Three-Dimensional Segmented Trajectory Optimization for Runway-Independent Aircraft Min Xue∗ and Ella M. Atkins† University of Maryland, College Park, MD 20742 Vertical or short takeoff and landing aircraft can increase passenger throughput at crowded urban airports via the use of vertiports or stub runways. The concept of simultaneous non-interfering operations has been proposed to reduce terminal area traffic delays by creating approach and departure corridors that do not intersect existing fixedwing routes. This paper introduces an optimization technique for segmented 3-dimensional simultaneous non-interfering trajectory design based on an incremental search strategy which combines k-ary tree and Dijkstra’s algorithm. Existing fixed-wing traffic corridors are modelled as impenetrable obstacles. The objective function is based on the existing Quasi-Static Acoustic Mapping noise database for Blade-Vortex Interaction noise prediction and also population density distribution. Flight envelope limits are represented as search-space constraints. Final approach trajectories for Baltimore-Washington International airport are presented, illustrate the effects of population density, entry region, varied number of trajectory segments. This optimization tool will provide airport and airspace designers with a host of alterative trajectory options for analysis of potential landing sites, associated traffic procedures, and entry options.

Nomenclature V˙ V g x y z αT P P γ β µ t

Acceleration, f t/s2 Flight velocity, knots Gravitational constant, f t/s2 coordinate with direction from west to east, f t coordinate with direction from south to north, f t coordinate upward, f t Main rotor tip-path-plane angle, degree flight path longitudinal angle (in x − z plane), degree flight path lateral angle (in x − y plane), degree advance ratio time, s

I.

Introduction

The National Airspace System must accommodate the increasing demand for commercial air transportation. In urban environments, runway real estate is limited and airspace bottlenecks form when traffic merges to final approach and departure corridors. Runway-independent aircraft (RIA) can increase passenger throughput by offloading short to medium-haul (<400nm) traffic from overcrowded runways, utilizing stub runways or vertiports as alternative landing sites. The RIA class includes vertical takeoff and landing (VTOL) and extremely short takeoff and landing (eSTOL) vehicles. High-capacity rotorcraft, tilt-rotor, and powered-lift fixed-wing RIA designs are being considered. Introduction of RIA traffic patterns in crowded ∗ Graduate † Assistant

Research Assistant, Aerospace Engineering Department, AIAA student member. email: [email protected] Professor, Aerospace Engineering Department, AIAA senior member. email: [email protected]

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terminal airspace has the potential to increase air traffic controller workload, creating new conflict-related delays rather than alleviating congestion. Simultaneous Non-Interfering (SNI) approach and departure procedures for RIA will minimize air traffic control overhead and maximize overall throughput.1 SNI paths do not intersect existing traffic corridors, so RIA SNI arrivals and departures can be sequenced independent of fixed-wing traffic. By definition, SNI trajectories occupy previously unused airspace thus may overfly noise-sensitive communities previously undisturbed by fixed-wing traffic. As new SNI routes are proposed, public acceptance mandates the development of noise abatement procedures (NAP). RIA approach and departure routes must also be acceptable to pilots and air traffic controllers, comfortable for passengers, and economical for the airlines. The goal of this research is to provide a segmented route optimization tool that enables identification of acceptable 3-dimensional NAPs as airport and airspace designers identify RIA landing sites and assess their impact on traffic and the surrounding communities. SNI routes are facilitated by approach and departure areas with few intersecting fixedwing traffic corridors. Automatically-generated NAPs can be compared with the traditional single-segment trajectories typically preferred by pilots.2 Our tool rapidly enables airport planners, controllers, and pilots to define trajectories with respect to cost (noise only for this work), providing solutions to be subsequently ranked in terms of pilot and ATC workload, impact on fixed-wing traffic, and safety. To design segmented routes, the three-dimensional airspace is decomposed as a k-ary tree, and Dijkstra’s search algorithm is employed to find an optimal solution over the discrete search space. Global minimum-noise trajectories are presented for an AH-1 rotorcraft as the RIA, an example where noise is a complex function of velocity and flight path angle as well as throttle setting, particularly during approach operations where BVI (blade-vortex interaction) noise is dominant. This paper begins with a description of k-ary tree-based incremental search method, which is used as a global optimization method to automatically generate a set of candidate low-cost SNI NAPs for final approach to landing. Next, an introduction to the AH-1 rotorcraft quasi-static noise model11 and the populationweighted cost function utilized for this work are presented. 2000 census population data are used. To find the strictly SNI routes typical East-flow traffic operations at Baltimore-Washington International airport are surrounded by safe separation zones and modelled as impenetrable obstacles. Results are presented to illustrative how population density, aircraft flight envelope limitations, and entry regions influence final trajectory shape and corresponding velocity/acceleration profiles. The paper concludes with a discussion of future work to complete the noise cost function and deploy the SNI trajectory optimizer as a systems analysis tool that complements ongoing RIA vehicle design and airport planning efforts.

