Abstract: In logistics transportation scenarios, unmanned vehicle formations require safe shape-shifting to navigate urban congested areas or avoid obstacles. However, existing trajectory planning methods for formation switching have significant shortcomings in dealing with complex environments, including low computational efficiency, suboptimal global solutions, and local optima entrapment. To address these challenges, in this paper a formation-switching trajectory planning method integrating Bézier curves with topological planning was proposed. First, a complex plane path function integration and graph search algorithm generated multiple topologically distinct candidate paths. Subsequently, Bézier curves modelled formation trajectories while minimum spacing constraints constructed a collision-avoidance objective function. Optimization along geodesic lines on the Bézier manifold ensured collision prevention between vehicles and obstacles. Finally, cost optimization across topological path classes yielded globally optimal trajectories. Simulations demonstrate that in elliptical obstacle scenarios, compared to traditional polynomial methods, Olfati-Saber algorithms, and model predictive control, the proposed method reduces average computation time by 50% while guaranteeing collision-free trajectories throughout navigation.