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 eta(4)-spline. Using this spline, generation and shaping of smooth feasible paths ismade possible as well as the transfer between arbitrary dynamic configurations of the articulated vehicle. The eta(4)-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 eta(4)-spline are established. An example on a parking maneuver of the articulated vehicle is presented and the pertinent optimal path planning is also discussed. Note to Practitioners-The general motivation of this paper is the motion automation of a truck and trailer vehicle. Specifically, given two arbitrary, dynamic configurations of the articulated vehicle the problem is to provide an efficient and flexible method to bring the automated vehicle from the initial configuration to a final desired configuration by means of feed forward control in such a way that: 1) control signals are smooth (i.e., truck's velocity and steering angle with their derivatives are continuous functions) and 2) the automated vehicle follows a Cartesian path that can be freely and easily shaped by adjusting or choosing parameters with clear geometrical meaning. The paper provides a solution by developing and presenting a new, parameterized, polynomial curve: the eta(4)-spline. Using this spline or a composition of these splines, a variety of path generation problems can be addressed also including nonconventional "on the fly" planning, such as, e. g., a parking maneuver starting when the articulated vehicle is operating or moving. With future research, it will be possible to efficiently integrate the use of the eta(4)-spline into a global motion planning framework so as to take into account both obstacle avoidance and technical constraints given by bounds on steering and trailer angles. To this end, the authors make available to colleagues and researchers the detailed, closed-form expressions of the eta(4)-spline.