heading angle study but with φid = φd fixed at 10◦ and φid = ψd varied. For the constant wind case, a constant East wind of 15 knots was set throughout the simulation. The error in achieving λiW P for the different values of ψd are presented in Fig. 8. In nil wind conditions less than 1◦ heading error at W PPi G can be seen, however the error is increased with wind, particularly for larger ψd , due to the size of drift angle which depends upon the wind direction. Wind induces a heading error at W PPi G due to unaccounted drift angle in the PG law, which translates into a heading error at W P i . If necessary, an estimate of drift angle due to wind may be included in λiW P to mitigate unaccounted drift angle. There will also be an accumulating heading error due to wind when the aircraft is in open loop BTT mode, and this can be reduced by choosing small dr . In these simulations, we examined the sensitivity and impact of wind on the BTT maneuver but found no improvement in performance when using a closed loop BTT technique, over an open loop BTT with short dr , in wind-present and wind-free conditions. This suggests that there is no great benefit to be gained in adopting a more complex closed-loop BTT approach for our aircraft type under test. B. Periodic Inspection Illustration Here the performance of the approach in periodic inspection is illustrated by simulated flight to a set of 5 inspection points in succession in the presence of a constant East wind of 7.7 m/s, with a commanded aircraft velocity of 40 m/s and altitude of 133 m. Each point was spaced 10 km apart with desired heading angle ψdi = ψd = −20◦ and bank angle φid = φd = 10◦ for each point. The flight path to each inspection point 1 to 5 is shown by Fig. 9. As seen the aircraft successfully reached each inspection point objective. Flight from one point to the next Fig. 9. Simulated flight path in periodic inspection to inspection Points 1 to 5, showing successful and stable flight to each inspection point. In the legend, Track is the ground track of the aircraft. Fig. 10. Showing capture of waypoint W PP G in PG mode, followed by flight in open loop BTT mode to inspection waypoint W P and achieving good alignment of the camera axis to the point inspection objective. PN Mode is then re-activated for flight to the next inspection point. In the legend, Track is the ground track of the aircraft, C Cam is the camera boresight axis, projected on the ground, L Cam is leftmost edge of the camera footprint on the ground, R Cam is rightmost edge of the camera footprint on the ground. consists of direct flight in PN mode to a certain distance away (time to go) from a W PPi G waypoint, switching to the PG mode to capture the W PPi G waypoint with required heading angle λ̄, conducting a BTT in open loop mode to achieve the look angle objectives at W P i , followed by a re-activation of the PN mode and re-activation of the command sequences in preparation for flight to the next point. These sequences are shown in greater detail by Fig. 10, where it is seen that the sequence of commands to intercept each waypoint and the point inspection objectives are achieved. In presence of wind and non-constant airspeed and altitude the approach was successful in achieving the ψd and φd TABLE I L INE OF SIGHT RANGE ERROR ∆R AND ANGULAR POINTING ERROR η TO EACH POINT IN PERIODIC INSPECTION . Point 1 2 3 4 5 ∆R (m) 0.7 0.8 0.9 1.2 0.9 η (◦ ) 0.7 1.1 1.1 1.0 1.1 objectives with small range ∆R and angular pointing errors η as given in Table I. V. CONCLUSIONS AND FUTURE WORKS We presented a guidance approach for controlling an aircraft to fly to a series of desired fixed points of inspection with specified attitude requirements so that requirements for downward looking sensors such as cameras, are achieved. We presented a guidance solution using a precision guidance law and a bank turn dynamics model. 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