Smooth Path Planning in On-line Mode for ... - Semantic Scholar

Smooth Path Planning in On-line Mode for Unmanned Air Vehicles Wei Liu, Zheng Zheng, Limeng Zhao, Kai-Yuan Cai Department of Automatic Control Beijing University of Aeronautics and Astronautics Beijing, China [email protected], [email protected], [email protected], [email protected]

I.

INTRODUCTION

The on-line path planning and its applications in unmanned air vehicles (UAVs) have an increasing development in civilian and military[1-3]. The basic objectives of path planning are to get a path which has the convergence ability to specified target, the ability of obstacle avoidance and a short flight distance. Besides, smoothness optimizing for flight path is also a meaningful and important requirement for UAVs, i.e., a UAV should fly along a smooth path without frequent turning in large-angle. The smoothness objective is especially crucial in many flight tasks with special demands or limitations, such as controllability requirement, physical limits of controlling organization, safety issues and that some UAVs are required to set up sensitive loads or security critical equipment. The primary motivation of our work is how to well handle the smoothness requirement and design a solution for UAVs, so that it not only realize the basic objectives, but also provide a flight path with slight maneuver as possible. Lots of planning methods have been proposed to satisfy the basic objectives, including evolution based algorithm[3], bouncing methods[4-6], mixed-integer linear programming based approaches[6-7], probabilistic approaches[6, 8], and etc. These methods mostly provide a feasible path under many practical restrictions, whereas without considering the smoothness requirement. Many researchers further consider the smoothness and present

1) Holistic smoothness. Holistic smoothness is regarded as an important aspect in evaluating path planning methods[4-5, 912] . It means less turning in the whole flight process, which is influenced by total waypoint planning times in a high degree. A planning result obtained by [5] without smoothness optimization is shown in Fig.1(a). Frequent planning performances (64 times) results in many unnecessary flight direction adjustments, and then brings much meaningless oscillation to the path. So, the holistic smoothness raises a global optimal requirement to path planning method design. 2) Turning angle optimization. Each waypoint planning may lead to yaw rate adjustment which directly influence the change value of turning angle. If UAVs can fly from one waypoint to another by changing a little turning angle, the flight path between the two waypoints will be regarded as smoothness. That is to say, the turning angle optimization is a necessary local requirement for path planning. A segment path in Fig.1(a) is intercepted and shown in Fig.1(b), we can see large turning angles occurs at point A, which make the local smoothness get worse. Similar turning also occurs at other

This research is supported by National Natural Science Foundation of China (Grant No. 60904066) and Aviation Science Foundation of China (Grant No. 2008ZG51092).

c 978-1-4244-8756-1/11/$26.00 2011 IEEE

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Keywords- Smooth Path Planning; Unmanned Air Vehicles (UAVs); Leader-follower Decision; Decision Rule Set

new path planning methods, such as Bezier curves based methods[9-10], steering methods[11], evolutionary multi-objective optimization methods[12], and so on. However, most of them are designed for autonomous robots or car-like vehicles. When considering the UAV’s realistic restrictions including limited information obtaining, sensory range and yaw rate limitation, the existing methods are hard to be used directly, or cannot get a smooth flight path at all. Inheriting the idea of programming flight path under basic objectives and necessary restrictions, we emphasize the smoothness requirement for the UAV’s path planning in the 2-dimension space. The smoothness effect can be described in the following two aspects:

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Abstract—With the basic objective of giving a feasible path in online path planning problem for unmanned air vehicles, smoothness requirement should be considered for further to satisfy more special applications. The paper emphasizes this realistic requirement, and presents an integrated solution based on a leader-follower decision idea. In the solution, global and local optimization strategies are analyzed, and then an improved leader-follower decision model is constructed to optimize the flight path in aspects of convergence to target, obstacle avoidance and smoothness. Discrete decision rule set are also introduced into the solution to improve the smoothness. Simulations based on typical scenarios are carried out under the guidance of the solution to verify the feasibility, especially the advantages in optimizing the global and local smoothness of flight path.

