As omnidirectional UAVs become increasingly prevalent, computationally efficient path planning algorithms are required to facilitate their autonomous traversal of dynamic environments. This thesis presents a real-time local path planning algorithm for an omnicopter, adapted from the Dynamic Window Approach into a 6D-DWA implementation. To ensure computational efficiency, the local path planner incorporates environment voxelisation, a 10-sphere omnicopter structure approximation, and adaptive velocity sampling. The avoidance of dynamic obstacles, detected via depth camera, is facilitated through context-aware 6D-DWA weight adjustments and a separate integrated fast-evasion strategy. Simulation testing in Gazebo demonstrates that the 6D-DWA is a feasible local planning solution, consistently performing below the 0.2 s real-time threshold. Future research into algorithm hybridisation may further mitigate the system's limited foresight and enhance the replanning capabilities.