Computationally Effective Approximation of Integral Curves Lengths for Target Assignment of Mobile Robots Moving in Task-Space with Obstacle

The paper proposes a new approach to distributed target assignment for a group of robots operating in a space with a circular obstacle. The simple approach of comparing functions of Cartesian distances, which works well in free space, does not give good results if a static obstacle exists. The authors aimed to find an approach that is as computationally effective as possible and yet produces a sufficiently good result. The proposed solution makes use of city block distance expressed in a specific reference frame that depends on the mutual positioning of the robot, the target, and the obstacle. In addition to presenting the idea, the results of numerical simulations were given to confirm the effectiveness of the proposed algorithm.