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Figure 1. Planning result without fully considering smoothness.

phases such as B and C, as indicated in Fig.1(a). The emphasis on smoothness increases difficulty in solving the on-line path planning problem. In this paper, we introduce new treatments to handle them. (1) For the holistic smoothness, a dynamic planning time interval is adopted to planning new waypoint only when necessary, so that the whole path is smoothed for a global optimizing effect. (2) For reducing each turning angle as much as possible, we model the turning capability to limit the UAV’s maneuver range, so that it can fly along a smoothness path even in local. Considering the global and local smoothness optimization together, a hierarchical optimization idea can be introduced naturally to formulize the on-line path planning problem. So, we present a practicable online path planning solution based on two level’s leader-follower optimization structure[13-14]. The solution is made up of two components: one is an two level’s leader-follower decision model with discrete decision rules; the other is a solving algorithm for the two level’s model. In the path planning process, the dynamic planning time interval is regarded as a decision variable to optimize the holistic smoothness of flight path, and the turning capability is described as constraint to smooth the flight path in local. The paper is organized as follows. Smoothness measure and realistic limitations are formulized in Section 2. Section 3 provides the leader-follower decision-making based solution. In Section4, simulation results are given and analyzed under guidance of the solution. Conclusions are provided in Section5. II.

PRELIMINARIES

The on-line path planning problem for UAVs in this paper considers not only the basic path planning demands, but also the smoothness requirement to realize slight maneuver all along the UAV’s flight process. We formulize these considerations for the convenience of describing the leader-follower decision based solution. A. Smoothness Measurement The smoothness of UAV’s flight path will be measured in two aspects: global smoothness and local smoothness. Definition 1 (Global Smoothness): The global smoothness is a measurement of how many turning operations and yaw rate adjustments UAVs have made during the whole flight process from start to target. We define GS as the global smoothness: PT

GS ൌ ( σCi )ോPT,

(1)

i=1

where PT is the change times of yaw rate(total number of planning times), Ci is the change value of yaw rate from the ith waypoint to the (i൅1)th waypoint, and GS ൒ 0. Less GS means better smoothness of the path in global. Definition 2 (Local Smoothness): The local smoothness measures the adjustment degree of yaw rate when UAVs fly from one waypoint to another. We define LS as the local smoothness: PT

LS = max Ci .

(2)

The local smoothness of flight path is quantitatively evaluated by the maximum change value of yaw rate when UAVs fly from start to target. It can be seen that less LS means better smoothness of the flight path in local. B. Threat Environment When flying to the specified target, UAVs should detect the surrounding environment on line to avoid possible obstacles. The detection ability of UAVs is described by sensory range. Definition 3 (Sensory Range): The UAV’s sensory range is defined as a constant and finite detectable area with the UAV’s current position as center. It is formulated as Sw: Swൌ{w|0 ൑ x2൅y2 ൑R2, wൌ[x, y]T},

where R is the detection radius which keep constant in whole flight process, w is UAV’s current location. Obstacles of opposition such as no-fly zones or SAMs (Surface to Air Missiles) form a threat environment in which UAVs preform the mission of planning path[15]. In the threat environment, UAVs must detect and avoid dangerous regions in on-line mode to keep safe. The description method of obstacles based on probabilistic risk shows good effects in many path planning applications[4-5], we formulize dangerous regions by way of defining real-time probabilistic risk. Definition 4 (Real-time Probabilistic Risk): The real-time probabilistic risk quantitatively measure the threaten degree that UAVs expose to known threats. It is formulated as P(w): M

