Feasible Dubins Paths in Presence of Unknown, Unsteady Velocity Disturbances

The ability to compensate for disturbances when following a Dubins path can be improved by artificially increasing the turn radius used in path planning. Monte Carlo simulations suggest that these feasible Dubins paths minimize the mean, final crosstrack error when the path is followed using a standard guidance algorithm. Furthermore, the simulation results indicate that there is no appreciable benefit in planning paths with a turn radius, the planning radius marks the knee in the cross-track error curve for a steady disturbance. The cost of using the (suboptimal) feasible turn radius for path planning is an increase in the nominal path length and travel time. This tradeoff can be illustrated, for a given final course angle, using a trade-space plot that indicates the relative path lengths of the ideal and feasible Dubins paths. These trade-space plots can be helpful in selecting a desired end state because they highlight regions where a given final state will result in a large increase in the relative path length.