具有渐近帕累托最优性的多目标运动动力学运动规划

中文摘要 AI 辅助

在本文中，我们解决了运动动力学约束下系统的多目标运动规划挑战。我们考虑三类问题：（i）字典序优化，目标按严格优先级顺序最小化；（ii）约束优化，主要目标在其余成本有界的情况下最小化；（iii）帕累托前沿优化，目标是逼近竞争目标间所有最优权衡。首先表明多目标问题的现有成本标量化方法不能扩展到有正确性保证的连续域系统。然后提出基于稳定稀疏RRT（SST）算法的统一算法框架，其中每个见证邻域维护的单个代表被局部帕累托最优节点的代表集取代。由此产生三种不同算法：用于字典序最小化的lexSST、用于约束优化的coSST和用于帕累托前沿逼近的poSST。我们为算法的完备性和最优性提供了理论保证，并通过广泛的实证评估证明了它们的有效性。

英文摘要

In this paper, we address the challenge of multi-objective motion planning for systems under kinodynamic constraints. We consider three problem classes: (i) lexicographic optimization, in which objectives are minimized according to a strict priority ordering, (ii) constrained optimization, in which a primary objective is minimized subject to bounds on the remaining costs, and (iii) Pareto front optimization, in which the goal is to approximate the full set of optimal trade-offs among competing objectives. We first show that established cost scalarization methods for multi-objective problems cannot be extended to continuous-domain systems with correctness guarantees. Then, we propose a unified algorithmic framework built upon the Stable Sparse-RRT (SST) algorithm, in which the single representative maintained at each witness neighborhood is replaced by a representative set of locally Pareto-optimal nodes. This structure gives rise to three distinct algorithms: lexSST for lexicographic minimization, coSST for constrained optimization, and poSST for Pareto-front approximation. We provide theoretical guarantees for the completeness and optimality of our algorithms and demonstrate their effectiveness through extensive empirical evaluations.

发表机构

• University of Colorado Boulder（科罗拉多大学博尔德分校）

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