  Within the context of in-field path planning and under the assumption of
nonholonomic vehicle models this paper addresses two tasks: smoothing of
headland path edges and smoothing of headland-to-mainfield lane transitions.
Both tasks are solved by a two-step hierarchical algorithm. The first step
differs for the two tasks generating either a piecewise-affine or a Dubins
reference path. The second step leverages a transformation of vehicle dynamics
from the time domain into the spatial domain and linear programming. Benefits
such as a hyperparameter-free objective function and spatial constraints useful
for area coverage gaps avoidance and precision path planning are discussed. The
method, which is a deterministic optimisation-based method, is evaluated on a
real-world field solving 3 instances of the first task and 16 instances of the
second task.
