Path generation using eta4-splines for a truck and trailer vehicle

Generation of high quality drive paths is a significant issue for automated wheeled vehicles. To achieve this aim for a truck and trailer vehicle, the paper proposes the use of a parameterized curve primitive, the eta4-spline. Using this spline, generation and shaping of smooth feasible paths is made possible as well as the transfer between arbitrary dynamic configurations of the articulated vehicle. The eta4-spline is a ninth order polynomial curve that can interpolate given Cartesian points with associated arbitrary unit tangent vector, curvature, and first and second derivatives of curvature. It depends on a set of eight (eta) parameters that can be freely chosen to modify the path shape without changing the interpolations conditions at the path endpoints. Completeness, minimality, and symmetry of the eta4-spline are established. An example on a parking maneuver of the articulated vehicle is presented and the pertinent optimal path planning is also discussed.