A Simulation Analysis of Formations for Flying Multirobot Systems

Transcription

1 A Simulation Analysis of Formations for Flying Multirobot Systems Francesco AMIGONI, Mauro Stefano GIANI, Sergio NAPOLITANO Dipartimento di Elettronica e Informazione, Politecnico di Milano Piazza Leonardo da Vinci 32, Milano, Italy Abstract. The ability of flying robots to navigate in a stable formation is the basis for a large number of applications, ranging from exploration to surveillance and rescue. However, the performances of 3D robot formations have not been extensively studied in literature. In this paper we present the results of a simulation study evaluating the adaptability of different flying robot formations to different kinds of environments. 1 Introduction Flying multirobot systems can effectively address several applications, including exploration, data acquisition, surveillance, rescue, inspection, and military operations [8]. In all these applications, the basic skill required to multirobot systems is the ability to flying while maintaining a stable formation, intended as the spatial arrangement of the robots in a given form [1, 9]. In this paper we present a simulation study evaluating the adaptability of different flying robot formations to different typologies of environments. This adaptability analysis, that constitutes the main original contribution of this paper, measures how well a formation behaves in an environment by referring to the average position error of the robots in the formation. Although several research projects are being pursued in this field, a systematic comparative study of the adaptability of 3D formations to environments is lacking in the current literature: this paper constitutes a first preliminary step in this direction. We run different sessions with a software tool we developed that simulates the flying robots, the environments, and their interaction and that allows for a detailed analysis of recorded data. Note that simulation is a valuable instrument in this case, since experiments with real flying robots are usually difficult and expensive to set up. This paper is organized as follows. The next section theoretically introduces the formations we considered. Section 3 presents the simulation setting used to produce the experimental evidence largely discussed in Section 4. Finally, Section 5 concludes the paper. 2 Formations for Flying Multirobot Systems The mathematical descriptions of the formations refer to the spatial relative position of a robot with respect to another robot given in spherical coordinates, namely horizontal (α i ) and vertical (β i ) angles and distance (ρ i ), as shown in Fig. 1. Each robot is uniquely identified by a number i, N is the total number of robots in the formation; ρ is the desired distance between two neighboring robots. All the formations we consider are

2 composed of a leader and of a number of followers. The relationships between the positions of the robots (the so-called control graph [2, 4, 5] or chain of friendship [6]) depend from the adopted control technique. According to [1], three main control techniques can be identified: neighbor-referenced, leader-referenced, and unit-center-referenced. In this paper we mainly consider the widely used neighbor-referenced technique, where each robot (except the leader) maintains its position with respect to the robot next to it. The formations of interest in this paper follow. Figure 1: The α i and β i angles and the distance ρ i between two robots Line (Fig. 2(a)). This is a 3D extension of a classical 2D formation (usually employed for mobile robots navigating on a surface) where β i = 0 i N/2 + 1 and, with neighbor-referenced control technique, 0 if i N/2 α i = π if i > N/ The robot i follows the robot i+1 if i N/2 or follows the robot i 1 if i > N/2 +1. The leader is the robot i = N/ Column (Fig. 2(b)). This is a 3D extension of a typical 2D formation where β i = 0 i 1 and (with the neighbor-referenced control technique) α i = π i 1. The robot 2 i follows the robot i 1. The leader is the robot i = 1. Wedge (or Arrowhead) (Fig. 2(c)). This is a 3D extension of another typical 2D formation, thus β i = 0 i N/2 + 1 and, with the neighbor-referenced control technique, α i = π if i N/2 4 3π 4 if i > N/2 + 1 As in the Line, the robot i follows the robot i + 1 if i N/2 or follows the robot i 1 if i > N/ The 2D versions of the above formations (Line, Column, and Wedge) are used in [6] (and in [3, 10] for the Line) with neighbor-referenced control technique. Snake (Fig. 2(d)). This is a formation possible only in 3D that generalizes the Column. α i and β i are not defined i 1. In the neighbor-referenced control technique, the robot i follows the robot i 1. The leader is the robot i = 1. The neighbor-referenced version of this formation extends the 2D convoy and chain (see, for example, [3]).

