Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory

Journal of Bionic Engineering 6 (2009) 270–279

Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory Xiao-lei Yu1,2, Yong-rong Sun1, Jian-ye Liu1, Bing-wen Chen3 1. Navigation Research Centre, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P. R. China 2. Institute for Technology, Research & Innovation, Deakin University, Vic 3217, Australia 3. Institute for Unmanned Aerial Vehicle Research, Beihang University, Beijing 100083, P. R. China

Abstract In this paper a new reactive mechanism based on perception-action bionics for multi-sensory integration applied to Unmanned Aerial Vehicles (UAVs) navigation is proposed. The strategy is inspired by the olfactory bulb neural activity observed in rabbits subject to external stimuli. The new UAV navigation technique exploits the use of a multiscroll chaotic system which is able to be controlled in real-time towards less complex orbits, like periodic orbits or equilibrium points, considered as perceptive orbits. These are subject to real-time modifications on the basis of environment changes acquired through a Synthetic Aperture Radar (SAR) sensory system. The mathematical details of the approach are given including simulation results in a virtual environment. The results demonstrate the capability of autonomous navigation for UAV based on chaotic bionics theory in complex spatial environments. Keywords: chaotic system, perception-action bionics, UAV, multi-sensory integration, autonomous navigation Copyright © 2009, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(08)60123-7

1 Introduction Unmanned Aerial Vehicles (UAVs) have become the research focus in recent years because of their broad application future both in military affairs and in civil aspects[1,2]. In military affairs, UAVs are able to fight and reconnoitre in very dangerous zones in order to reduce the injuries and death of people. On the other hand, UAVs can be used to achieve heavy and repeated tasks such as resource surveys, observation of the situation of disaster, communication transfer, environment monitoring and so on. The study on autonomous navigation of UAVs is a frontier problem of flight control. The goal is to realize the autonomous flight control, decision making and management for UAVs. Because of the huge complexity and high intelligence of autonomous navigation of UAVs, the research is still in the early stage. Under traditional control strategies, the navigation of UAVs can be implemented by close-distance communication chains constructed by other formation of aircrafts. In longer distance, the navigation of UAVs can be controlled by command platform either on the ground Corresponding author: Xiao-lei Yu E-mail: [email protected]

or in the sky. In addition, the satellite communication can be used to assist the navigation of UAV[3]. However, all the methods reviewed above adopted the way of controlling the UAVs by external data communication chains. In an atrocious environment, the result will be unpredictable if the communication chain is neither credible nor smooth. Therefore, the ability of independence, self-adaptability and self-determination is the key of the new generation of UAVs. Verschure and his co-workers developed a perceptual scheme, called Distributed Adaptive Control (DAC), as a neural model for classical and operant conditioning[4,5]. In DAC three tightly connected control layers are introduced: the reactive layer, the adaptive layer and the contextual layer. The reactive control layer implements a set of reflexes based on low level sensorial unconditioned inputs. The adaptive control layer allows the system to associate more complex stimuli with the basic ones. The contextual layer constructs high-level representations by means of memory structures. All forms of adaptive hehaviors require the processing of multi-sensory information and their transfor-

