EXPERIMENTAL DEMONSTRATION OF MULTIPLE ROBOT COOPERATIVE TARGET INTERCEPT

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1 EXPERIMENTAL DEMONSTRATION OF MULTIPLE ROBOT COOPERATIVE TARGET INTERCEPT Timothy W. McLain Ranal W. Bear Je M. Kelsey Department of Mechanical Engineering, Brigham Young University, Provo, Utah 86 Department of Electrical an Computer Engineering, Brigham Young University, Provo, Utah 86 Department of Electrical an Computer Engineering, Brigham Young University, Provo, Utah 86 ABSTRACT This paper presents experimental results for the simultaneous intercept of preassigne targets by a team of mobile robots. The robots are programme to mimic the ynamic behavior of unmanne air vehicles in constant-altitue flight. In proceeing to their targets, robots must avoi both known static threats an pop-up threats. An overview of the cooperative control strategy followe is given, as well as a escription of the robot harware an software use. Experimental results emonstrating simultaneous intercept of targets by the robot team are presente. INTRODUCTION Recent military conflicts have emonstrate the strategic value of unmanne air vehicles (UAVs). In the past UAVs have been use primarily for reconnaissance an surveillance purposes. More recently, they have been use in offensive missions as a bombing or missile-launching platform. In these scenarios, UAVs have operate inepenent of other vehicles with little or no cooperation. Although they have been successful as single agents, UAVs will make greater contributions to military missions as their cooperative capabilities are increase. As cooperative control strategies for teams of multiple UAV agents are evelope, the potential impact of UAVs on future military operations will certainly broaen. Cooperative control of multiple-uav teams is a subject to which increasing attention has been given. Research has focuse primarily on three areas: UAV formation flight, cooperative path planning (e.g., renezvous), an resource allocation (e.g., target assignment). The motivation for formation flight of Corresponing author, tmclain@et.byu.eu UAVs is increase stealth an fuel economy. In close formations, UAVs are couple ynamically by the aeroynamic interactions among the vehicles. As such, the entire formation can be consiere as a single large system for which a control strategy must be evelope. Strategies for formation flight of UAVs are evelope in [,,, ]. Unlike formation-flight problems, cooperative path planning an resource allocation problems usually involve UAVs that are physically inepenent of one another, although they may be couple ynamically by their cooperative control algorithms. Several important UAV cooperative control problems can be formulate as resource allocation problems. This inclues target assignment problems [5, 6], cooperative classification problems [7], an cooperative search problems [8]. The majority of cooperative path planning problems consiere in the literature involve timing or sequencing of UAVs for arrival at targets or other specifie locations, such as the cooperative intercept problem consiere here. A cooperative control strategy for UAV renezvous was presente in [9]. Cooperative path planning is also employe in cooperative search an cooperative classification problems []. Up to the present time, UAV cooperative control research has consiste of simulation stuies. This paper presents initial results in cooperative path planning for a team of wheele robots. These robots are programme to simulate, in harware, UAVs in constant-altitue flight. This work presents a ecentralize cooperative control strategy an examines its suitability for real-time implementation. The specific problem treate in this paper is similar to that presente in an earlier simulation stuy [9]. As epicte in Figure, three robots must navigate through a fiel of known threats (epicte by re ots) to arrive at preassigne targets (epicte by stars). The cooperation objective is for

