A novel method to generate three-dimensional paths for vehicles with bounded pitch and yaw

This paper presents a method for generating three-dimensional paths for a vehicle with a bounded maximum curvature in both yaw and pitch rotations. We build upon the two-dimensional time-optimal path generation for constant speed vehicles with bounded steering that produces the socalled Dubins curves. We formulate a similar problem in three-dimensional space and solve it with the additional constraints imposed by real systems such as the maximum vertical climbing angle of an underwater or aerial vehicle. We generate the paths by using simple geometric construction that allows for explicit curve representation that in turn allows for real-time implementation on any three-dimensional maneuvering vehicle.