II.

Trajectory Optimization Algorithm

Individual aircraft trajectories may be mathematically optimized and precisely followed by existing autopilots with advanced navigation and control technologies. However, segmented routes3 enable intuitive comprehension by pilots and ATC, facilitate communication of trajectory, and typically reduce computational complexity relative to complex numerical global optimization processes. For this work, SNI final approach trajectory optimization is defined as a two-point boundary value problem in three dimensions, and ”optimized” noise abatement procedures are described by a sequence of one or more segments, each with constant velocity or acceleration. As described by Latombe,4 several techniques, including roadmap, potential field, and cell decomposition, exist for motion planning in obstacle fields. Probabilistic roadmap5 and the Rapidly-exploring Random Tree (RRT)6 are currently popular in motion/path planning field. Most of these methods were developed for ground robots with few motion constraints or for identifying nonoptimal solutions quickly, while, in our case, the complex cost (BVI noise database + population distribution) must be optimized in the presence of dynamic constraints and impenetrable airspace obstacles. Given these requirements, an incremental search method, which couples k-ary tree decomposition and Dijkstras’ algorithm, is adopted for this work. A.

Decomposition Strategy

In previous work,7 we utilized a cell decomposition strategy that could model arbitrary obstacles, guarantee globally-optimal results limited only by discrete cell size, and allow arbitrarily complex cost functions f . In 3-D, however, it is difficult manage computational complexity when sufficient resolution is present in the discretized cell map. To better manage complexity, we now represent the search-space as a k-ary tree, defined

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as a search tree with no more than k children for each node. As a preliminary to k-ary tree construction, we impose the following dynamic constraints for stable flight operation with an AH-1 helicopter, our reference flight vehicle in this work. First, we impose a constraint on flight path angle γ (−9◦ ≤ γ ≤ 9◦ ) . Next, for passenger comfort considerations and flight well within the performance envelope, acceleration V˙ constraints are also imposed (−0.05g ≤ V˙ ≤ 0.05g ). For turning flight,a the rotorcraft is restricted to fly with lateral angle β(−80◦ ≤ β ≤ 80◦ ) . Given these restrictions, we use four variables γ, V˙ , β and ∆d during threedimensional optimization processes as control variables, where ∆d is the distance step in the lateral (xy) plane and along the direction of radius of the circle, whose origin is located at the touchdown site.(Note that the set of control variables is reduced to 3 variables γ, V˙ and ∆x in 2-D cases). The control variables are discretized and the combinations over these variables form an upper bound of the branching factor for the k-ary tree.

