Multi-agent systems are integral parts of advanced robotic technologies, particularly in sweep coverage algorithms. This article proposes an approach to solve the sweep coverage problem of paths with uneven workload distribution and dramatically varying borders. Primarily, the workload uncertainty is addressed by optimal partitioning of the sweeping area through a path with fluctuating borders. To tackle the unavailability of borders to the following agents with second-order dynamics, two leaders, with virtual second-order ball-spring characteristics, are employed to adapt to the edges of the route and to optimally execute the partitioning. A major contribution of this paper is the calculation of the upper bound for the excess time of the sweep algorithm. Two scenarios are investigated to assess the practical efficiency of the proposed algorithm. Validity of the sweeping algorithm in presence of uncertainties was lastly observed.