  Basis splines enable a time-continuous feasibility check with a finite number
of constraints. Constraints apply to the whole trajectory for motion planning
applications that require a collision-free and dynamically feasible trajectory.
Existing motion planners that rely on gradient-based optimization apply time
scaling to implement a shrinking planning horizon. They neither guarantee a
recursively feasible trajectory nor enable reaching two terminal manifold parts
at different time scales. This paper proposes a nonlinear optimization problem
that addresses the drawbacks of existing approaches. Therefore, the spline
breakpoints are included in the optimization variables. Transformations between
spline bases are implemented so a sparse problem formulation is achieved. A
strategy for breakpoint removal enables the convergence into a terminal
manifold. The evaluation in an overtaking scenario shows the influence of the
breakpoint number on the solution quality and the time required for
optimization.