Yu et al.: Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory

mation into a series of goal-directed actions. In the most primitive animal species the entire process is regulated by external (environmental) and internal feedback through the animal body. Freeman and his co-workers, in their long experimental studies on the bionics of sensory processing in animals, conceived a dynamic theory of perception[6–10]. The hypothesis is that cerebral activity can be represented by chaotic dynamics. They attained this result by different experiments on rabbits which inhaled several smells in a pre-programmed way. Through the electroencephalogram (EEG), Freeman evaluated the action potentials in the olfactory bulb and noticed that the potential waves showed a complex hehavior. So he concluded that an internal representation (cerebral pattern) of a stimulus is the result of complex dynamics in the sensory cortex in cooperation with the limbic system that implements the supporting processes of intention and attention. In more detail, the dynamics of the olfactory bulb is characterized by a high-dimensional chaotic attractor with multiple scrolls. The scrolls can be considered as potential memory traces formed by learning through the animal’s life history. In the absence of sensory stimuli, the system is in a high dimensional itinerant search mode, visiting various scrolls. In response to a given stimulus, the dynamics of the system is constrained to oscillate in one of the scrolls, which is identified with the stimulus. Once the input is removed, the system switches back to the high-dimensional, itinerant basal mode. According to their works, neural system activity persists in a chaotic state until sensors perturb this hehavior. The result of this process is that a new attractor emerges representing the meaning of the incoming stimuli. The role of chaos is fundamental to provide the flexibility and the robustness needed by the system during the migration through different perceptual states. A discrete implementation of Freeman’s model was developed and applied to navigation control of autonomous agents[11]. The controller parameters have been learned through an evolutionary approach and also by using unsupervised learning strategies. Furthermore, some work on Knowledge-oriented Information Visualization (KIV) sets and robotics applications referring to Freeman’s model have been presented in recent years[12–15]. In this paper, taking inspiration from Freeman’s experiments showing the presence of chaotic dynamics in neural system activities, and paying attention to the

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reactive layer in DAC, we adopt a new bionic control architecture to implement the perception-action loop. We apply the proposed architecture to the navigation control problem for UAV. We do not try to reproduce a bio-relevant model of neural assemblies; our main objective is to propose reactive control architectures for autonomous UAVs, taking care of the functional properties discovered by Freeman in the olfactory bulb. The idea is to use a simple but chaotic dynamic system with suitable characteristics that can functionally simulate the creation of perceptual patterns. The bionic patterns can be used to guide the UAVs actions and the control system can be easily extended to include a large number of sensors.

2 Bionic evolution theory of the multiscroll chaotic system Recently, multiscroll chaotic technique has motived many scientists from different disciplines. From the application point of view, the double scroll attractor has been successfully employed towards true random bit generation[16]. Furthermore, the design, generation and analysis of multiscroll chaotic attractors become the leading edge gradually[17–20]. Since this UAV system should be able to deal with a great number of sensorial stimuli and represent them, a chaotic system, able to generate multiscrolls, has been adopted[17]. This can generate a chaotic attractor consisting of multiple scrolls distributed in the phase space. In this paper a three-dimensional (3D) multiscroll system is chosen, which is able to generate 3D n × m × l grid scroll chaotic attractors by using saturated function series. It is described by the following linear differential equations:

O2 ­ ° x y  b f ( y, k2 , h2 , p2 , q2 ) ° ° y z  O3 f ( z , k , h , p , q ) , (1) 3 3 3 3 ® c ° ° z ax  by  cz  O1 f ( x, k1 , h1 , p1 , q1 )  ° O2 f ( y, k2 , h2 , p2 , q2 )  O3 f ( z , k3 , h3 , p3 , q3 ) ¯ where the following so-called saturated function series f(x,k,h,p,q) is used: f  x , k , h, p , q

x ! qh  1 ­ 2q  1 k , ° ° k ( x  ih)  2ik , x  ih d 1,  p d i d q ®  p d i d q 1 ° 2i  1 k , °   2 p  1 k , x   ph  1 ¯ (2)

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The system represented by Eq. (1) can generate a grid of (p1+q1+2) × (p2+q2+2) × (p3+q3+2) scroll attractors. Parameters (p1,q1), (p2,q2), (p3,q3) control the number of scroll attractors in the direction of variables x, y, z, respectively. In Eq. (1) the coefficients a, b, c, Ȝ1, Ȝ2 and Ȝ3 are all positive constants. In particular, coefficients a, b, c control the shape and area of the limit cycle scroll. Coefficients Ȝ1, Ȝ2, Ȝ3 control the convergence during the evolution of the multiscroll system when controlled by reference dynamics associated with sen-

sors. The parameters used in Eq. (3) have been chosen according to the guidelines introduced by Lu et al. to generate a 3D 6 × 6 × 6 grid of scroll attractors[17]. Under these conditions, the saturated function series (Eq. (2)) is given in Fig. 1, and an example of the chaotic dynamics of system (Eq. (1)) is given in Fig. 2. a

0.7, b

c

k2

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k3 p1

40, h1 p2

p3

0.7, O2

O3

200, h2

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í400

í200

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200

400

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(a) k = 100, h = 200, p = q = 2

0.8, k1 100,

(b) k = 40, h = 80, p = q = 2

Fig. 1 Saturated function series.

