This study addresses the task assignment problem with robot coalitions, as encountered in practical scenarios, such as multiplayer reach-avoid games. Unlike the classical assignment problem where a single robot performs each task, the problem considered here involves tasks that require execution by a robot coalition consisting of two robots. This task assignment problem is a special instance of 3-set packing problem, which is known to be nondeterministic polynomial time (NP)-hard. We introduce the concept of$\epsilon$-coalition-competitive equilibrium ($\epsilon$-CCE) to characterize a kind of approximate solution that offers guaranteed performance. A distributed auction algorithm is developed to find an$\epsilon$-CCE within a finite number of iterations. In addition, several enhancements have been implemented to adapt the auction algorithm for practical applications where the task assignment problem may vary over time. Numerical simulations demonstrate that the distributed algorithm achieves satisfactory approximation quality.

This paper investigates autonomous navigation for mobile robots with a low-cost monocular camera. The main challenge lies in: i) how to accurately detect prior unseen obstacles and acquire obstacles position from monocular images without depth information, and ii) how to get the constraints for path planning to generate safe and stable path for the robot. To accurately locate surrounding obstacles using only a monocular camera, we adopt a weakly-supervised semantic segmentation network trained from LIDAR data and perform inverse perspective transformation based on ground plane constraint. Meanwhile, to reduce segmentation noise, we establish a probability occupancy map based on the distance between robot and obstacles. For path generations, we present a novel search-and-optimization based planning approach to get boundary constraints in Frenet frame and generate stable local path with consecutive image inputs. In the simulation, segmentation Intersection over Union (IoU) of the drivable area achieves more than 99% and the average mapping accuracy is less than 10cm, showing feasibility and robustness of our navigation scheme.