Multi-unmanned aerial vehicle trajectory planning is one of the most complex global optimum problems in multi-unmanned aerial vehicle coordinated control. Results of recent research works on trajectory planning reveal persisting theoretical and practical problems. To mitigate them, this paper proposes a novel optimized artificial potential field algorithm for multi-unmanned aerial vehicle operations in a three-dimensional dynamic space. For all purposes, this study considers the unmanned aerial vehicles and obstacles as spheres and cylinders with negative electricity, respectively, while the targets are considered spheres with positive electricity. However, the conventional artificial potential field algorithm is restricted to a single unmanned aerial vehicle trajectory planning in two-dimensional space and usually fails to ensure collision avoidance. To deal with this challenge, we propose a method with a distance factor and jump strategy to resolve common problems such as unreachable targets and ensure that the unmanned aerial vehicle does not collide into the obstacles. The method takes companion unmanned aerial vehicles as the dynamic obstacles to realize collaborative trajectory planning. Besides, the method solves jitter problems using the dynamic step adjustment method and climb strategy. It is validated in quantitative test simulation models and reasonable results are generated for a three-dimensional simulated urban environment.