2 the robots to arrive at their targets simultaneously to maximize the element of surprise. The robots must be able to respon to unknown pop-up threats as well Figure : Cooperative intercept problem. COOPERATIVE CONTROL METHOD The cooperative control strategy followe in this work is similar to the approach first presente in [9, ]. For completeness, a brief review of the approach is presente here. The team objective is to minimize the collective threat exposure of the team over the mission. The cooperation objective is simultaneous intercept of the assigne targets. Given the battle scenario epicte in Figure, each robot has numerous possible trajectories that it can take to its assigne target. Caniate trajectories for the robots are erive from a search of a Voronoi graph that is constructe from the known threat locations [9]. The ten safest paths for each robot are etermine using a k-best paths search [] of the Voronoi graph. The trajectories for each robot are parameterize by a sequence of waypoints an a constant velocity. These parameters are calle agent ecision variables. In general, ecision variables for the i th agent, ξ i, are those variables that can be freely etermine by the agent that govern its behavior. To arrive at their targets simultaneously, the robots must have the same time-over-target (TOT). In this problem, TOT is efine as the coorination variable, θ. Notice that for each robot, TOT is a function of the trajectory parameters, i.e., θ i = f i (ξ i ). The threat exposure of each robot is also a function of the trajectory parameters. In this problem, the threat exposure of each robot is calle the agent influence, φ. The influence of the i th agent on the team objective is escribe by this function: φ i = h i (ξ i ). For this problem, the team objective can be written as min ξ i J T = φ i (ξ i ), i= while achieving the cooperation objective (simultaneous intercept): θ (ξ ) = θ (ξ ) = θ (ξ ). This centralize formulation of the cooperation problem is cumbersome an inefficient. It requires the simultaneous etermination of all trajectory parameters for all robots. This requires trajectory planning for all robots to be centralize an communication of potentially large amounts of information (robot state, threats, trajectory parameters). A more efficient, ecentralize approach is enable through the efinition of a coorination function, ˆφ. For this problem, the coorination function escribes the relationship between threat exposure an TOT: ˆφ i = g i (θ i ). For the caniate paths consiere, TOT an threat exposure can be reaily etermine from path length, velocity, an threat location information. From this information, coorination functions for each of the robots can be compute. With coorination functions for each agent efine, the cooperative control problem can be reformulate as θ = arg min θ Θ T ˆφ i (θ) i= where Θ T is the team-feasible range of TOT values. Once the team-optimal TOT has been etermine, trajectories for each of the robots can be foun by inverting the coorination-variable relationship ξ i = f (θ ). This ecentralize strategy is epicte graphically in Figure.

3 ^ Choose θ * θ * to minimize Σ φ i (θ) Θ ^ φ Determine: CV relation: θ = f (ξ ) Feasible range for CV: Θ Agent influence: φ = h (ξ ) ^ CF: φ = g (θ ) = h [f (θ )] subject to θ * Θ i agent agent agent Determine best ξ that matches θ * : ξ = f (θ * ) the two segments, then the time-optimal trajectory connecting the segments is inicate by the re line of Figure. If the trajectory is constraine to pass through the intermeiate waypoint, then the timeoptimal trajectory between the segments is inicate by the blue line. waypoint ξ Figure : Cooperative path planning algorithm. R i TRAJECTORY GENERATION The output of the cooperative path planner, ξ i, is a set of waypoints an the esire velocity for each robot. Given this information, a trajectory generator is neee to generate time-parameterize trajectories that are feasible within the ynamic constraints of the vehicle. In this work, we impose UAV ynamic constraints on the robots. The unerlying iea for the trajectory generator is to use a nonlinear filter that has a mathematical structure similar to the kinematics of a UAV to generate trajectories that smooth through the waypoints in real time while the vehicle traverses the trajectory. For a UAV with heaing-hol an altitue-hol autopilots, flying at constant altitue an velocity, the governing kinematics are given by Ẋi Ẏi = Vi cos ψi = Vi sin ψi ψ i < ψ max V i = ḣ i =. Base on the esire velocity an the heaing rate constraint, a minimum turning raius for the vehicle can be etermine: R i = V i ψ max. Note that as the esire velocity increases, then the minimum turning raius increases. Conversely, as the heaing rate capability of the vehicle increases, the minimum turning raius ecreases. Consier the problem of turning from one waypoint path segment onto another in minimum time at constant velocity. If the trajectory is not constraine to pass through the waypoint connecting Figure : Time-optimal transitions between waypoint path segments. One of the isavantages of both minimum-time transitions an transitions constraine to go through the waypoint is that the trajectories generate will have ifferent path lengths than the original Voronoi path. Since the Voronoi path is use for etermining intercept times, it is esirable that the smoothe trajectory have the same length as the original Voronoi path. waypoint Figure : Length-matching transitions between waypoint path segments. From Figure, it is clear that the path length of the minimum-time trajectory is shorter than the path length of the Voronoi path, while the path length of the constraine trajectory is longer than the Voronoi path. As Figure shows, by positioning the transition circle between the inscribe circle an the circle that intersects the waypoint, a transitioning trajectory can be etermine that has the R i

