Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Trajectory Generation for an On-Road Autonomous Vehicle



John A. Horst, Anthony J. Barbera


We describe an algorithm that generates a smooth trajectory (position, velocity, and acceleration) for a non-holonomic vehicle autonomously navigating within the constraints of lanes in a road. The technique models both vehicle paths and lane segments as straight line segments and circular arcs for mathematical simplicity and elegance. We use the following approach. Develop the path in an idealized space, warp the path into real space and compute path length, generate a one-dimensional trajectory along the path length that achieves target speeds and positions, and finally, warp, translate, and rotate the one-dimensional trajectory points onto the path in real space. The algorithm moves a vehicle in lane safely and efficiently within speed and acceleration maximums. We also describe how the algorithm functions in the context of other autonomous driving functions within a carefully designed vehicle control hierarchy.
NIST Interagency/Internal Report (NISTIR) - 7262
Report Number


autonomous vehicle, on-road, on-road autonomous vehicle, radial warping, trajectory generation, vehicle trajectory generation


Horst, J. and Barbera, A. (2006), Trajectory Generation for an On-Road Autonomous Vehicle, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed July 16, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created June 26, 2006, Updated November 10, 2018