Fig. 2 Projection of the 6 × 6 × 6 grid of scroll attractors in the x-y-z space.

(3)

Yu et al.: Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory

In our approach the perceptual system is represented by the multiscroll attractors in Eq. (1), whereas sensorial stimuli can interact with the system through constant or periodic inputs that can modify the internal chaotic behavior. Since one of the main characteristics of perceptive systems is that sensorial stimuli strongly influence the spatial-temporal dynamics of the internal state, a suitable scheme to control the chaotic behavior of the multiscroll system on the basis of sensorial stimuli should be adopted. Briefly, chaos control refers to a process wherein a tiny perturbation is applied to a chaotic system in order to realize a desirable behavior (e.g. chaotic, periodic and others). Several techniques have been developed for the control of chaos. Traditionally, chaotic control often means converting or constraining chaos to other dynamics, however, what we are adopting here is a broader and more general approach, and more powerful. In view of our application, a continuous-time technique like the Pyragas’s method is a suitable choice[21]. In the method, the following model is taken into account:

F t

k ¬ª yˆ  t  y  t ¼º ,

(4)

where F(t) is the feedback perturbation which forces the chaotic system to follow the desired dynamics, that is, the stabilization of unstable periodic orbits of a chaotic system is achieved by combining feedback with the use of a specially designed external stimulus; yˆ  t represents the external input (i.e. the desired dynamics); and k represents a vector of experimental adjustable weights (adaptive control). The method can be employed to stabilize the unstable orbits in the chaotic attractor, reducing the high order dynamics of a chaotic system. The desired dynamics is provided by a constant or periodic signal associated with more than one sensorial stimulus. Hence, the equations of the controlled multiscroll system can be written as follows:

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where i is the number of external stimulus acting on the system, xsi, ysi and zsi are the state variables of the stimulus signals that will be described in details below in Eq. (6), and kxi, kyi and kzi represent the control gains in the direction of x, y and z respectively. Each stimulus signal (xsi, ysi, zsi) can be a constant input or a periodic trajectory representing a native cycle. In a more simple way, these stimulus signals can be built using sinusoidal oscillators: ­ xsi  t Axsi sin Z xsi t  M xsi  xcenter °° ® ysi  t Aysi sin Z ysi t  M ysi  ycenter ,(6) ° °¯ zsi  t Azsi sin Z zsi t  M zsi  zcenter

where  xcenter , ycenter , zcenter is the centre of the stimulus cycle, Ȧ is the frequency, ij is the phase, and A defines the amplitude of the stimulus signal. The geometry of stimulus cycle can be adjusted by changing these parameters above. The bionic evolution of the multiscroll chaotic system is closely related to the stimulus. When no stimuli are added to the system, the hehavior of chaotic dynamics is shown in Fig. 3a. When stimuli are perceived, the system immediately converges to a limit cycle that constitutes a representation of the concurrent activation of the sensorial stimuli, as seen in Fig. 3b. When the stimuli are perceived consistently, the system will be constrained to oscillate in one of the scrolls, as shown in Fig. 3c. When stimuli are no longer active, the multiscroll returns to its default chaotic dynamics, and this process is shown in Fig. 3d.