3 Star (Fig. 2(e)). It is a 3D extension of a 2D formation and does not exist in neighbor-referenced version. Thus, we employ the leader-referenced version in which each robot maintains its position with respect to that of the leader. β i = 0 and α i is not defined. All robots follow the leader, which is the robot 1. Sphere (Fig. 2(f)). It is an exclusively 3D formation that generalizes the Star formation and that, therefore, we consider in the leader-referenced version. β i and α i are not defined. All robots follow the leader, which is the robot 1. These last two formations are firstly introduced in this paper as an original contribution. We stress that they require the leader-referenced control technique. Figure 2: Flying robots formations (with N = 5) 3 Simulation Setting Simulator Overview. The simulator we developed (see Fig. 3) manages 3D world models with a set of obstacles (see The Environments below) and a number of flying robots. The simulator engine detects collisions between objects (robots and obstacles) and performs the moving and sensing activities of the robots. For each robot, the simulator provides a control interface via a tcp/ip socket that an external application (see Robot Controllers below) uses to determine the movements of the robot in the environment on the basis of the data acquired from the simulated sensors of the robot. We consider very simple proximity sensors placed in a star-like configuration to detect obstacles around the robot; the simulator allows also to define other types of sensors. The robots (actually, they controllers) communicate, for example to exchange their positions, by means of a radio-link channel managed by a socket-based component of the simulator. The simulator shows the evolution of the situation as a vrml model and generates some log files that record robot positions and other parameters (see Controllable and Measurable Parameters below) for subsequent analysis. All the software has been coded in c++. The Environments. The simulator allows to define structured environments composed of a plane (the ground) and of some regular solids (the obstacles). The size and the position of the obstacles are chosen during the initial definition of the environment. These environments are intended to be rough models of open areas with buildings. We study the adaptability of robot formations to the following four types of environments:

4 ENIVRONMENTS VRML SIMULATION DATA ANALYSIS ROBOTS, SENSORS SIMULATOR ENGINE SIMULATOR ROBOT CONTROLLERS Figure 3: The architecture of the simulator (a) the empty environment, (b) an environment with a large low obstacle, (c) an environment with a large high obstacle, and (d) an environment with many scattered obstacles (see Fig. 4). These environments represent particularly meaningful applicative scenarios for flying robots. In (a), we evaluate the effectiveness of robots control techniques and to provide a term of comparison with the other scenarios. In (b) and (c), we evaluate the basic obstacle avoidance properties of the formations. Finally, in (d), we evaluate the robustness of formations in presence of several irregular obstacles. Figure 4: An environment with many scattered obstacles (left) and a detail of a formation navigating in it (right) Controllable and Measurable Parameters. The controllable parameters regulate the behavior of the single robot in the formation (and, indirectly, of the team). The observable parameters evaluate the behavior of the robots in the formation. The only controllable parameter in our simulator is the robot position with respect to a given reference point. This reference point can be the position of the neighbor or of the leader (as discussed in the previous section). Each robot can control separately α i, β i, and ρ i, thus enabling a very simple holonomic control of robots. The robots move with constant velocity; a possible improvement could be the control of velocity and acceleration too. The main observable parameter we used is the average position error of a robot: the average (over the simulation steps) distance between the real position and the nominal position of the robot in the formation. The average position error expressed in spherical coordinates can be divided in the three components α, β, and ρ. The same observable parameter (calculated at every single time instant and not averaged) is also used in [2, 5] (in spherical coordinates, as in our case) and in [4, 7, 9] (in cartesian coordinates x, y, and, when applicable, z). The analysis, moreover, can be conducted with respect to a single robot or to the collective behavior of the formation (considering a second average over the robots); in the latter case, the parameter is still called average position error [1]. Robot Controllers. The robot controllers (Fig. 5 left) refer to an abstract model of holonomic flying robots (see above). This is a strong assumption since it does not

