SOURCE-LINKED INTELLIGENCE

Achieving Asymptotic Near-Optimality Without $δ$-Similarity

arXiv · AI, language, vision and robotics · article · Sep 3, 2026 · UTC

Sampling-based motion planning algorithms are a popular class of trajectory planning algorithm due to their speed in complex, high-dimensional environments and ability to handle kinodynamic constraints, specifically through the use of forward dynamics propagation. Many such planners claim to achieve asymptotic near-optimality by proving the almost sure sampling of trajectories that are close to an optimal trajectory in the state space, known as $δ$-similar trajectories. This paper shows that the proof behind asymptotic $δ$-similarity relies on an unstated assumption that $δ$-similar trajectory

Read original source ↗ Open in workspace

recordType

paper

region

Global