(a) side view

(b) top view

Figure 1. k-ary Tree Decomposition and Merging (spatial view)

The incremental search method, in which the search graph is expanded until the final solution is found, is adopted in our work. This means the next available node for exploring in k-ary tree would be selected by the search algorithm in order of increasing cost, as will be discussed. When exploring a k-ary tree node, k candidate ”child” nodes are generated. To minimize search-space size, new nodes are merged with existing nodes if they are in a small ”error box”, which denotes the same velocity and in the adjacent region. Here ”adjacent region” is defined as the region where the geometric (x,y,z) coordinates match to within a specified tolerance. This decomposition and merging strategy is shown in Figure 1, which shows only the spatial view without control variable V . For two-dimensional optimization (e.g., approach in the longitudinal plane), our previous cell decomposition7 and new k-ary tree strategies are comparable in representational ability and efficiency. For 3-D trajectories, the k-ary representation enables more accurate representation, and node merging efficiency improves significantly. The pseudocode for the k-ary tree decomposition strategy is shown below in procedure T reeBuild, where M ,N and R are the resolutions of γ, β, and V , respectively. In this paper, these intervals are approximately set as ∆γ = 1◦ , ∆β = 4◦ and ∆V = 3 knots. During expansion of a node enode, the procedure will find all potential child nodes and put them into the node stack if not merged. Additionally, they are marked as the neighbors of enode and node level would also be increased and stored. B.

Search Algorithm

Given landing site boundary condition (xf , yf , (zf ), Vf )b , approach boundary constraints (xinit , yinit , (zinit ), Vinit ), and our segmented solution requirement, a Dijkstra search algorithm, with average computational requirements significantly lower than those of dynamic programming8 ,9 was employed to minimize the numa In current work, we assume instantaneous transition with no extra cost, and constraints on lateral angle are imposed artificially. b z and z init are not included in 2 dimensional cases. f

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Procedure TreeBuild(enode, nodes, obstacles) global γ[M ], β[N ], V [R], ∆d; Node nnode; begin for each combination of γ[i], β[j], V [k], ∆d do (x, y, z, V [k]) ← CalculateState(γ[i], β[j], V [k], ∆d, enode); nnode ← new Node (x, y, z, V [k]); nnode.level ← enode.level + 1; if not M erge(nnode, nodes) and not Intercept(nnode, obstacles) do push nnode into stack enode.neighbor; nnode.cost ← ∞; nnode.status ←0 open0 ; push nnode into stack nodes; end end end

Figure 2. T reeBuild Algorithm

ber of expanded search states. Dijkstra’s algorithm explores nodes in order of increasing value of the cost function g(n), the accumulated cost from the initial search node to current node n. The Dijkstra search procedure for our work is shown in SeachAlgorithm. In this algorithm, the inputs are the nodes stack built so far, number of flight segments, landing state, and initial approach state. Here ’c’ is the cost from explored node ’u’ to a neighboring successor node. Since we are searching backward, the landing state/node is put into the stack nodes at the very first and will be initialized. Then, the main while loop will find the node with minimum cost, explore its child nodes and adjust those child nodes’ cost if necessary. The loop will terminate when the minimum-cost node is within the desired approach state region. This Dijkstra algorithm with k-ary search-space decomposition is a global optimization technique. However, the solution is ”optimal” only with respect to the level of discretization when dividing the continuous space into a segmented path. Theoretically, this error can approach zero with infinite resolution on the search variables γ, V˙ and β; however, computational complexity and path complexity also increase with resolution. We have wrapped an iterative deepening strategy10 around the search algorithm to identify optimal trajectories with 2 to n segments, enabling insight into the effect of discretization on solution properties. Initial low-resolution solutions are simple (few segments) but may be costly. Higher-resolution solutions approach the globally-optimal cost but will contain numerous flight segments that would only be feasible as standard flight procedures given a capable autopilot that could follow arbitrary continuous flight trajectories. Our iterative deepening procedure is shown in Figure 4. In our work, we halt at a resolution where the difference between current and last cost is within a user-defined threshold ε . In practice, this solution acts as an anytime algorithm, allowing the pilot/airspace planner to break the loop manually to obtain intermediate solutions with lower resolution.