5 take into account the technological limitation of the real flying robots (e.g., aerostat, helicopter, flapping-wings, or their combinations); however, it allows to preliminary explore the performance of the formations. A robot controller operates according to the following cycle: acquire the current position of the robot (from the simulator), communicate this position to the other robots, update the known positions of the other robots, acquire the sensor readings (from the simulator), determine the new position, communicate the new position to the simulator engine that performs collision checking. In the case of the leader of the formation, the new position accounts for navigation toward the goal and for obstacle avoidance. In the case of the followers, it accounts for obstacle avoidance and for flight in formation (respecting the positions to be maintained, calculated according to the formulas of Section 2). The overall formation behavior emerges from the behaviors of the single robots. Figure 5: The robot controller interfaces (left) and the results of a simulation (right) 4 Experimental Results In this section, we present some preliminary experimental results that shed some light on the relation between formations and environments. The experimental scenarios we considered consist in a formation composed of 5 flying robots that moves along the Y axis from a start point to a target point. The robots start in formation. The size of the environment is 400 (X), 600 (Y), 100 (Z), with respect to a generic measure unit. The formations we evaluated are those illustrated in Section 2. For each experimental scenario we report the average position errors (introduced in Section 3) calculated averaging the position error over the simulation steps (Fig. 5 right shows this error relative to β angle for Line). The computation time of a simulation of a formation flight in an environment is of the order of some seconds. The Empty Environment. Table 1 summarizes some of the obtained results. The distances are signed values; a negative distance means that two robots are closer than prescribed by the formation. The average position errors are calculated over all the simulation steps needed to reach the target point (ranging from 267 in the case of Column to 783 in the case of Snake). The (always positive) values reported in the last row are calculated by averaging the absolute values of the followers. In the

6 Robot Line (L) Column (C) Wedge (W) Snake (Sn) Star (St) Avg Table 1: The average position errors relative to the distance in the empty environment Line, the robots substantially respects they nominal positions. The control of the α angle (the results are not reported here) is a little bit problematic, since it induces some latency for the followers. This is particularly emphasized in the Wedge, where the latency in adjusting the α angle generates a waterfall of corrections that are not parallel to the main flying direction. As expected, Column and Snake do not suffer from the above problem but, instead, they show the whipping effect. Since the leader has no feedback from following robots and all the robots navigate at the same velocity, sometimes it keeps moving without considering the difficulties of the followers that can loose contacts. The whipping effect is more evident in the robot that immediately follows the leader, while it is attenuated in tail of the formation. Star has an acceptable behavior since the control parameters are less constrained. However, in the Star a robot that went out from the formation has problems in re-entering it, because other robots obstacle the maneuver by their mere presence. An Environment with a Large Low Obstacle. In this experimental scenario, we put a single large low obstacle with dimension (100, 100, 30) in the empty environment to evaluate the obstacle avoidance behavior of the formations when the obstacle can be jumped (see Table 2; simulation steps range from 674 for the Line to 775 for the Snake). The Line behaves good but it still shows some latency in the followers. At the beginning and at the end of the jump some irregularities in the Line alignment appear (see In the Wedge the effort to control the α angle negatively influences the distance keeping. An interesting entangling effect shows up in this case: when the leader dives after jumping the obstacle and the followers are still over the obstacle, there are difficulties in maintaining the correct β angle, especially for the robot that immediately follows the leader. This entangling effect significatively influences also the Column (a long formation along the navigation direction), but not the Snake, since it relaxes the β angle control. However, the Snake suffers from a sort of intersection effect. This problem emerges when the (imaginary) segment that joins the position of a robot with that of its preceding reference intersects the obstacle; the robot, therefore, cannot follow directly the reference since it has to avoid the obstacle, with obvious loss of control efficiency. Finally, the Star and Sphere behave quite well: their great flexibility constitutes an advantage in this case. An Environment with a Large High Obstacle. In this experimental scenario, we put a single large high obstacle with dimension (100, 100, 90) in the empty environment to evaluate the obstacle avoidance behavior of the formations when the obstacle can be encircled (see Table 3; simulation steps range from 649 for the Snake to 1019 for the Line and the Wedge). The Line shows a sort of wall effect: since the formation distribution is perpendicular to the flight direction, the leader passes very close to the left side of the obstacle causing control problems to the right part of formation (robots 4 and 5). Robot 4 has serious problems in keeping the distance and the α angle

