Continuous trajectory planning for non-convex utility functions using hybrid optimization

Efficient trajectory generation is essential for applications such as environmental monitoring using autonomous systems, where navigating complex, non-convex environments poses significant challenges. In this paper, we introduce a novel hybrid continuous optimization method that extends gradient techniques to continuous-time frameworks for trajectory planning in non-convex landscapes. The method combines adaptive step-size adjustments with momentum-based gradient techniques, enabling robust navigation through plateau regions and accurate convergence to optimized trajectories. We apply the method to drone trajectory optimization in environments modeled by Gaussian Mixture Models (GMMs), specifically focusing on wildfire monitoring in northern Mexico. The proposed approach generates smooth trajectories and achieves faster convergence when compared to traditional discrete and continuous methods without the hybrid adaptation. Simulation results showcase the method’s potential for broader applications in control systems and other domains requiring optimization in high-dimensional non-convex environments.