Abstract
Trajectory optimization in multi-vehicle scenarios faces challenges due to its non-linear, non-convex properties and sensitivity to initial values, making interactions between vehicles difficult to control. In this paper, inspired by topological planning, we propose a differentiable local homotopy invariant metric to model the interactions. By incorporating this topological metric as a constraint into multi-vehicle trajectory optimization, our framework is capable of generating multiple interactive trajectories from the same initial values, achieving controllable interactions as well as supporting user-designed interaction patterns. Extensive experiments demonstrate its superior optimality and efficiency over existing methods. We will release open-source code to advance relative research.