Waypoints Matter: A Systematic Study for Sampling-Based Trajectory Planning

Figure 1: Waypoint selection strategies : Uniform sampling, RDP/RDP*, and Curvature-adaptive sampling. For RDP, \blacktriangle denotes the plain simplification and \blacksquare the augmented RDP* variant, which enforces a maximum inter-waypoint distance d_{s} by inserting additional waypoints ( \square ). For curvature-adaptive sampling, ✖ uses a centered window while \bigstar uses a forward window, biasing waypoints upstream of high-curvature segments.

Figure 5: Curvature-adaptive sampling performance across maps . For this method, the sensitivity parameter \alpha (how much curvature affects the waypoint spacing) is varied from 5 to 40 in increments of 2.5, while d_{s} spans from 2\text{\,}\mathrm{m} to 10\text{\,}\mathrm{m} in increments of 1\text{\,}\mathrm{m} . Color scales are shared between the two smoothing modes, centered-window ( \gamma=1 ) and forward-window ( \gamma=0 ), for direct comparison. The forward window consistently shifts performance toward better reliability and candidate yield; the top configurations under J are at \gam

Figure 2: Systematic evaluation framework. (A) Scenario selection : five CommonRoad maps span road layouts of increasing geometric complexity. (B) Planning poses : from each map we extract a fixed-length corridor along the centerline and define elliptical sampling regions along it; within each ellipse we draw ego states with uniformly sampled positions (b.1) and Gaussian perturbations to heading and curvature (b.2), with curvature magnitude encoded from purple ( |\kappa|=0 ) to yellow ( |\kappa|=0.25 ). (C) Evaluation : for each ego state, waypoint configuration, and map, the trajectory genera

Figure 3: Uniform sampling performance across maps . The waypoint separation distance d_{s} is varied from 0.5\text{\,}\mathrm{m} to 10\text{\,}\mathrm{m} in increments of 0.25\text{\,}\mathrm{m} . For each variation, columns report (left to right): total failed planning queries, mean valid candidates, mean trajectory length, and mean diversity; aligned with f_{1} – f_{4} , these contribute 70%, 20%, 8%, and 2% respectively to the weighted score J shown in the last column. Brighter cells indicate more desirable values. The bold entry marks the best J ; \boldsymbol{\oplus} indicates the top-3 c

Figure 4: RDP and RDP* performance across maps . Plain RDP ( \blacktriangle ) and the augmented RDP* variant ( \blacksquare ) are evaluated as a function of simplification tolerance \varepsilon , swept from 0.01 to 1.00 m; for RDP*, gap-filling is applied at d_{s}\in\{2,3,5,7\} m. Columns and color convention follow Fig. 3 . Color scales are set independently for RDP and RDP* due to their markedly different metric ranges. RDP* consistently outperforms plain RDP across all metrics except trajectory length; within RDP*, the best configurations favor large d_{s} and moderate to high \varepsilon ,