Sequential Convex Programming with Filtering-Based Warm-Starting for Continuous-Time Multiagent Quadrotor Trajectory Optimization

Abstract

Optimizing the trajectories of multiple quadrotors in a shared space is a core challenge in various applications. Many existing trajectory optimization methods enforce constraints only at the discretization points, leading to violations between discretization points. They also often lack warm-starting strategies for iterative solution methods such as sequential convex programming, causing slow convergence or sensitivity to the initial guess. We propose a framework for optimizing multiagent quadrotor trajectories that combines a sequential convex programming approach with filtering-based warm-starting. This framework not only ensures constraint satisfaction along the entire continuous-time trajectory but also provides an online warm-starting strategy that accelerates convergence and improves solution quality in numerical experiments. The key idea is to first transform continuous-time constraints into auxiliary nonlinear dynamics and boundary constraints, both of which are compatible with sequential convex programming. Furthermore, we propose a novel warm-starting strategy by approximating the trajectory optimization problem as a Bayesian state estimation problem. This approximation provides an efficient estimate of the optimal trajectories. We demonstrate the proposed framework on multiagent quadrotor trajectory optimization with collision avoidance constraints. Compared with benchmark methods, the proposed framework achieves not only continuous-time constraint satisfaction, but also reduces computation time by up to two orders of magnitude.