7 Robot L C W Sn St Sphere (Sp) Avg L C W L C W St Table 2: The average position errors relative to the distance (left), α angle (center), and β angle (right) in an environment with a large low obstacle Robot L C W Sn St Sp Avg L C W Table 3: The average position errors relative to the distance (left) and α angle (right) in an environment with a large high obstacle but avoids the obstacle to the left side; robot 5 avoids the obstacle to the right side breaking the formation. The Wedge improves the control of the α angle but it is worse in distance control: both robot 4 and robot 5 avoid the obstacle from the right side breaking the formation (see For the Column, an horizontal entangling effect disturbs the control of α angle (see In Snake, the intersection and whipping effects are present. However, when we exclude robot 2 from the analysis, the Snake outperforms the Column. We note that the intersection effect is often emphasized by the whipping effect, but this point (and, more generally, the relationships among the effects we identified) deserves more attention. Finally, note that some of the effects could be reduced by changing the formation of the team during navigation. An Environment with Many Scattered Obstacles. In this experimental scenario, formations basically behave as in the previous ones by jumping and encircling the obstacles, but other interesting situations emerged (see Table 4; simulation steps range from 699 for the Snake to 1024 for the Line). For the Column, there is an interesting blade effect by which an obstacle cuts the formation after the leader. It happens when the leader surpasses the obstacle and continues toward the target and the followers (trying to control the β angle) stay in a stall position (see The blade effect can be both horizontal and vertical. In the Snake, the whipping effect is attenuated since the horizontal translation of the leader is often reduced while encircling or jumping obstacles and the followers can easily maintain the formation. Moreover, the blade effect does not affect the Snake (see /formations/mo-snake.avi). In conclusion, the Snake, according to the adopted observable parameter, appears to be the most suitable formation for environments with several scattered obstacles. This also shows that, in general, the 2D formations could not be directly employed for effective 3D flying robots without relaxing some constraints, such as those on α and β angles.

8 Robot L C W Sn St Sp Avg L C W L C W St Table 4: The average position errors relative to the distance (left), α angle (center), and β angle (right) in an environment with many scattered obstacles 5 Conclusions The (preliminary) results of the simulation study presented in this paper show several effects that can influence the adoption of a formation in a given environment. However, the task often imposes the formation to be adopted; for example, the Sphere is used when there is a strong need to protect the leader in the center. Future work will be devoted to extend the experimental analysis by including other formations proposed in literature (such as diamond, rectangle, triangle, circle, and arc), other control techniques (leader-referenced and unit-center-referenced), and more controllable and measurable parameters. References [1] T. Balch and R.C. Arkin. Behavior-based formation control for multi-robot teams. IEEE Transactions on Robotics and Automation, 14(6): , [2] A. Das, R. Fierro, V. Kumar, J. Ostrowski, J. Spletzer, and C. Taylor. A visionbased formation control framework. IEEE Transactions on Robotics and Automation, 18(5): , [3] G. Dudek, M. Jenkin, E. Milios, and D. Wilkes. Experiments in sensing and communication for robot convoy navigation. In Proc. IEEE/RSJ Conf. on Intelligent Robots and Systems, volume 2, pages , [4] R. Fierro, C. Belta, J. Desai, and V. Kumar. On controlling aircraft formations. In Proc. IEEE Conf. on Decision and Control, volume 2, pages , [5] R. Fierro, A. Das, V. Kumar, and J. Ostrowski. Hybrid control of formation of robots. In Proc. IEEE Conf. on Robotics and Automation, pages , [6] J. Fredslund and M. Mataric. A general algorithm for robot formations using local sensing and minimal communication. IEEE Transactions on Robotics and Automation, 18(5): , [7] J.K. Hall and M. Pachter. Formation manuevers in three dimensions. In Proc. IEEE Conf. on Decision and Control, volume 1, pages , [8] M. Tambe. Towards flexible teamwork. Journal of Artificial Intelligence Research, 7:83 124, [9] P.K.C. Wang. Navigation strategies for multiple autonomous robots moving in formation. Journal of Robotics Systems, 8(2): , [10] E. Yoshida, T. Arai, J. Ota, and T. Miki. Effect of grouping in local communication system of multiple mobile robots. In Proc. IEEE/RSJ Conf. on Intelligent Robots and Systems, volume 2, pages , 1994.