Sampling of Pareto-Optimal Trajectories Using Progressive Objective Evaluation in Multi-Objective Motion Planning

Lee, Jeong-Seok; Yi, Daqing; Srinivasa, Siddhartha S.

doi:10.1109/iros.2018.8593735

Cited by 15 publications

(5 citation statements)

References 25 publications

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“…Moreover, the requirement of a user-preferred direction is not assumed in our work. In [25] a Pareto front approximation is proposed using Markov chain random walks. Their goal is to uniformly place samples on the Pareto front, while our goal is to minimize error in the space of Pareto-optimal costs.…”

Section: Related Workmentioning

confidence: 99%

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Botros

Sadeghi²,

Wilde³

et al. 2022

Springer Proceedings in Advanced Robotics

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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.

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Section: Related Workmentioning

confidence: 99%

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Botros

Sadeghi²,

Wilde³

et al. 2022

Springer Proceedings in Advanced Robotics

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show abstract

“…Given a set of quantitative objectives and system model, the goal of multi-objective analysis is to calculate the set of all optimal trade-offs between the objectives, called the Pareto front. Recent studies explore applications in robotics [9], path planning [10], [11], multi-agent coordination [12]- [14], and sensor scheduling [15]. The latter specifically focuses on resource and performance objectives and develops a scheduling framework for the usage of a high precision, high cost sensor.…”

Section: {Firstnamelastname}@coloradoedumentioning

confidence: 99%

Pareto Optimal Strategies for Event-Triggered Estimation

Anne¹,

Ahmed²,

Lahijanian³

2022

Preprint

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Although resource-limited networked autonomous systems must be able to efficiently and effectively accomplish tasks, better conservation of resources often results in worse task performance. We specifically address the problem of finding strategies for managing measurement communication costs between agents. A well understood technique for trading off communication costs with estimation accuracy is event triggering (ET), where measurements are only communicated when useful, e.g., when Kalman filter innovations exceed some threshold. In the absence of measurements, agents can use implicit information to achieve results almost as well as when explicit data is always communicated. However, there are no methods for setting this threshold with formal guarantees on task performance. We fill this gap by developing a novel belief space discretization technique to abstract a continuous space dynamics model for ET estimation to a discrete Markov decision process, which scalably accommodates threshold-sensitive ET estimator error covariances. We then apply an existing probabilistic trade-off analysis tool to find the set of all optimal trade-offs between resource consumption and task performance. From this set, an ET threshold selection strategy is extracted. Simulated results show our approach identifies non-trivial trade-offs between performance and energy savings, with only modest computational effort.

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“…c) Approximating Pareto-fronts: Given the wide-spread applications of multi-objective optimization, several fundamental techniques for computing Pareto-fronts have been studied over the years [9], [20]- [23]. However, popular approaches such as gradient descent methods, evolutionary algorithms [9] or random walks [25] assume that objective values can be easily obtained and thus make use of frequently evaluating the objectives for different parameters. Computing MRPD solutions is computationally burdensome even when using heuristic solutions, making such approaches impractical.…”

Section: B Related Workmentioning

confidence: 99%

Online Multi-Robot Task Assignment with Stochastic Blockages

Wilde

Alonso–Mora

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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We study the problem of finding statistically distinct plans for stochastic planning and task assignment problems such as online multi-robot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings robot fleets do not only need to fulfil delivery requests, but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multiobjective optimization problem where the goal is to find MRPD policies that yield different trade-offs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of trade-offs that can reasonably be computed, and 2) due to the random task arrivals, one needs to consider statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies which i) are approximately optimal, ii) approximate the set of all optimal solutions, and iii) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multi-objective setting for three example objectives. In a series of simulation experiments we demonstrate the advantages of the proposed method compared to baseline approaches and show its robustness in a sensitivity analysis. The approach is general and could be adapted to other multi-objective task assignment and planning problems under uncertainty.

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Sampling of Pareto-Optimal Trajectories Using Progressive Objective Evaluation in Multi-Objective Motion Planning

Cited by 15 publications

References 25 publications

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Pareto Optimal Strategies for Event-Triggered Estimation

Online Multi-Robot Task Assignment with Stochastic Blockages

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