Path Generation Using η⁴-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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">η⁴</tex></formula> -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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">η⁴</tex> </formula> -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 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">η⁴</tex></formula> -spline are established. An example on a parking maneuver of the articulated vehicle is presented and the pertinent optimal path planning is also discussed.