Analytic chance constraints for the robust guidance of autonomous parafoils

Abstract

Autonomously guided parafoil systems can deliver supplies and aid to remote, geographically diverse locations, while providing important safety and logistical advantages over ground-based transportation methods. A key challenge facing modern airborne delivery systems, such as parafoils, is the ability to accurately and consistently deliver supplies into difficult, complex terrain. Parafoil guidance algorithms must be able to generate feasible trajectory solutions to the target location within highly constrained terrain environments and from a wide range of initial conditions. Robustness is critical for successful payload delivery in the presence of uncertain atmospheric wind disturbances. This thesis presents two online trajectory planning algorithms for autonomous parafoil guidance in complex terrain and wind environments. These -algorithms are capable of operating from arbitrary initial conditions, including altitude, and are robust to wind disturbances that may be highly dynamic throughout terminal descent. The first algorithm, known as Analytic CC-RRT, builds upon the framework of chance-constrained rapidly-exploring random trees (CC-RRT). This planner enables fast incremental trajectory construction in cluttered, non-convex environments, while using chance constraints to ensure probabilistic feasibility. The designed cost-to-go function prioritizes target accuracy and upwind landings through the selection of partial paths that intelligently consider current and reachable future states. A trained multi-class wind uncertainty model is introduced to classify and anticipate the effect of future wind disturbances online. Utilizing this model, robustness to wind variations is achieved via a novel analytic uncertainty sampling technique, allowing the probability of constraint violation to be efficiently evaluated against arbitrary and aggressive terrain. The second algorithm, known as CC-BLG, incorporates the Analytic CC-RRT proactive wind model and uncertainty sampling technique into the optimized Band- Limited Guidance (BLG) framework. Through the design of a novel risk-based objective function, CC-BLG trajectories efficiently balance the parafoil performance metrics of landing accuracy and landing speed with the risk of off-nominal terrain collisions caused by future wind disturbances. Proposed extensions to the analytic uncertainty sampling technique are shown to yield enhanced planning robustness by refining the estimation of trajectory risk. Multi-phase CC-BLG path planning enables initialization of parafoil terminal guidance from potentially high altitudes, while discrete reachability set approximation is used to maintain robust obstacle avoidance over disjoint planning horizons. Extensive Monte Carlo simulation analysis demonstrates that the Analytic CCRRT and CC-BLG algorithms achieve significant improvements in mean and worst-case landing accuracy within complex terrain scenarios relative to the state-of-the-art Band-Limited Guidance (BLG) algorithm. Flight test experiments conducted with a full-scale UltraFly parafoil system confirm that the more computationally efficient CC-BLG algorithm is capable of robust parafoil guidance and precision landings subject to real-world testing conditions, hardware limitations, and challenging terrain environments.