Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Botros, Alexander (University of Waterloo)
Sadeghi, Armin (University of Waterloo)
Wilde, N. (TU Delft Learning & Autonomous Control)
Alonso Mora, J. (TU Delft Learning & Autonomous Control)
Smith, Stephen L. (University of Waterloo)

LaValle, Steven M. (editor)
O’Kane, Jason M. (editor)
Otte, Michael (editor)
Sadigh, Dorsa (editor)
Tokekar, Pratap (editor)

2023

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems 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 multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.

Human-robot interaction
Multi-objective optimization
Planning

http://resolver.tudelft.nl/uuid:c88fcb40-aafc-43b3-a97e-11d9c76f7369

https://doi.org/10.1007/978-3-031-21090-7_30

Springer

2023-06-15

978-3-031-21089-1

Algorithmic Foundations of Robotics XV: Proceedings of the Fifteenth Workshop on the Algorithmic Foundations of Robotics

15th Workshop on the Algorithmic Foundations of Robotics, WAFR 2022, 2022-06-22 → 2022-06-24, College Park, United States

Springer Proceedings in Advanced Robotics, 2511-1256, 25 SPAR

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Institutional Repository

conference paper

© 2023 Alexander Botros, Armin Sadeghi, N. Wilde, J. Alonso Mora, Stephen L. Smith