Multi-Objective Kinodynamic Motion Planning with Asymptotic Pareto Optimality

2026-07-16

AI Summary

This work addresses multi-objective motion planning for systems subject to dynamic constraints by proposing a unified framework based on Stable Sparse-RRT (SST), encompassing lexicographic optimization, constrained optimization, and Pareto front approximation. The approach introduces three algorithmic variants—lexSST, coSST, and poSST—by replacing the single sample within each witness neighborhood with a locally Pareto-optimal set of nodes. This method is the first to simultaneously guarantee both completeness and asymptotic Pareto optimality in continuous dynamical systems, thereby overcoming the limitations of conventional scalarization strategies. Theoretical analysis establishes the correctness and convergence properties of the proposed algorithms, while empirical evaluations demonstrate their effectiveness in efficiently approximating multi-objective optimal solutions in complex dynamical environments.

Abstract

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.

Problem

• multi-objective
• kinodynamic
• motion planning
• Pareto optimality
• constrained optimization

Innovation

• multi-objective motion planning
• kinodynamic constraints
• Pareto optimality
• Stable Sparse-RRT
• asymptotic completeness