Geometric Optimisation of Unmanned Aerial Vehicle Trajectories in Uncertain Environments

Abstract

The problem of efficient trajectory optimisation for Unmanned Aerial Vehicles (UAVS) in dynamic and constrained environments is one where energy efficiency, spatial coverage, and path smoothness need to be balanced. The existing methods, namely RRT*, A*, and Dijkstra, are popular but generally heuristic and do not provide globally optimal solutions. They face significant limitations while dealing with complex geometries, dynamic obstacles, and multi-objective requirements. These challenges call for a mathematically sound framework that seamlessly integrates convex analysis and computational geometry to provide an optimal trajectory planning framework. This research work introduces a convex optimisation framework for UAV trajectory planning which unifies multiple objectives, like minimising energy consumption, maximising spatial coverage, and ensuring the smoothness of the path, into a single convex objective function. More importantly, it indicates that obstacle dynamics and uncertain environmental conditions are handled better by it, so it is relatively easier for safe and efficient navigation. Proven to converge faster and with higher precision than RRT*, A*, and Dijkstra, the approach proposed here enjoys intrinsic convex properties, which ensure global optimality. Qualitative measurements show the efficiency of the proposed framework. The result is energy efficiency of 90%, with 92% coverage, 98% constraint satisfaction, and 95% path smoothness, which is 15-25% better on all metrics than traditional approaches can offer. By bridging between theory in convex optimisation and practice for solving multi-objective problems in a dynamic setting, this study provides a more robust solution for UAV trajectory planning.