A heterogeneous robot system is composed of an unmanned aerial vehicle(UAV) and an unmanned ground vehicle(UGV). By cooperating with each other to complete continuous monitoring tasks, the work efficiency can be improved and the problem of insufficient endurance capacity of the UAV can be solved. In this heterogeneous robot system, the UGV can recharge energy for the UAV to ensure the continuity of the monitoring task. Since periodic monitoring paths are prone to leakage of monitoring regularity information, it is significant to improve the randomness of the UAV's monitoring path. Aiming at this problem, this paper introduces the Gini impurity index to evaluate the randomness of the monitoring path. With the optimization goal of minimizing the weighted sum of normalized visit interval time of target nodes and their Gini impurity, a continuous monitoring path planning model of the UAV&UGV cooperative system is established,which improves the privacy of monitoring path. Finally, the ant colony algorithm is used to optimize the UAV's monitoring path and the UGV's energy supply path, which verifies the validity and rationality of the model. Compared with other algorithms, it is proved that the ant colony algorithm has faster search speed and operation efficiency.