Geometric methods for aircraft planning and control

Path planning and control of autonomous aircraft is a critical problem, particularly under conditions of model and sensor uncertainty. This paper presents a hierarchical control architecture that integrates geometric and probabilistic methods to address these challenges. The proposed framework combines a high-level controller, a low-level controller, and an observer, leveraging Lie group theory for geometric modeling. The high-level controller formulates the planning problem as a Markov Decision Process (MDP), solved using Monte Carlo Tree Search (MCTS) to generate reference trajectories while avoiding no-fly zones. The low-level controller exploits the relationship between tangent space velocities and left-trivialized velocities in the Lie algebra to produce control commands. State estimation is achieved using a second-order optimal minimum-energy filter formulated on Lie groups, ensuring robust performance under noisy measurements. Simulation results show the efficacy of the proposed architecture in guiding an aircraft from a start point to a target while satisfying operational constraints.