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Procedure Search(nodes, segnum, land, appr) integer segnum; Node land, appr, u; begin push land into stack nodes; u ← land; land.level ← 0; land.cost ← 0; appr.cost ← ∞; while (u 6= appr) do u ← F indM in(nodes); if (u = N U LL) break ; else u.status ←0 closed0 ; if (u.level < segnum − 1) then T reeBuild(u, nodes); else push appr into stack u.neighbor; for each adjacent node ni of u do if (ni .status 6=0 closed0 ) then c ← F indCost(ni , u); if (u.cost + c < ni .cost) then ni .cost ← u.cost + c; ni .previousnode ← u; end end

Figure 3. Search Algorithm

Procedure IterativeDeepening(land, appr) integer i, j, k; float cost, segnum, newcost; Node land, appr; Node stack solution, nodes; begin cost ← 0; segnum ← 1; solution ← N U LL; do Search(nodes, segnum, land, appr); solution ← P ath(appr); newcost ← solution.cost; D ← |newcost − cost|; cost ← newcost; segnum ← segnum + 1; while D ≥ ² return solution; end

Figure 4. IterativeDeepening Algorithm

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III.

Cost Function

Traditional trajectory synthesis tools permit optimization over fuel and/or time. Pilot or airline preferences and air traffic control constraints contribute to the relative importance (weight) of these two optimization factors. NAP design requires an additional noise cost function term, the relative importance of which can be varied with time/fuel by varying relative weighting factors. For our SNI airspace design work, the cost function Jn for trajectory optimization over an n-segment trajectory is given by Jn =

n X

[c1 × Ni,i−1 × ti,i−1 + c2 × ti,i−1 + c3 × m(f uel)i,i−1 ]

(1)

i=1

In this expression, ti,i−1 is the duration for the single trajectory segment between boundary nodes i and i − 1, m(f uel)i,i−1 is the total fuel consumed in this time period. BVI noise is given by Ni,i−1 for each segment. c1,2,3 are adjustable weights for noise, time and fuel respectively. Detailed tradeoff studies for 2D cases have been done in previous work.7 In this work for 3D cases, we focus on noise abatement, thus c2 and c3 are set to zero, while c1 =1.

Figure 5. Population Distribution Map (BWI) and Reference Frame

Figure 6. Q-SAM BVI noise model database

Since segmented trajectories for this work must be designed to minimize noise, especially over populous

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areas, we employ a cost function in which noise propagated to the ground is weighted by population density area. BWI area population data was downloaded from the year 2000 census.13 Figure 5 shows the population distribution around BWI. The blocks with darker red denote high population density area, while lighter red represents low density. For this work, only the blocks within 7 miles of BWI airport are taken into account, as illustrated in Figure 5. To integrate population and noise data into a single measure of cost, the center points of population data blocks are defined as ”microphone locations” for a ground noise measurement matrix over which noise is summed. Cost function penalty weight for each ”microphone” is proportional to the population density at that site. Figure 5 also shows the position and orientation of the inertial reference coordinate system, in which the z coordinates coincide with the altitude. BVI noise for the AH-1 rotorcraft is computed with the experimentally-verified Quasi-Static Acoustic Mapping (Q-SAM) method built by Gopalan et. al11 and conceptually depicted in Figure 6. Here Robs is the distance between the observer and the vehicle, elevation angle is counter-clockwise and starts from horizon and azimuth angle is clockwise with zero angle pointing back from the rotorcraft. Spherical distributions of radiated noise are developed as a function of tip-path plane angle αT P P and advance ratio µ. Interpolation will be applied when the observer is not located at the exact grid point of the sphere defined in the noise database. In the quasi-static model, rotorcraft trim state transitions (e.g. longitudinal path angle, lateral path angle) are presumed instantaneous, and we do not include effects from atmospheric absorption, wind, temperature, or ground reflection. For a single trajectory segment with two extreme nodes i and i − 1, noise level for each microphone is computed as: Pi,i−1 = q(αT P Pi,i−1 , µi,i−1 , Robs , elevationi,i−1 , azimuthi,i−1 )