P(w)ൌ1െšሼ1െ[1െStep(di, R{l,m,s}, k1)]‫ڄ‬Step(di, 0.1‫ڄ‬R{l,m,s}, iൌ1

k2)‫ڄ‬Step(arcsin(hȀdi), ɀ, k3)},

(4)

where w is UAV’s current location; M is the total number of current detected obstacles, i is the index of detected obstacles; di is the distance between w and the ith detected obstacle; h is UAV’s flight altitude. R{l,m,s} is the functional purview of threats and can take values of long, medium or short, ki(iൌ1,2,3) is the softness parameter of Step function which is defined as[5]: Step(a,aͲ,k)ൌ{1൅(aെaͲ)ോ[k2൅(aെaͲ)2]1ോ2}ോ2. Based on (4), the probabilistic risk threshold (denoted as ȡ, ȡ൐Ͳ) is introduced to indicate the minimal real-time probabilistic risk that can keep UAVs safe. In other words, UAVs will enter obstacle regions once the value of real-time probabilistic risk becomes larger than ȡ. Then, the probabilistic risk based method provides the formulized description for obstacle avoidance, that is: P(w) ൏ȡ. C. Dynamic Planning Time Interval According to the new requirement of holistic smoothness, an effective treatment is planning new waypoint only when necessary. UAVs calculate the real-time probabilistic risk on line and decide whether or not the current yaw rate need to be adjusted to avoid obstacles at the same time of approaching target point. If necessary, a new waypoint will be planned immediately. Otherwise, UAVs keep flying without any adjustment. The new idea gives up planning mode of frequently

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calculating new waypoint in fixed time interval by means of treating the time interval as a decision item (denoted as t). The value range of t is limited by the UAV’s sensory range Sw and flight velocity(denoted as v, v > 0). Here we assume v is a constant. Considering that a UAV does not know whether there have obstacles outside the sensory range, a reasonable processing is to chooses new waypoint only within the sensory range. It can be expressed as vt ൑ R ֜ t ൑ Rോv. Rോv means the maximal planning time interval (or the maximum flight time) between two waypoints. So the value range of t is: t ‫( א‬0, Rോv]. D. Turning Capability In order to smooth the local flight path, the flight maneuver of turning in large-angle should not happen or at least happens as few as possible. Many existing methods have not thought much of such aspect, e.g. method in [5], large-angle turning occurs in the flight path shown in Fig.1. Furthermore, these turning maybe unable to practically realize at all with the limitation of UAV’s turning capability. So, the turning capability should be formulized to help optimize the local smoothness and improve the accessibility to a new waypoint. When a UAV needs to turn, the yaw rate is appropriate to describe its angular rate of turning. Let Ȧ denote the possible yaw rate when UAVs turns, we define maximum yaw rate to restrict the value range of Ȧ. Definition 5 (Maximum Yaw Rate): The maximum yaw rate is the absolute value of maximal angle that a UAV can turn per unit time with an invariable flight velocity. The maximum yaw rate is constant for a given UAV, and is denoted as ȍ ( ȍ ൒ 0). Larger maximum yaw rate means better turning capability. With Definition 5, we know that Ȧ ൑ȍ.

possible, but unreasonable when considering the performability. III.

The on-line path planning is to determine new waypoint time and again all along the whole flight process until UAVs reach the specified target, as illustrated in Fig.3. Let wk ൌ ሾxk, ykሿ be the kth waypoint, if wk and the flight direction at wk are known, the (k൅1)th waypoint wk൅1 will be determined when giving the values of yaw rate and flight time. Also, the local flight path between wk and wk൅1 can be generated. All the local flight paths form a complete flight path. So, the decision process for waypoint can be regarded as a repeated decision process for Ȧ and t. A. Optimization Strategies In the path planning (Ȧ and t decision-making) process, the basic objectives including convergence and obstacle avoidance must be achieved firstly, and then the smoothness should be optimized as an additional but essential requirement. For giving a feasible and optimal flight path in on-line mode, we classify these considerations into two categories: global optimization and local optimization. The global optimization strategies can be expatiated in the following: •

In order to reach target, UAVs should try its best to fly to the target all the time. The demand of pointing to target is a global requirement. For the reason that the flight direction may be unable to always point the target point exactly, we can minimize the angle between UAV’s flight direction at the (k൅1)th waypoint and the line connecting the (k൅1)th waypoint with target point, so that UAVs will have a good tendency of looking forward the target point. Here we denote the angle at the kth waypoint by Ʉk.

