Regret-Based Sampling of Pareto Fronts for Multiobjective Robot Planning Problems

Many problems in robotics seek to simultaneously optimize several competing objectives. A conventional approach is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the origin...

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Bibliographic Details
Published in:IEEE transactions on robotics Vol. 40; pp. 3778 - 3794
Main Authors: Botros, Alexander, Wilde, Nils, Sadeghi, Armin, Alonso-Mora, Javier, Smith, Stephen L.
Format: Journal Article
Language:English
Published: IEEE 2024
Subjects:
Cost function
Costs
Human-robot interaction
Motion and path planning
multi-objective optimization
optimization and optimal control
Planning
Robots
robust/adaptive control of robotic systems
Trajectory
Vectors
ISSN:1552-3098, 1941-0468
Online Access:Get full text
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Summary:Many problems in robotics seek to simultaneously optimize several competing objectives. A conventional approach is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multiobjective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Uniformly spaced weights are often inefficient and do not provide error bounds. We address the problem of computing a finite set of weights whose optimal solutions closely approximate the solution of any other weight vector. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector. We propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the regret. We extend our method to include suboptimal solvers for the scalarized optimization, and handle stochastic inputs to the planning problem. Finally, we illustrate that the proposed approach significantly outperforms baseline approaches for different robot planning problems with varying numbers of objective functions.
ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2024.3428990