(2)

where function q represents the Q-SAM noise value and ni,i−1 refers to the A-weighted average Sound Exposure Level(SEL). Furthermore total noise over all K ’microphones’ for a single segment can be computed as: K X Pi,i−1 (3) Ni,i−1 = 10 10 × Wk k=1

where each Wk is the population-based weighting factor for ’microphone’ k. Total cost over all n trajectory segments is: n X Jn = Ni,i−1 × ti,i−1 (4) i=1

where ti,i−1 is the duration for this single trajectory segment between boundary nodes i and i − 1. The optimization goal given our iterative deepening strategy is then to progressively find solutions for n = 1, 2, . . . , nmax defined as trim flight segment sequences that minimize cost Jn .

IV.

Obstacles Model

To explore the RIA SNI noise-optimal trajectories, flight track data was acquired for BWI airport. Normally, daily departure/approach tracks in BWI airport can be grouped into either east-flow or west-flow, which depend on the prevailing wind. In our work, track data for all arrivals and departures on July 3, 2003 was selected as a sample for east-flow operations. Figure 7 shows the daily track data in top and side views and also presents the layout of runways. The short runways 33R/15L are statistically much less used compared with other runways, as described in a BWI Noise Report.12 These runways typically only carry 3%-4% of overall traffic. Based on this, it is noted that the tracks utilizing the short runway 33R/15L could be removed without significant capacity decrease given current operations and safety requirements, and we adopt 33R/15L as a stub runway for the new RIA operations. With few outliers, we wrapped the existing fixed wing flight tracks in a set of cylinders and cones to define no-fly areas for SNI operations. For our case study, the ceiling is set as 4,000 f t, so only the parts beneath the ceiling are modelled. Top and side views of our obstacle field are shown in Figure 8. A 1,000 f t clearance is imposed, the set of obstacles are enlarged accordingly and treated as impenetrable.

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4

4

x 10

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3

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above ceiling 15R

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Land 33L

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(a) top view

1

(b) side view

Figure 7. East Flow Operation at BWI airport, July 03, 2003

(a) top view

(b) side view

Figure 8. Obstacles modelled for East Flow Operation

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2

3

4 4

x 10

V.

Experimental Results

Based on the BVI noise database, population density data and flight track data discussed above, we now study the design of noise optimal trajectories for BWI airport, since BVI noise is most prevalent during descent. For all approach cases, the initial velocity is prescribed as 95 knots and final velocity 45 knots, longitudinal path angle |γ| ≤ 9◦ , and the acceleration is restricted as |V˙ | ≤ 0.05g, a value set to ensure passenger comfort. The trajectory spans the area within 7 miles (approximately 40,000 f t) away from BWI and to a ceiling of 4,000 f t, while the lowest altitude is 100 ft, given that the Q-SAM noise model is only valid above 100 ft and that population is not dense near the touchdown site. For turning flight, we assume the horizontal path angle |β| ≤ 80◦ . A.

2-Dimensional Results With No Obstacles

As a connection to our previous work,7 we build from 2-dimensional trajectories, in which the helicopter approaches from state (x = 40,000ft, y = 0 ft, z = 2000ft, V = 95 knots) to state (x = 0 ft, y = 0 ft, z = 100 ft, V = 40 knots) with no lateral turning permitted and no landing orientation specified. Similar to our previous study, a noise-optimal two-dimensional longitudinal-plane approach is then a sequence of accelerated climbs and decelerating descents, a ”bang-bang” solution, which always utilizes saturated TipPath-Plane angle αT P P (Figure 9). From the BVI noise perspective, this result maximizes the distance of the wake from the rotor, thereby minimizing vortex-induced noise.

