Trajectory generation for an on-road autonomous vehicle

We describe an algorithm that generates a smooth trajectory (position, velocity, and acceleration at uniformly sampled instants of time) for a car-like 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, which we contrast with cubic spline approaches. We 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. The algorithm functions in the context of other autonomous driving functions within a carefully designed vehicle control hierarchy.