Generation of Window-Traversing Flyable Trajectories Using Logistic Curve

This work considers point-to-point flyable trajectory generation through constrained planar regions referred as windows. A four parameter logistic curve trajectory planning tool is proposed for generating feasible trajectories that (i) connect the given initial and final positions with (ii) smooth bounded velocity and acceleration variations (flyability), and (iii) pass through the prescribed windows. A two-step approach is proposed, first narrowing down the search space to a restricted set in six dimensions, parameterizing a variety of trajectories that satisfy the derived closed-form flyability conditions. The final solutions are found by sampling that set using closed-form window traversal conditions. Numerical examples are presented to analyze the performance of the proposed approach in terms of number of solutions and computation time.