The capacity for autonomous functionality serves as the fundamental ability and driving force for the cross-generational upgrading of unmanned aerial vehicles (UAVs). With the disruptive transformation of artificial intelligence technology, autonomous trajectory planning based on intelligent algorithms has emerged as a key technique for enhancing UAVs' capacity for autonomous behavior, thus holding significant research value. To address the challenges of UAV trajectory planning in complex 3D environments, this paper proposes a multi-UAV cooperative trajectory-planning method based on a Modified Cheetah Optimization (MCO) algorithm. Firstly, a spatiotemporal cooperative trajectory planning model is established, incorporating UAV-cooperative constraints and performance constraints. Evaluation criteria, including fuel consumption, altitude, and threat distribution field cost functions, are introduced. Then, based on its parent Cheetah Optimization (CO) algorithm, the MCO algorithm incorporates a logistic chaotic mapping strategy and an adaptive search agent strategy, thereby improving the home-returning mechanism. Finally, extensive simulation experiments are conducted using a considerably large test dataset containing functions with the following four characteristics: unimodal, multimodal, separable, and inseparable. Meanwhile, a strategy for dimensionality reduction searching is employed to solve the problem of autonomous trajectory planning in real-world scenarios. The results of a conducted simulation demonstrate that the MCO algorithm outperforms several other related algorithms, showcasing smaller trajectory costs, a faster convergence speed, and stabler performance. The proposed algorithm exhibits a certain degree of correctness, effectiveness, and advancement in solving the problem of multi-UAV cooperative trajectory planning.