Continuous-Curvature Path Generation Using Fermat's Spiral for Unmanned Marine and Aerial Vehicles

A novel methodology in which the Fermat's spiral (FS) is used to smooth the polyline path for generating curvature-continuous parametric paths in the horizontal plane is presented. The FS curve has the characteristic that its curvature can change continuously from zero, which allows it to be connected with polyline lines smoothly. That is, the shortcoming of the curvature discontinuity at the point of connection between the circular and line when generating dubins paths is overcome. And compared to clothoids, the calculation of the FS curve is much smaller. How to generate curvature-continuous paths using FS is illustrated in details.