400 300 200 100 0 í100 í200 í300 í400 400

Z

O2 ­ ° x y  b f  y, k2 , h2 , p2 , q2  ¦ k xi  xsi  x i ° O3 ° ° y z  c f  z , k3 , h3 , p3 , q3  ¦ k yi  ysi  y i °° 200 800 400 600      z ax by cz f x k h , (5) O , , , 0 ® 1  1 1 p1 , q1  200 Y í200 í200 0 ° X í400 f y k h p q f z k h p q   O O , , , , , , , , í600   í400 2 2 2 2 2 3 3 3 3 3 ° í800 ° (a) ¦i k zi  zsi  z ° Fig. 3 An example of the bionic evolution of the multiscroll ° system when controlled by stimuli dynamics. °¯

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400 300 200 100 0 í100 í200 í300 í400 400 200 Y

0

200 í200 0 í200 í400 X í600 í400 í800

800 400 600

Z

(b)

Z

(c)

the stimuli in relation to its body. The loop is closed by an action that is chosen to accomplish a given target behavior (e.g. exploration with obstacle avoidance). In the previous section we have defined the bionic evolution theory based on a dynamic system involved in realizing a reactive navigation layer. It is based on a chaotic control technique, used to enslave the dynamics of a multiscroll attractor to follow one or more trajectories. In this paper, each sensor equipped on the UAV provides a stimulus cycle. This is addressed by associating, for instance, the perception of an obstacle with a stimulus and associating it with a representation (pattern). Therefore the controlled multiscroll system is the perceptual system and the emerged orbit stands for the internal representation of the external environment. Finally, according to the characteristic of the emerged cycle (amplitude, frequency, centre position), an action, in terms of rotation angle, is associated. In this bionic strategy, action is linked to perception (the emerged cycle) using a deterministic algorithm. However, this association can be obtained through a bio-inspired adaptive structure which is suitable to control the UAV navigation in an unknown environment because it is adaptive and unsupervised. The adaptive structure is called the perception-action dynamics loop shown in Fig. 4. In the structure, the multiscroll chaotic reaction system can be described by Eq. (1), while the controlled multiscroll chaotic system with state feedback is presented by Eq. (5), and the actuator refers to the steering engine of UAV, associated with rotation angle.

Fig. 4 Structure of perception-action dynamics loop. (d)

Fig. 3 Continued.

3 Autonomous navigation of UAV When a UAV is placed in an unknown environment, it is subject to a huge amount of external stimuli. To explore the area avoiding obstacles, the UAV, sensing the environment, can create an internal representation of

Synthetic Aperture Radar (SAR), with high resolution, was widely used in some military fields. In our work, SAR sensor is chosen as a good candidate placed on the UAV. Among the possible stimulus cycles which can be used, in the application here reported, their distribution in the 3D phase space reflects the topological distribution of UAV sensors. Fig. 5 shows a scheme of

Yu et al.: Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory

the UAV equipped with a SAR sensor. The corresponding stimulus cycles in the phase space are related to the sensor positions. Since SAR sensor is characterized by an omnidirectional field of view, it is associated with more than one stimulus cycle. Surely, the stimulus cycles are distributed in 3D space symmetrically. The offsets assigned to each input cycle are defined to match the position of the scroll centers. Moreover we choose to link the value of the control gains with the intensity of perceived sensorial stimuli. The technique, based on placing stimulus cycles in the phase space in accordance with the distribution of sensors on the UAV, is important to strictly connect the internal representation of the environment with the UAV geometry. z

Stimuli cycle

y

Fig. 5 Scheme of the UAV equipped with a SAR sensor.

The action (in terms of absolute value of heading) performed by the UAV depends on the multiscroll be+

Stimulus 1

+

ys1

í

í zs1

xs1íx ys1íy

ky1 kz1

í

xs2 Stimulus 2

+ +

ys2 zs2 + í

í

í

In the following simulations, the parameters are given in Eq. (3), and the controlled multiscroll chaotic reaction system is represented by Eq. (5). Essentially, the selection of control gains kxi, kyi and kzi is very significant, in particular, taking into account a single stimulus signal, for low values of kxi, kyi and kzi (as shown in Fig. 7a only in x-y plane), the control of multiscroll attractor has a residual error, however for the cases as weak signals respecting the remote targets, the navigation control is

