# Path Planning for Minimizing the Expected Cost until Success

arXiv: https://arxiv.org/abs/1802.00898 · HTML: https://mlsanity.com/paper/1802.00898/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2018.

## Built on by (most cited first, 1 of 1)

- [Almost Sure Convergence of Networked Policy Gradient over Time-Varying Networks in Markov Potential Games](https://mlsanity.com/paper/2410.20075/) (2024)

## Abstract (arXiv)

Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the robot on the graph that minimizes the expected cost until success. In this paper, it is our goal to bring a foundational understanding to this problem. We start by showing how this problem can be optimally solved by formulating it as an infinite horizon Markov Decision Process, but with an exponential space complexity. We then formally prove its NP-hardness. To address the space complexity, we then propose a path planner, using a game-theoretic framework, that asymptotically gets arbitrarily close to the optimal solution. Moreover, we also propose two fast and non-myopic path planners. To show the performance of our framework, we do extensive simulations for two scenarios: a rover on Mars searching for an object for scientific studies, and a robot looking for a connected spot to a remote station (with real data from downtown San Francisco). Our numerical results show a considerable performance improvement over existing state-of-the-art approaches.