•

Considering the holistic smoothness requirement, the introduction of dynamic planning time interval can reduces the planning times by calculating new waypoint only when necessary. Because the time interval means flight time between two waypoints, a concrete method is to regard flight time as a decision item. Thus, the decision process for t will be benefit to the optimization of global smoothness effect.

When planning new waypoint, ȍ provides a constraint to the UAV’s turning rate. Considering the limited flight time from one waypoint to another for further, the change scope of flight direction will be limited to the range: [െȍ‫ڄ‬Rോv, ȍ‫ڄ‬Rോv]. Obviously, this limitation can help optimize the local smoothness effect of the flight path by means of avoiding flight direction adjustment in large-angle or infeasible angle. Fig.2 shows three different flight paths (dotted line) starting from point W after flying tƒš (tƒšൌRോv). The end points of them are E1, E2 and E3 respectively. The gray region includes all the possible location of next waypoint under the limitations of UAV’s maximum yaw rate and maximum flight time. We can see that only E1 is a feasible waypoint among the three points. If E2 or E3 is decided to be the next waypoint by a planning method, UAVs will be hardly to reach them directly. The choice of E2 or E3 is of benefit to approach the target as Current flight direction

The local optimization strategies can be expatiated in the following:

E1

E2

W

Start

A LEADER-FOLLOWER DECISION BASED SOLUTION

Based on the smoothness measurement and the description of limitations, global and local optimization strategies should be analyzed to help design a smoothness considered solution. According to these strategies, a leader-follower decision structure introducing discrete rules will be adopted to optimize the smoothness of flight path both in global and local.

E3

The kth waypoint wk Target

Figure 2. Flight path with different turning mode.

On-line Obstacle detection

Determine ɘ and t

The (k൅1)th waypoint wk൅1

k ൌ k ൅1 Figure 3. Waypoint decision process.

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•

•

Approaching the target as possible is another important global requirement. However, in the on-line path planning mode, a UAV is unable to obtain enough information with the limited sensory range. So, we minimize the temporary distance between the (k൅1)th waypoint and target, so that the attempting of being close to target as possible will be translated into a local optimization consideration to some extent. Here we denote the distance the kth waypoint by Dk. Considering the local smoothness requirement, UAVs should turn only in the allowable and realizable range of flight direction. The formulization of turning capability in (4) prevents UAVs from unreasonable adjustment in large-angle, which can be used as a strict constraint of Ȧ for on-line path planning in optimizing the local smoothness effect.

In the following sections, we will formulize these proposed strategies and give a leader-follower decision based solution. B. Optimal Objective Functions with Discrete Rules The strategy of minimizing Șk+1 is a necessary condition for path planning. It has a higher priority than other strategies. That is because if UAVs unable to reach the target, the solving result will become meaningless no matter how short the distance between new waypoint and goal is, or how smooth the flight path is. So, the tendency of flying toward the target is an optimization objective in leader’s level. Șk+1 is formulated as: Ʉk൅1 ൌ F(Ȧ, t) ൌ Ʌk൅Ȧt ൅arcos[(yt െ yk൅1)ോDk൅1],

(5)

where wt is the target point, wt ൌ ሾxt, ytሿ; Ʌk is the UAV’s flight direction at wk. F(Ȧ, t) is the leader’s objective function: F: RൈR൅՜R. Dk൅1 will be refined below. Dk൅1 minimizing is also necessary for being close to target as short as possible. It is an assistant optimization in follower’s level, and influence Ʉk൅1 conversely by means of reflecting its decision to leader’s optimal objective. Dk൅1 is formulated as: Dk൅1 ൌ f (Ȧ, t) ൌ‫צ‬wtെwk൅1‫צ‬.