kx1

zs1íz

+

havior. In particular, in the absence of constraints the system evolves chaotically. Also, it can be chaotic even with constraints, just different types. Moreover, the possible exploring strategy taken into consideration is that the UAV continues to explore the environment flying without modifying its orientation. When external stimuli are perceived, the controlled system converges to a cycle (i.e. a periodic pattern) that depends on the contribution of active stimulus through the control gains from different directions kxi, kyi and kzi. The action to be executed is chosen according to the characteristics of the cycle, in particular its centre position in the phase space. A vector pointing to the center of the limit cycle of the controlled multiscroll attractor is defined. Predefined actions are chosen on the basis of the orientation of this vector. When the stimuli stop, the multiscroll returns to evolve in a chaotic way. Fig. 6 describes the block diagram of the control scheme when two distinct stimulus signals (i.e. sensorial stimuli) are perceived by the multiscroll system.

4 Simulation results

x

xs1

275

xs2íx ys2íy zs2íz

kx2

+

X control

+ +

Y control

+ +

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x Multiscroll chaotic reaction system

+

ky2 kz2

Fig. 6 Block diagram of the control scheme when two distinct stimulus signals are perceived.

y z

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still acceptable and in accordance with practice. For higher values of kxi, kyi and kzi (as shown in Fig. 7b only in x-y plane), the steady error becomes smaller.

(a) Low control gains kx = ky = kz = 0.3

trol gains, the resulting cycle will be placed exactly halfway between them. This result is shown in Fig. 9. In this case, the centre of one stimulus signal cycle is (250,150,150), and the centre of another one is (250,150,í150). k1x = k1y = k1z = k2x = k2y = k2z = 1.3, A1 = A2 = 30, Ȧ1 = Ȧ2 = 1, ij1 = ij2 = 0. So the centre of emerged cycle is (250,150,0). If the control gains of the two stimulus systems are not equal, the resulting controlled limit cycle (emerged cycle) will be placed, in the phase space, near the stimulus cycle associated with the higher control gain. This result is shown in Fig. 10. In this case, the centre of one stimulus signal cycle is (250,150,150), and the centre of another one is (250,150, í150). k1x = k1y = k1z = 1.2, k2x = k2y = k2z = 2.4, A1 = A2 = 30, Ȧ1 = Ȧ2 = 1, ij1 = ij2 = 0. So the centre of emerged cycle is (250,150, í50).

300 200

Z

Y

100 0

í100 í200 í300 300

200

(b) High control gains kx = ky = kz = 1.3

Fig. 7 Behavior of the constrained multiscroll system with different control gains.

0

0 í100 í100 X í200 í200 í300 í300

100

200

300

Fig. 8 Behavior of the reactive system of UAV controlled by a single stimulus cycle.

In the following section the proposed reactive control scheme will be applied to UAV navigation control. The SAR sensor is supposed to be located in the origin of the state space (i.e. (0,0,0)) in the following simulations. If the centre of stimulus signal cycle  xcenter , ycenter , zcenter is (250, í150,í150), kx = ky = kz =

300 200 100 Z

1.3, A = 30, Ȧ = 1, ij = 0, the equation of the controlled multiscroll system are adopted as Eq. (5), and the parameters in the equation are listed in Eq. (3). So when the single stimulus is perceived, the system immediately converges to the cycle whose centre is (250, í150, í150) (as shown in Fig. 8). Again, for example, let us consider the case in which there are two concurrently active inputs, and so there are two stimulus signals in the phase space. If the two stimulus dynamics have the same con-

100 Y

0

í100 í200 í300 300

200

100 Y

0

0 í100 í100 X í200 í200 í300 í300

100

200

300

Fig. 9 Behavior of the reactive system of UAV controlled by two equal stimulus cycles.

