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ABSTRACT Implementation of Robot Formation Control and Navigation Using Real-Time Panel Method

Potential flows have inherent properties such as smooth streamlines which do not cross each others or the objects in the environment. Moreover, they do not suffer from the local minima problem to the same extend as the other potential functions methods. Therefore, they are suitable for collision free path planning and navigation in robots, ground and marine vehicles, or unmanned air vehicles (UAV’s). Realizing this potential, there have been recent investigations using potential flows. A method that uses stream functions to produce paths convenient for an aircraft-like vehicle is developed in [1]. They provide analytical solution for the case in which there is a single stationary or moving circular obstacle in the environment. In the case of multiple circular obstacles since analytical solution is not tractable, they treat each obstacle separately. The algorithm is tested on RoboFlag/Robocup experimental platform showing promising results. In [2] Sullivan et al. use similar procedure to develop a navigation algorithm for a group of flying UAV’s. In addition to the stream functions they use virtual spring forces to maintain a predefined formation for the robot group. In [3] Ye et al. discuss a similar procedure for a swarm of robots. The coordinated motion control for the robot swarm is guaranteed by using artificial inter-agent forces, while safe navigation is provided using stream functions augmented with repulsive potential functions based obstacle avoidance. Moreover, they discuss the stagnation point problem and a hydrodynamics based analytical solution is provided. In a consider a more realistic connectivity algorithm with different singular association rules and test it using simulation. In addition, a testbed for future experimental implementations is discussed. To the best of our knowledge the first work using panel method for robot navigation is the paper of Kim and Khosla [5]. There, the authors first build an artificial potential field using the flowlines found using panel method with harmonic functions. The authors use real shaped obstacles discretized with panels and sink or source singularities are placed at each panel to express the rigid boundary of the obstacles. The stagnation point problem is also stated and defined, and two solutions are suggested. After that, a control strategy for collision-free navigation of a nonpoint robot or a manipulator in this artificial field is developed. Also, two solutions are stated for the structural local minimum problem that occurs in mobile robots and manipulators unable to be considered as point robots. Another pioneering study on using potential flows as well as the panel method for robot or UAV navigation is the work by Zhang and Valavanis [6], [7]. In [6], panel method is used to generate a collision free path for mobile robots navigating in an uncertain obstacle filled 2-D environment. To minimize the complexity they fit simple larger convex polygons to the obstacles (which are not necessarily in the same shape as the obstacle). The panel method is applied to calculate the flow lines to form safe trajectories for the robots to reach the target. They consider also a dynamic environment in which at each instance the panel method is used to solve for the flow lines based on the data sensed from the environment and generate a sequence of way-points. The algorithm is tested using numerical simulations to generate the discrete waypoints and no implementation or consideration of low-level agent dynamics is done. In [7] the algorithm is extended to 3-D space. There, they transform arbitrary shaped obstacles using 24 simple convex polyhedrons to simpler shaped ones to simplify computational complexity. In a recent study, Uzol et al. [8] use panel method to develop a target tracking methodology for a swarm of UAV’s using unsteady streamline patterns in real environments. They use the map of a real city (from Google maps) but design the panels manually off-line. Obstacle avoidance is guaranteed by following the streamlines generated, while collision avoidance between the agents is provided by setting a repulsive singularity element at each agent. The algorithm is tested using numerical simulations. In the above studies only [1] considers implementation/testing on real robotic systems. Howeveri as mentioned above, they consider only circular obstacles. Similarly, the works in [5], [6], [7], and [8], which consider complex shaped obstacles and panel method do not consider implementation on real robotic system. This paper combines the ideas from the above studies to implement the potential flow concept on real robotic system composed of differentially driven non-holonomic robots. The robots navigate in an unknown environment and use their laser scanners for sensing and obstacle detection. Based on the sensed data the panel method is used to solve in real-time for the flow lines to generate safe path to the target. When the robots encounter new obstacles (which they were unable to detect before because they were too far or the obstacles were occluded by other objects/obstacles), they re-solve for the streamlines in real-time to re-plan their paths. Moreover, we use potential functions in order to keep cohesiveness or to achieve and keep a predefined formation in the group during the motion. The algorithm is implemented in a laboratory environment with real robots and real complex shaped obstacles. This work is build on an earlier work in [9] where implementation was performed on a different robotic setup under the assumption that the map of the environment is known a priori