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

Time-Optimal Trajectory Planning in Highway Scenarios using Basis-Spline Parameterization