<p>In this paper, a framework for solving cooperative trajectory optimization problems is proposed. Unlike some cooperative trajectory planning strategies that need to determine cooperative parameters in advance, the cooperative trajectory optimization problem is directly solved in a unified multi-model framework. This not only allows for the rapid acquisition of cooperative trajectories but also ensures that they are optimal when an overall objective function is defined. In the proposed framework, cooperative constraints are considered individually, and the trajectory optimization problem is first discretized into multiple Nonlinear program (NLP) problems using the direct collocation method. Subsequently, new unified NLP variables and a combined Jacobian matrix are designed to form a multi-model problem that contains all vehicles, thereby solving the cooperative trajectory optimization problem as a unified NLP problem. Furthermore, a fast generation method for the multi-model Jacobian matrix is designed to improve solving efficiency, and the optimality verification conditions are derived to assess the optimized results. Finally, two numerical examples involving homogenous and heterogeneous coordination tasks, are solved to demonstrate the feasibility of the framework. The results are consistent with theoretical analysis results, confirming the effectiveness of cooperative trajectory optimization.</p>