4 same length of the original Voronoi path. Details of this trajectory generation strategy an algorithms for implementing it can be foun in [5, ]. The en prouct of the trajectory generator is a smooth trajectory (Xi, Y i ) for the robots to follow that is calculate in real time as the they move between waypoints. EXPERIMENTAL APPARATUS Experiments were conucte in the Multi-AGent Intelligent Coorinate Control (MAGICC) Laboratory at Brigham Young University. The lab facility consists of five two-wheele, mobile robots shown in Figure 5. Each robot is equippe with a Pentium grae PC processor an is connecte via a wireless LAN to the other robots an host PC computers in the lab. The host an robot computers use the operating system. Given the relatively slow ynamics of the robots, is aequate to provie the soft realtime capabilities neee for controlling the robots. Robot positions are etermine using a vision system with an overhea camera. Encoer measurements from the robot rive wheels are also utilize to reuce the effects of noise in the vision ata. The robot fiel is 5 m square. 5 CONTROL IMPLEMENTATION The cooperative control algorithms escribe previously an low-level tracking controllers require for simultaneous target intercept were implemente on the MAGICC Lab host an target computers. Each computer runs uner the operating system. Each controller utilizes the MAGICC Mobile Robot Toolbox () [] that runs uner Simulink. provies software tools (e.g., evice rivers, timing routines, TCP/IP sockets, controller software) for rapi implementation of mobile robot control algorithms. Figure 6 shows how the cooperative control architecture was implemente. Camera Vision target HP esktop Pentium Point Tracker robot, target, threat positions es traj Robot target PC Pentium Tracking controller Host HP esktop Pentium CF calc Traj gen act traj es traj Intercept Mgr CF calc Traj gen act traj Robot target PC Pentium Tracking controller CF calc Traj gen es traj act traj Robot target PC Pentium Tracking controller Figure 6: Control architecture implementation. Figure 5: BYU MAGICC Lab robots. To emulate UAVs, the robot velocities were constraine to be between.96 an.7 m/sec for the results reporte here. These slow velocities maintain the time scaling between the robot workspace an a typical UAV battle area. These robot velocities correspon to a UAV flying between. an.9 km/sec (7 to mph) in a 6 km by 6 km battle area. The heaing rate of the robots was limite to be less than eg/sec. Control computations are istribute among the host an robot computers. Because position information for the robots, targets, an threats comes from a global vision system to the host computer, most of the cooperative control computations are carrie out on the host. In future implementations, position information will be passe own to the robots an control computations will be carrie out on the robots irectly. Currently, trajectory information an coorination functions are compute for each robot inepenently on the host computer. Coorination function information is utilize to etermine the team-optimal trajectory for each robot. Desire trajectory information is passe own to each robot. On each robot, a tracking controller is implemente to follow the esire trajectory. Actual robot state information is passe from the robot up to the host. All control computations on the robots an host are carrie out at Hz.

5 6 RESULTS AND DISCUSSION Three MAGICC robots were programme to execute the simultaneous intercept task escribe earlier. Figures 7 through show the trajectories trace out by each robot. The threats to be avoie are inicate by small re ots. Pop-up threats are marke by cyan-colore ots. The targets are marke by stars. The thin lines inicate the esire waypoint paths for each robot, while the actual paths traverse by the robots are marke by bol lines. Figure 7 shows the initial trajectories of the robots proceeing the etection of the first pop-up threat by robot. Referring to the esire waypoint paths, it can be seen that robot takes a fairly irect path through the threats to its target. In orer to ensure simultaneous TOT, robot takes an inirect route that is safe, but longer in length than other more irect options. The initial jog in the path of robot accomplishes this same objective robot robot robot Figure 8: Robot trajectories secon pop-up robot robot robot up threat, etecte by robot, is also shown in Figure 9. Final paths to each of the targets are shown in Figure. In avoiing the thir pop-up threat, the path of robot is lengthene significantly. To enable simultaneous TOT, the path of robot is lengthene slightly with the inclusion of an aitional waypoint near the target. Figure clearly shows the robots.5.5 robot robot robot Figure 7: Robot trajectories first pop-up..5 Upon etecting the pop-up threat, the cooperative path planning algorithm is execute to etermine new waypoint paths that avoi both the existing an newly iscovere threats. Figure 8 shows the paths planne in response to the first pop-up threat. The paths for robots an are unchange, while the path for robot avois the pop-up threat. Figure 8 also shows the etection of a secon pop-up threat by robot. Waypoint paths avoiing this secon pop-up threat are shown in Figure 9. A thir pop Figure 9: Robot trajectories thir pop-up. 5