Yu et al.: Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory

determined by different initial rotation angles associated with the steering engine of the UAV. Simulation results in Fig. 11 show the trajectories of the UAV for surveillance of several buildings (represented by four large cylinders) followed by chaotic control strategy. From the results we can see if the UAV wants to fly over the four buildings, it must avoid obstacles from z-direction, meaning that the system must perceive stimulus from z-direction and take effective action. On the other hand, however, the system must perceive stimuli from x-direction and y-direction and take effective action to avoid obstacles if the UAV chooses the route that passes around the buildings. So from the simulation we can conclude that the perception-action dynamics system has enough flexibility and robustness in 3D space. Since the explored area and cumulative number of detected targets are two key parameters in evaluating the performance of a robot moving hehavior[11], here we can try some changes to evaluate the performance of UAV navigation hehavior in 3D space. We choose the cumulative number of obstacles found in an environment calculated in time windows of 10000 actions (i.e. epochs), as well as the volume explored by UAV during each simulation to test

300 200

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í100 í200 í300 300

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Fig. 10 Behavior of the reactive system of UAV controlled by two unequal stimulus cycles.

To test the performance and the potential impact of the proposed perception-action dynamics loop we developed a 3D virtual simulation environment. In this environment, obstacles and no-fly zones are modelled as cylinders. A small UAV involved in the task of obstacle avoidance as well as surveillance of several buildings is planned to go along the trajectories considering the perceived stimulus. Three different trajectories were

3 2 3

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Fig. 11 Trajectories followed by chaotic control strategy for UAV.

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the performance of the UAV under designed perception-action dynamics system. Fig. 12 and Fig. 13 show the cumulative number of detected obstacles and the volume explored by UAV in the four-buildings environment (Fig. 11) respectively. The capability of autonomous navigation of UAV is demonstrated from the results.

Number of detected obstacles

Number of detected obstacles

30 25 20 15 10 Route 1 Route 2 Route 3

5 0

that by APF algorithm (APF) while the number of detected obstacles by CC method is less. Anyway, the results demonstrate that the chaotic control method guarantees a higher exploration capability compared with the traditional APF control method.

0

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Fig. 12 Cumulative number of detected obstacles by UAV.

Fig. 14 Comparison of cumulative number of detected obstacles. 80 70 60

Explored volume (%)

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Fig. 15 Comparison of volume explored by UAV. Fig. 13 Volume explored by UAV.

Subsequently, to evaluate the performance of the proposed control scheme, a comparison with a traditional navigation control method is reported here. The traditional navigation strategy chosen here is the Artificial Potential Field (APF) approach[22]. Also in this case the UAV can use only local information, acquired from its sensory system to react to the environment conditions (i.e. PF). The parameters of the APF algorithm (e.g. UAV speed, constraints for the movements) are chosen in order to allow a comparison with our method. Route 1 is a good candidate as the trajectory for the comparison. Fig. 14 and Fig. 15 show that the explored volume by chaotic control method (CC) is generally bigger than

5 Conclusions In this paper the problem of multi-sensory integration is treated using a new technique called chaotic bionics control based on perception-action dynamics. This approach takes inspiration from the Freeman’s bionic theory of brain pattern formation, although it makes use of a more abstract model, and is applied to the UAV navigation control problem. The phenomenon of encoding information stabilizing the unstable orbits endowed in a chaotic attractor is investigated. The 3D multiscorll chaotic system was chosen for its simple model and to extend the emerging multiscroll attractor to 3D varying also the number of scrolls. The feedback from the environment is introduced by using a

Yu et al.: Autonomous Navigation for Unmanned Aerial Vehicles Based on Chaotic Bionics Theory

continuous multi-stimuli chaos control technique. Finally, simulation results demonstrate the capability of autonomous navigation for UAV in complex spatial environments.

Acknowledgements This work was supported by the National High Technology Research and Development Program of China (863 Program) (2006AA12A108) “Multi-sensor Integrated Navigation in Aeronautics Field” from the Ministry of Science and Technology of China, CSC International Scholarship (2008104769) from Chinese Scholarship Council, as well as International Postgraduate Research Scholarship Program (2009800778591) from Australian Government.

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