# Probabilistic Motion Planning under Temporal Tasks and Soft Constraints

## TL;DR

This paper presents a probabilistic motion planning framework for mobile robots under uncertainty, optimizing task satisfaction probability and cost, with novel multi-objective control synthesis and validation through simulations and experiments.

## Contribution

It introduces a multi-objective optimization approach using coupled Linear Programs for probabilistic task satisfaction and cost minimization, including a new algorithm for zero-probability scenarios.

## Key findings

- Outperforms Round-Robin policies in trajectory suffix
- Provides guarantees on probabilistic satisfaction and cost optimality
- Includes a new control synthesis method for zero-probability cases

## Abstract

This paper studies motion planning of a mobile robot under uncertainty. The control objective is to synthesize a {finite-memory} control policy, such that a high-level task specified as a Linear Temporal Logic (LTL) formula is satisfied with a desired high probability. Uncertainty is considered in the workspace properties, robot actions, and task outcomes, giving rise to a Markov Decision Process (MDP) that models the proposed system. Different from most existing methods, we consider cost optimization both in the prefix and suffix of the system trajectory. We also analyze the potential trade-off between reducing the mean total cost and maximizing the probability that the task is satisfied. The proposed solution is based on formulating two coupled Linear Programs, for the prefix and suffix, respectively, and combining them into a multi-objective optimization problem, which provides provable guarantees on the probabilistic satisfiability and the total cost optimality. We show that our method outperforms relevant approaches that employ Round-Robin policies in the trajectory suffix. Furthermore, we propose a new control synthesis algorithm to minimize the frequency of reaching a bad state when the probability of satisfying the tasks is zero, in which case most existing methods return no solution. We validate the above schemes via both numerical simulations and experimental studies.