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.

翻译：B样条能够通过有限约束实现时间连续的可行性检验。对于需要无碰撞且动态可行的轨迹的运动规划应用，约束条件需适用于整个轨迹。现有依赖梯度优化的运动规划器采用时间缩放策略实现逐渐缩小的规划时域。这类方法既无法保证递归可行性，也无法在不同时间尺度上同时到达两个终端流形分量。本文针对现有方法的缺陷提出非线性优化问题，将样条断点纳入优化变量。通过实施样条基函数间的变换，实现了稀疏问题公式化。所提出的断点移除策略使系统能够收敛至终端流形。超车场景下的评估结果表明，断点数量对解质量及优化耗时具有显著影响。