3000

Altitude(ft)

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(a) Path, Velocity & αT P P Profile (Longitudinal Plane)

(b) BVI SEL Distribution (Top View)

Figure 9. 2-Dimension 3 Segment Noise-Optimal Trajectory

Application of our iterative deepening algorithm enables comparison between different numbers of approach segments, the results of which are provided in Table 1 for a longitudinal-plane approach. Table 1 shows the longitudinal-plane path and velocity, the BVI SEL distribution, execution time, and noise index cost from Eq. (4). All cases are run on a 2.8GHZ Linux platform. As shown in the table, while the path becomes increasingly complex, the optimizer is better able to design a path that reduces BVI noise, illustrating the tradeoff between path complexity and noise.

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Table 1. Comparison With Varying Segment Number in 2D

Segment

Path & Velocity

SEL Distribution

Time Complexity

Noise Index

7 sec

70.7 dB

201 sec

65.5 dB

2393 sec

63.1 dB

3500

Altitude(ft)

3000 2500 2000 1500 1000 500 0

0

0.5

1

1.5

2

2.5

3

3.5

4 4

2

10

100

5

50

0

0

0

0.5

1

1.5

2

2.5

3

3.5

Distance(ft)

4

αtpp (deg)

Velosity (kt)

x 10 150

−5

4

x 10

3000

Altitude(ft)

2500 2000 1500 1000 500 0

0

0.5

1

1.5

2

2.5

3

3.5

4 4

3

10

100

5

50

0

0

0

0.5

1

1.5

2

2.5

3

3.5

Distance(ft)

4

αtpp (deg)

Velosity (kt)

x 10 150

−5

4

x 10

2500

Altitude(ft)

2000 1500 1000 500 0

0

0.5

1

1.5

2

2.5

3

3.5

4 4

5

B.

20

100

10

50

0

0

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0.5

1

1.5

2

Distance(ft)

2.5

3

3.5

4

αtpp (deg)

Velosity (kt)

x 10 150

−10

4

x 10

3-Dimensional Results With No Obstacles

The 3-dimensional approach problem is defined from start state (x = -28,000 ft, y = -28,000 ft, z = 2000 ft, V = 95 knots) to final state ( x = 1000 ft, y = 5000 ft, z = 100 ft, V = 40 knots) to land on Runway 15L, which means the rotorcraft flies from the southwest corner to the touchdown site. The behaviors of final optimal solutions are similar to the 2-dimensional cases. Figures 10 shows the 3-segment trajectories path and velocity profiles and the ground noise (SEL) distribution. Table 2 illustrates the tradeoff between path complexity and noise cost minimization. Note, however, the rapid increase in optimization execution time as number of segments increases due to the increase in search-space size as the k-ary tree is built to a greater 3-D depth. Although there will be a computational bound on the total number of 3-D flight segments that can be explored, we do not view this as a significant limitation since neither pilot nor air traffic controller will want to manage an approach procedure with more than 3-5 distinct low-altitude segments.

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4000

120

3500

100

Decelerating

2500

Velocity(knots)

Altitude(ft)

3000

Start

2000 1500

Landing site

80 60

Landing site 40

1000

20 500 0 −4

0 −4

4

Projection

2

−2 0

4

x 10

y label

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−4

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−4 y axis

x axis

x axis

(a) Path Shape

(b) Velocity Profile

(c) BVI SEL Distribution (Top View) Figure 10. 3-Dimension 3 Segment Noise-Optimal Trajectory

Table 2. Comparison With Varying Segment Number in 3D

Segment

Path

Velocity

SEL Distribution

Time Complexity

Noise Index

4

50 sec

72.2 dB

4

47225 sec

63.6 dB

120

4000 3500

Start

100

Decelerate

3000

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Altitude(ft)

Start 2500 2000 1500

Landing

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60

Landing

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20 500

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C.