(6)

In (6), if Ȧൌ0, UAVs fly ahead without any direction adjustment, then wk൅1ൌሾvt‫ڄ‬sinɅk, vt‫ڄ‬cosɅk]; otherwise, UAVs need turn, then wk൅1ൌሾxk൅(2vോȦ)‫ڄ‬sin(Ȧtോ2)‫ڄ‬cos(Ɏോ2െɅkെȦt), yk൅(2vോȦ)‫ڄ‬sin(Ȧtോ2)‫ڄ‬sin(Ɏോ2െɅkെȦt)]. f(Ȧ,t) is the follower’s objective function: f : RൈR൅՜R൅. In the two level’s optimal objective functions, Ȧ and t are the decision variables. On one hand, they decide the leader and follower’s objects together; on the other hand, t reflects the intention of planning waypoint dynamically which will optimize the holistic smoothness, and Ȧ restrict the turning capability which will optimize the local smoothness. Further considering the characters of the on-line path planning problem, the following discrete rules can be introduced to optimize the new requirement of smoothness. •

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If wt has been detected by UAVs, it is possible to try to reach the target by once waypoint planning. If it works, UAVs may be able to avoid more direction adjustment and decrease waypoint planning times.

TABLE I. b1 true true true false false

b2 uncertain true false true false

b3 true false false uncertain uncertain

DECISION RULE SET F |Șk+1| |Șk+1| |Șk+1| |Șk+1| |Șk+1|

Ȧ constant Ȧ ȍ Ȧ Ȧ

f Dk+1 Dk+1 Dk+1 Dk+1 Dk+1

t constant t t t R⁄v

“ uncertain” means “true” or “false”. The actual line number of the decision rule set is 23=8.

•

If no obstacles are between the current waypoint and wt, UAVs can try its best to fly for a long time. It can avoid abrupt maneuver in a little range.

•

If UAVs have detected the target but cannot reach it directly for the limitations of control performances, it is profitable by directly turning a large angle. That is because one times smoothness damage may decrease many times adjustment later.

These experiential assertions can help decrease planning times and reduce change range of yaw rate. We introduce decision rule set function to describe them synthetically. Definition 6 (Decision rule set function[16]): A decision rule set function rs from X to Y is a subset of the Cartesian product X × Y, such that for each x in X, there is a unique y in Y generated with RS such that the ordered pair (x, y) is in rs. Here, RS is called a decision rule set, x is called a condition variable, y is called a decision variable, X is the definitional domain, and Y is the value domain. RS is given in Table I. We define decision rule set function rs: (X ൈ Y). X ൌ [b1, b2, b3]. b1, b2 and b3 are the condition variable denoted by boolean values. b1 means whether wt ‫ א‬Sw; b2 means whether the line connecting wk and wt pass through known obstacles; b3 means whether existing a decision pair (Ȧ, t) which satisfies P(wnext) ൑ȡ and wk൅1 ൌ wt together. Y ൌ [F, Ȧ, f, t]. F, Ȧ, f and t are the decision variable. wnext denotes any point in the path between wk and wk൅1. We can see the leader and follower’s decision variables are both influenced by the values of discrete variables b1, b2 and b3. It is reasonable to regard them as new decision variables. Then, F(Ȧ, t) and f (Ȧ, t) will be updated as new mappings from Ȧ, t, b1, b2 and b3 to |Șk+1| and Dk respectively: F: (Ȧ, t, b1, b2, b3) ՜|Ʉk+1| f : (Ȧ, t, b1, b2, b3)՜Dk

(7) (8)