6 intercepting their targets simultaneously. range to target (m) robot robot robot Figure : Robot trajectories over targets. robot robot robot The effects of the computational latency involve in the cooperative path planning can be seen in Figure. Upon etection of a pop-up threat, the cooperative path planning algorithm is execute. In its present implementation, the algorithm takes approximately 5 to secons to run. During the execution of the path planning algorithm, the robots continue to move accoring to the last motor commans they receive. Position information is not acquire uring the path planning phase. The white gaps in the robot trajectories of Figure inicate the motion of the robots uring the execution of the cooperative path planning algorithm. The faster the nominal spee of the robots, the greater the egraation of the system performance ue to computational latency. Experiments performe at three times the spee of those presente here showe significant egraation that resulte in threats being hit an large ifferences in TOT. If the spacing of the threats ivie by the spee of the robots is comparable to the computational latency, then latency will negatively affect the performance of the system. It is anticipate that this latency coul be reuce significantly by more effectively istributing the computation among the robots, improving the coing of the algorithms, an by porting the algorithms to a compile programming language. Furthermore, effective strategies for mitigating the egraing effects of computational latency can be evelope. Figure emonstrates that the robots intercepte their respective targets at the same time. The smooth bumps in the range curve for robot at secons an robot at secons an secons inicate that they move away from their targets momentarily to enable the team cooperation objective: simultaneous intercept. The convergence of the ranges to zero near 9 secons emonstrates that this objective is achieve. The abrupt rops in range that occur at 5,, an secons inicate the change in range that occurre uring the computation of cooperative path planning algorithm. The time variable oes not inicate true real time in that the time clock i not avance while the cooperative path planner was executing time (sec) 7 CONCLUSIONS Figure : Robot range to target. This paper presents results for experiments in multi-robot cooperative interception of preassigne targets. Results inicate that the propose cooperative path planning strategy is a promising approach for cooperative timing problems requiring implementation in real-time. Results also show that the metho can reaily accommoate pop-up threats provie that the effects of computational latency are small relative to the specifie robot velocities an istances between threats. 6

7 ACKNOWLEDGMENTS This work was supporte in part by Air Force Office of Scientific Research Grant No. F REFERENCES [] F. Giuletti, L. Pollini, an M. Innocenti, Autonomous formation flight, IEEE Control Systems Magazine, vol., pp. 5 5, December. [] C. Schumacher, Nonlinear control of multiple UAVs in formation flight, in Proc. of the AIAA GN&C Conf., August. [] S. Singh, M. Pachter, P. Chanler, S. Bana, S. Rasmussen, an C. Schumacher, Inputoutput invertibility an sliing moe control for close formation flying, in Proc. of the AIAA GN&C Conf., August. [] P. Chanler, M. Pachter, D. Swaroop, J. Fowler, J. Howlett, S. Rasmussen, C. Schumacher, an K. Nygar, Complexity in UAV cooperative control, in Proc. of the ACC, June. [] T. McLain, P. Chanler, an M. Pachter, A ecomposition strategy for optimal coorination of unmanne air vehicles, in Proc. of the ACC, pp. 69 7, June. [] D. Eppstein, Fining the k shortest paths, SIAM Journal of Computing, vol. 8, no., pp , 999. [] E. Anerson an R. Bear, An algorithmic implementation of constraine extremal control for UAVs, in Proc. of the AIAA GN&C Conf., August. [] J. Kelsey, MAGICC multiple robot toolbox (): A Simulink-base control an coorination toolbox for multiple robotic agents, Master s thesis, Brigham Young University, Provo, Utah, April. [] F. Giuletti, L. Pollini, an M. Innocenti, Formation flight control: A behavioral approach, in Proc. of the AIAA GN&C Conf., August. [5] R. Bear, T. McLain, M. Goorich, an E. Anerson, Coorinate target assignment an intercept for unmanne air vehicles, IEEE Transactions on Robotics an Automation,. Accepte for publication. [6] K. Nygar, P. Chanler, an M. Pachter, Dynamic network optimization moels for air vehicle resource allocation, in Proc. of the ACC, pp , June. [7] P. Chanler, M. Pachter, K. Nygar, an D. Swaroop, Cooperative Control an Optimization, ch. Distribute Cooperation an Control for Autonomous Air Vehicles. Kluwer,. [8] C. Schumacher, P. Chanler, an S. Rasmussen, Task allocation for wie area search munitions via network flow optimization, in Proc. of the AIAA GN&C Conf., August. [9] T. McLain, P. Chanler, S. Rasmussen, an M. Pachter, Cooperative control of UAV renezvous, in Proc. of the ACC, pp. 9, June. 7