Stream Function-Based Navigation for Complex Quadcopter Obstacle Avoidance

Abstract: This article presents a novel stream function-based navigational control system for obstacle avoidance, where obstacles are represented as two-dimensional (2D) rigid surfaces in inviscid, incompressible flows. The approach leverages the vortex panel method (VPM) and incorporates safety margins to control the stream function and flow properties around virtual surfaces, enabling navigation in complex, partially observed environments using real-time sensing. To address the limitations of the VPM in managing relative distance and avoiding rapidly accelerating obstacles at close proximity, the system integrates a model predictive controller (MPC) based on higher-order control barrier functions (HOCBF). This integration incorporates VPM trajectory generation, state estimation, and constraint handling into a receding-horizon optimization problem. The 2D rigid surfaces are enclosed using minimum bounding ellipses (MBEs), while an adaptive Kalman filter (AKF) captures and predicts obstacle dynamics, propagating these estimates into the MPC-HOCBF for rapid avoidance maneuvers. Evaluation is conducted using a PX4-powered Clover drone Gazebo simulator and real-time experiments involving a COEX Clover quadcopter equipped with a 360 degree LiDAR sensor.