C. Leader-follower Decision Model The leader-follower decision model with discrete rules for on-line path planning problem is formally described as: min F(Ȧ, t, b1, b2, b3) F(Ȧ, t, b1, b2, b3) ൌ |Ʉk+1| min f (Ȧ, t, b1, b2, b3) f (Ȧ, t, b1, b2, b3) ൌ Dk s.t. t ‫( א‬0, Rോv] |Ȧ| ൑ ȍ Ȧt ‫[א‬íȍ‫ڄ‬Rോv, ȍ‫ڄ‬Rോv] P(wnext) ൏ȡ b1, b2, b3 ‫[א‬true, false] rs ‫ ك‬RS

2011 6th IEEE Conference on Industrial Electronics and Applications

(9) (10) (11) (12) (13) (14) (15) (16)

Note that, The two objectives are constructed to realize the basic intents of path planning. With the flight time being decision variable, the global smoothness is optimized. With (13), the local smoothness is optimized too. (11)-(14) model the basic restrictions needed in typical path planning problem. (14) guarantees the obstacle avoidance. (15)-(16) is introduced to further optimize the smoothness of the path by simplify the planning process. Based on the optimum solution definition of the two level’s leader-follower decision model[13-14], an algorithm for the online path planning problem is given and described below. Algorithm Procedure Step 1: Initialization. Initialize the start point as the first waypoint w0, and set index kൌ0; Update the known obstacle regions. Construct a finite sequence IRൌ((Ȧi, ti)) to save the inducible region and initialize it empty. Step 2: Discretize continuous decision variables. Discretize Ȧ and t as nonempty finite sequence (Ȧi) and (ti) according to (11) and (12) respectively. Step 3: Determine concrete expressions of the leaderfollower decision model. Decide the values of b1, b2 and b3ҏ, and then use RS to determine the of leader and follower’s variables. If b1ൌtrue and b2ൌtrue, the follower’s optimal solving will be R⁄v, then goto Step 6; otherwise, goto Step 4. Step 4: Construct follower’s feasible set. For each element in (Ȧi), search all the element in (ti) ascendingly and determine the follower’s feasible set for each fixed (Ȧi). (13) will be considered in the searching process to decrease search steps. Then the leader’s decision space can be constructed too. Step 5: Give follower’s optimal decision. With each pair element in leader’s decision space and follower’s feasible set, the element in (ti) which makes Dk be minimum will be found, it is the follower’s optimal decision, denoted as tmin. If b1ൌfalse and b2ൌfalse, the leader’s optimal solving will be ȍ, then goto Step 8, otherwise, goto Step 6.

Step 8: Update waypoint. Update the current waypoint to the new one, and clear IR. If wk്wt,, kൌk൅1, return to Step 2; otherwise, UAVs reach the target point so that the on-line path planning finished. IV.

SIMULATIONS

We now solve the on-line path planning problem under the guidance of our proposed solution in simulation environments. Typical scenarios are generated for the solution to show the implementation effect in aspects of convergence to target point, obstacle avoidance and smoothness optimization. Ten typical simulation scenarios used in [4], [5] and [6] are adopted, and denoted by (I)-(X). In all scenarios, the values of necessary parameters are taken as: Rൌ40 km, vൌ0.05 km/s, ȍൌʌ/60 rad/s, ȡൌ0.1. The UAV’s initial heading direction point to the target. The quantitative simulation results with the ten scenarios are given in Table II. Here we use M1 and M2 to denote the results of our solution and [5], respectively. With these results, we evaluate the planning effect in the following three aspects. 1) Convergence to target and flight distance. We can see that the two solutions both successfully provide a flight path from the start to the target. However, the flight distances in M1 are shorter than those in M2. Especially in (X), the flight distance in M2(2312.1km) is too much longer than that in M1(321.5km), it is because UAV has to adjust the flight direction for many times to fly off the two dend ends, as seen in Fig.5(b) and Fig.6. Too many adjustments also damage the smoothness of the flight path. 2) Obstacle avoidance. We use peak risk denote the maximum threat degree during the whole flight process. It can be seen in M1 the peak risks are less than the probabilistic risk threshold ȡൌ0.1; whereas in M2 one of the peak risk is 0.1010 (in (V)) which make UAV fails to avoid some obstacles.