Effects of Population Density Distribution

Previous results were optimized over the cost function from Eq. (4) that included population-based weighting factors. To investigate the effects of population density weighting, we set all population weights Wk to 1.0 (uniform density distribution) and re-computed a representative three-segment 3-D approach. Consider an approach with start state (x = 28,000 ft, y = 28,000 ft, z = 2000 ft, V = 95 knots) to final state ( x = 1000 ft, y = 5000 ft, z = 100 ft, V = 40 knots) landing on Runway 15L. A comparison of population-weighted and uniform cost weight trajectories is provided in Figure 11. Figure 11(a) and 11(b) show the case with no effect of population density distribution, while Figure 11(c) and 11(d) present the case with population weighting. It is shown that, while the total noise integrated over the entire trajectory is lower for uniform density weighting, inclusion of the population weighting terms yields a result with significantly lower noise during the initial approach, where the rotorcraft overflies high-population areas.

4000 3500

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(a) Optimal Trajectory (Wk = 1.0)

(b) BVI SEL Distribution (Wk = 1.0)

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(c) Optimal Trajectory

(d) BVI SEL Distribution

Figure 11. Effects of Population Density on Noise-Optimal Solution

D.

SNI Noise-Optimal Trajectories

The practical objective of this work is to design SNI approach procedures for RIA. To illustrate the use of our design tool, and to show that SNI approaches are feasible at a major airport (BWI) with existing fixed-wing procedures, we conducted a series of optimization runs with traffic obstacles as well as the population and BVI noise models used above. As described previously, east flow traffic at BWI on July 3, 2003 is modelled as a series of cylinders and cones. Rather than finding a single optimal solution, we investigated solutions for different approach entry regions, allowing RIA to directly enter the approach rather than circling around BWI to a single entry gate. Four entry regions are defined for this case study, with each of them representing a quadrant of the 7-mile radius circle with altitude above 2,000 ft (shown in Figure 12(b)). Trajectories were designed for

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each region, and the optimal entry region and trajectory for an incoming AH-1 helicopter was identified. Figure 12(a) gives the four locally optimal trajectories for runway Runway 15L, while Figures 12(c)-(f) show the SEL distribution. The final solutions for Sector I and II are similar, utilizing constant descent followed by decelerating climb and descent. The optimum for Sector III climbs over airspace obstacles with deceleration, then descends to join the base leg and has a similar final segment to Sector I and II. For Sector IV, the SNI optimum tries to avoid the traffic on its left. Similarly, it follows alternative decelerating descent and climb. Table 3 shows the comparison between these four solutions. From this comparison, we find: SNI approaches are feasible without too much noise generated; The sector II solution is best from a noise perspective and would be a good default routine; The sector III and IV solutions would enable more efficient approaches for traffic entering from the south and also are acceptable from a noise perspective particularly if used infrequently. Given the proximity of the Sector I and II solutions,we redefined the incoming traffic as three sectors (red dash lines in Figure 12(b)) . By this means, all RIA traffic entering from the southwest and southeast would fly the trajectory from Figure 12(e) and (f), respectively, while all traffic from North would utilize the trajectory from Figure 12(d). With rotorcraft as a RIA, numerous alternative landing sites at BWI could be identified in future work, and this optimization tool can assist with the selection of such a vertiport by efficiently defining SNI RIA traffic procedures and then impact on the community. Table 3. Comparison of SNI Noise-Optimal Trajectories

Sector I II III IV

Noise Index (dB) 65.6 63.8 69.5 68.6

People Exposed to noise ¿ 70 dB 12,458 5,996 80,784 52,315

VI.

