Analysis and Comparison of Clothoid and Dubins Algorithms for UAV Trajectory Generation

Abstract

The differences between two types of pose based UAV path generation methods clothoid and Dubins are analyzed in this thesis. The Dubins path is a combination of circular arcs and straight line segments; therefore its curvature will exhibit sudden jumps between constant values. The resulting path will have a minimum length if turns are performed at the minimum possible turn radius. The clothoid path consists of a similar combination of arcs and segments but the difference is that the clothoid arcs have a linearly variable curvature and are generated based on Fresnel integrals. Geometrically, the generation of the clothoid arc starts with a large curvature that decreases to zero. The clothoid path results are longer than the Dubins path between the same two poses and for the same minimum turn radius. These two algorithms are the focus of this research because of their geometrical simplicity, flexibility, and low computational requirements. The comparison between clothoid and Dubins algorithms relies on extensive simulation results collected using an ad-hoc developed automated data acquisition tool within the WVU UAV simulation environment. The model of a small jet engine UAV has been used for this purpose. The experimental design considers several primary factors, such as different trajectory tracking control laws, normal and abnormal flight conditions, relative configuration of poses, and wind and turbulence. A total of five different controllers have been considered, three conventional with fixed parameters and two adaptive. The abnormal flight conditions include locked or damaged actuators (stabilator, aileron, or rudder) and sensor bias affecting roll, pitch, or yaw rate gyros that are used in the feedback control loop. The relative configuration of consecutive poses is considered in terms of heading (required turn angle) and relative location of start and end points (position quadrant). Wind and turbulence effects were analyzed for different wind speed and direction and several levels of turbulence severity. The evaluation and comparison of the two path generation algorithms are performed based on generated and actual path length and tracking performance assessed in terms of tracking errors and control activity. Although continuous position and velocity are ensured, the Dubins path yields discontinuous changes in path curvature and hence in commanded lateral accelerations at the transition points between the circular arcs and straight segments. The simulation results show that this generally leads to increased trajectory tracking errors, longer actual paths, and more intense control surface activity. The gradual (linear) change in clothoid curvature yields a continuous change in commanded lateral accelerations with general positive effects on the overall UAV performance based on the metrics considered. The simulation results show general similar trends for all factors considered. As a result, it may be concluded that, due to the continuous change in commanded lateral acceleration, the clothoid path generation ...

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