Step 6: Construct the inducible region. Determine whether (14) can be satisfied when tൌtmin and ȦൌȦi. if so, add element (Ȧi, tmin) to IR, and go to Step 7; otherwise, iൌi൅1, search continuously until reach the last Ȧi.

3) Global and local Smoothness. The global smoothness of flight path is measured by GS. It is obviously GS in M1 are much less than the values in M2. The local smoothness of flight path is measured by LS. The values in M1 are much less than those in M2. So, the proposed solution can successfully optimize the smoothness in global and local.

Step 7: Get optimal solving. Search IR ascendingly to get an element which makes |Șk൅1| minimum, then the element in IR is the optimal solving of the model. The new waypoint is determined too with the optimal solving.

Besides, the total number of planning times PT is given too. Waypoint planning will increase the computation burden of UAVs, so it is necessary to decrease PT. In Table II, we can see the values in M1 are much less than those in M2.

TABLE II. Scenarios Convergence to target Flight distance (km) Peak risk GS (rad/s) LS (rad/s) PT

M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2

I true true 66.2 71.7 0.0867 0.0978 0.0040 0.0177 0.0099 0.0887 5 64

II true true 107.9 111.1 0.0893 0.0902 0.0030 0.0093 0.0115 0.0544 9 103

III true true 121.5 146.1 0.0782 0.0926 0.0014 0.1295 0.0042 0.1295 8 138

SIMULATION RESULTS VI true true 124.8 164.3 0.0808 0.0912 0.0028 0.0683 0.0094 0.0683 7 152

V true true 167.2 213.2 0.0944 0.1010 0.0028 0.0161 0.0094 0.0785 14 187

VI true true 191.1 727.5 0.0969 0.0961 0.0045 0.0205 0.0168 0.1571 15 625

VII true true 234.1 244.4 0.0892 0.0957 0.0011 0.0048 0.0047 0.0508 16 235

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VIII true true 269.9 482.5 0.0904 0.0966 0.0027 0.0168 0.0230 0.1571 19 443

IX true true 284.5 528.0 0.0907 0.0988 0.0033 0.0188 0.0241 0.1571 21 479

X true true 321.5 2312.1 0.0919 0.0964 0.0024 0.0190 0.0225 0.1571 25 1974

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measurement for the global and local smoothness. Hierarchical optimization idea based solution are proposed to describe and meet the requirement. The solution formulizes the on-line path planning problem as a leader-follower decision based model with discrete decision rules embedded, which can not only achieve the basic objectives of providing a feasible path, but also optimize the smoothness of flight path in global and local.

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Figure 4. Planning paths in scenario(I). (a) M1. (b) M2. 



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Figure 5. Planning paths in scenario(X). (a) M1. (b) M2.

 

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UAVs have to adjust the height when flying in complex terrain. Therefore, the immediate future work will be dedicated to the path planning in 3-dimension space by introducing new variables, such as flight height, flight velocity, pitch angle and rolling angle. Also, based on this solution we intend to make experiments on a quadrotor aircraft we have developed.



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Figure 6. Planning paths when avoiding dead ends without considering smoothness in scenario(X). (a) Dead end 1. (b) Dead end 2.

In order to analyze the optimization effect of smoothness with our solution, we take (I) and (X) for examples and plot the flight paths, as illustrated in Fig.4-Fig.5. (a) is our results, (b) is the results from [6]. We can see that (a) provide smooth paths from the start to the target point in (I) (PTൌ5, GSൌ0.004radോs, LSൌ0.0099radോs) and (X) (PTൌ25, GS ൌ0.0024radോs, LS ൌ0.0225radോs). However, (b) suffer lots of waypoint planning and many large-angle turning in (I) (PTൌ64, GSൌ0.0177radോs, LSൌ0.0887radോs) and (X) (PTൌ1974, GSൌ0.019radോs, LSൌ0.1571radോs). Especially, obstacles in (X) form two dead ends, the path in (a) successfully avoids them without too many adjustments. the path in (b) has to frequently update waypoint and adjust the flight direction in large-angle to escape from the two dead ends, as shown in Fig.6. In conclusion, the simulation results in typical scenarios show that the flight paths become smooth and easily performable when considering the global and local smoothness as an important decision criterion for the proposed solution.