Fuel Consumption (lb) 26.1 28.0 26.0 30.7

Flight Time (s) 417 441 440 501

Conclusion

We have described an incremental search method for modelling and optimizing segmented approach procedures for simultaneous, non-interfering (SNI) runway-independent aircraft (RIA) operations. Our method utilizes a k-ary tree for search space representation and Dijkstra’s algorithm to identify the optimal solution. This method is being applied to the problem of designing and implementing SNI RIA routes for BWI, a long-term task we are only beginning to tackle. Results based on a quasi-static BVI noise model and population density data have been presented, illustrating the application of the k-ary tree to 2-D and 3-D approach trajectory optimization as well as the effects of population density inclusion on the optimal result. We also assess the impact of increased path complexity (number of segments) on cost. Finally, we incorporate fixed-wing traffic data for BWI and present the solutions for incoming RIAs at different approach entry regions. Such analysis is an important first step toward the design of practical low-noise SNI procedures for an airport such as BWI. In future work, we will incorporate coordinated turning flight into the BVI noise database. More complete noise model including engine noise and tail rotor noise will also be included in cost, and we will again consider tradeoffs between noise and time/fuel efficiency in approach designs. As RIA operations grow closer to reality, we will expand our models to the RIA (VTOL, eSTOL) vehicle of choice and will work with airport personnel (e.g., at BWI) to build viable SNI procedures.

Acknowledgments The authors would like to thank Arnat Vale for discussion of BWI airport operations and for providing the flight track data to enable our research on true SNI approach optimization.

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Sector II (63.8dB)

4000 3500

Sector III (69.5dB)

Sector I (65.6dB)

3000

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4

2500

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x 10

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North

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−2 0

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Sector IV

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x 10

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−4 −4

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(a) Optimal Trajectories

(b) Sector Definition

(c) Sector I

(d) Sector II

(e) Sector III

(f) Sector IV

Figure 12. Path Shape and BVI SEL Distribution for Traffic from Different Sectors

14 of 15 American Institute of Aeronautics and Astronautics

References 1 D. Newman and R. Wilkins, ”Rotorcraft Integration into the Next Generation NAS,” Proceedings of the American Helicopter Society (AHS) 54th Annual Forum, Washington, DC, May 1998. 2 Clarke, J.-P., Systems Analysis of Noise Abatement Procedures Enabled by Advanced Flight Guidance Technology, Journal of Aircraft, Vol. 37, No. 2, pp. 266-273, March-April 2000. 3 F. J. Vormer, M. Mulder, M. M. van Paassen and J. A. Mulder, ”Design and Preliminary Evaluation of Segmentedbased Routing Methodology”, Proceedings of AIAA Guidance, Navigation, and Control Conference, August 2002, Monterey, California. 4 J.-C.Latombe, Robot Motion Planning, Kluwer Academic Press, 1991. 5 A. M. Ladd and L. E. Kavraki, ”Measure Theoretic Analysis of Probabilistic Path Planning”, IEEE Transactions on Robotics and Automation, Vol.20, No.2, pp.229-242, April 2004. 6 P. Cheng, Z. Shen and S. M. LaValle. ”RRT-based trajectory design for autonomous automobiles and spacecraft” Archives of Control Sciences, 11(3-4):167–194, 2001. 7 E. Atkins and M. Xue, ”Noise-Sensitive Final Approach Trajectory Optimization for Runway-Independent Aircraft”, Journal of Aerospace Computation, Information and Communication. Vol.1 (269-287), July, 2004. 8 J. Albus, N. DeClaris, A. Lacaze and A. Meystel, ”Neural Network Based Planner/Learner for Control Systems”, Proceedings of the 1997 International Conference on Intelligent Systems and Semiotics, Gaithersburg, MD, 1997, pp.75-81. 9 D. Bersekas and R. Gallager, Data Networks. Prentice Hall, 1992. 10 S. Russell and P. Norvig, Artificial Intelligence: a Modern Approach, Prentice Hall Series, New Jersey, 1995. 11 G. Gopalan, F. H. Schmitz and B. W. Sim, ”Flight Path Management and Control Methodology to Reduce Helicopter Blade-Vortex (BVI) Noise,” in Proceedings of the American Helicopter Society (AHS) Vertical Lift Aircraft Design Conference, San Francisco, CA, January 2000. 12 Quarterly Noise Report - Fourth Quarter 2002, Airport Noise and Abatement Office, Maryland Aviation Administration. 13 http://www.geographynetwork.com/freeresources.html.

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