Time-optimal motion planning for autonomous flight using spatial reformulation

Abstract

The advancement of Unmanned Aerial Vehicles (UAVs), particularly quadcopters, has facilitated their adoption in a wide range of applications, including search-and-rescue operations, surveillance, and agricultural automation. Among these, urban drone delivery has emerged as a key aspect of Urban Air Mobility (UAM), with the potential to revolutionize urban logistics by alleviating vehicular traffic congestion and reducing reliance on human labor in distribution networks. A critical challenge in drone delivery lies in ensuring efficient and reliable navigation within dense and complex urban environments. These environments are characterized by limited airspace, numerous static and dynamic obstacles, restricted no-fly zones, and rapidly changing conditions, all of which complicate motion planning. Furthermore, the constraints of limited battery capacity, coupled with the anticipated growth in demand, underscore the necessity of minimizing flight time to achieve operational efficiency and scalability. To address these challenges, this thesis proposes a time-optimal motion planning framework for drone delivery systems, specifically for quadcopters and cable-suspended quadcopter (CSPQ) systems. We present a complete system design with novel methodologies, with specific focuses on aspects that have been underexplored. Firstly, the mathematical models of both systems are developed. For the CSPQ system in particular, we investigate the integration of physics-based modeling with deep learning techniques, as conventional physics-based models fail to fully capture the complex, nonlinear behaviors of CSPQ systems, such as downwash on the payload and ground effects. Although this approach is not adopted in the subsequent framework, it lays the groundwork for enabling neural network-based models in motion planning. Secondly, we introduce an efficient global path planning method with a focus on homotopy paths, which are essential for subsequent trajectory optimization but have often been overlooked. Additionally, the effect of wind dynamics in urban environments on the global path is also considered. Thirdly, based on the predefined global path, we develop a novel path-parametric method for three key motivations: (1) it captures the natural progression along the path, (2) it integrates the geometric characteristics of the path, such as curvature and torsion into the dynamics, and (3) it transforms spatial constraints into convex formulations in the orthogonal components of the spatial states. We adopt a Gravity-Normal (GN) frame spatial reformulation method, which outperforms the conventional Frenet-Serret frame and Parallel-Transport frame in UAV scenarios. Subsequently, the GN frame allows us to define a flight corridor easily and intuitively, paving the way for optimal and safe trajectory optimization of the system. Lastly, we describe the full framework in detail, including the offline planning module arising from previous discussions and the online trajectory tracking module. This thesis presents extensive experimental results, comparative analyses, and a detailed description of the system setup. In conclusion, we reflect on the motivations driving each chapter, highlight the existing limitations in aerial autonomy development, and outline potential research directions informed by our experiences.