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[9]

[10]

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V. CONCLUSIONS AND FUTURE WORKS The smoothness of the flight path is a crucial requirements for UAV’s on-line path planning in many flight tasks. This paper emphasizes the new significant requirement of optimizing the smoothness both in global and local, and give a primary

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J. Canny, The complexity of robot motion planning. Boston: MIT Press, 1988. Tom Schouwenaars, Safe trajectory planning of autonomous vehicles. Boston: MIT Press, 2006. C. Zheng, L. Li, F. Xu, F. Sun, and M. Ding, “Evolutionary route planner for unmanned air vehicles,” IEEE Transactions on Robotics and Automation, vol.21, August 2005, pp. 609–620. Z. Zheng, S. J. Wu, W. Liu, and K. Y. Cai, “A feedback based CRI approach to fuzzy reasoning,” Applied Soft Computing, vol.11, 2011, pp.1241-1255. Kim, D. W. GU, and I. Postlethwaite, “Real-time path planning with limited information for autonomous unmanned air vehicles,” Automatica, vol.44, 2008, pp. 696–712. D. W. GU, I. Postlethwaite, Y. Kim, “A comprehensive study on flight path selection algorithms,” IEEE Control & Automation and Signal Processing Professional Network, Herts, UK, October 2005, 77–90. A. Chaudhry, K. Misovec, R. D. Andrea, “Low observability path planning for an unmanned air vehicle using mixed integer linear programming,” Proceedings of the 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, December 2004, 3823– 3829. K. Klasing, D. Wollherr, and M. Buss, “Cell-based probabilistic roadmaps (CPRM) for efficient path planning in large environments,” The 13th International Conference on Robotics, Jeju, Korea, August 2007, pp.1075–1080. Y. J. Ho and J. S. Liu, “Collision-free curvature-bounded smooth path planning using composite bezier curve based on Voronoi diagram,” IEEE International Symposium on Computational Intelligence in Robotics and Automation, Korea, December 2009, pp.463-468. Y. J. Ho and J. S. Liu, “Simulated Annealing based Algorithm for Smooth Robot Path Planning with Different Kinematic Constraints,” SAC’10, Sierre, Switzerland, March 2010, pp.1277-1281. Yumiko Suzuki, Simon Thompson, and Satoshi Kagami, “Smooth path planning with pedestrian avoidance for wheeled robots: implementation and evaluation,” Proceedings of the 4th International Conference on Autonomous Robots and Agents, Wellington, New Zealand, February 2009, pp.657-662. K. T. Hunga, J. S. Liua, and Y. Z. Chang, “A comparative study of smooth path planning for a mobile robot by evolutionary multi-objective optimization,” Proceedings of the 2007 IEEE International Symposium on Computational Intelligence in Robotics and Automation, Jacksonville, USA, June 2007, pp.254-259. W. Candler, and R. Norton, Multilevel Programming. Technical report 20, World Bank Development Research Center, Washington D.C., 1977. J. F. Bard, Practical bilevel optimization – algorithms and applications. Kluwer Academic Publishers. 1998. B. M. Albaker, N. A. Rahim, “Unmanned aircraft collision detection and resolution:concept and survey,” Proceedings of the 5th IEEE Conference on Industrial Electronics and Applications, 2010, pp.248-253. Z. Zheng, J. Lu, G. Q. Zhang, and Q. He, “Rule sets based bilevel decision model and algorithm,” Expert Systems with Applications vol. 36, 2009, 18-26.

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