Most existing works in Probabilistic Simple Temporal Networks (PSTNs) base their frameworks on well-defined, parametric probability distributions. Under the operational contexts of both strong and dynamic control, this paper addresses robustness measure of PSTNs, i.e. the execution success probability, where the probability distributions of the contingent durations are ordinary, not necessarily parametric, nor symmetric (e.g. histograms, PERT), as long as these can be discretized. In practice, one would obtain ordinary distributions by considering empirical observations (compiled as histograms), or even hand-drawn by field experts. In this new realm of PSTNs, we study and formally define concepts such as degree of weak/strong/dynamic controllability, robustness under a predefined dispatching protocol, and introduce the concept of PSTN expected execution utility. We also discuss the limitation of existing controllability levels, and propose new levels within dynamic controllability, to better characterize dynamic controllable PSTNs based on based practical complexity considerations. We propose a novel fixed-parameter pseudo-polynomial time computation method to obtain both the success probability and expected utility measures. We apply our computation method to various PSTN datasets, including realistic planetary exploration scenarios in the context of the Mars 2020 rover. Moreover, we propose additional original applications of the method.

A critical challenge in temporal planning is robustly dealing with non-determinism, e.g., the durational uncertainty of a robot's activity due to slippage or other unexpected influences. Recent advances show that robustness is a better measure of solution quality than traditional metrics such as flexibility. This paper introduces the Robust Execution Problem for finding maximally robust dispatch strategies for general probabilistic temporal planning problems. While generally intractable, we introduce approximate solution techniques — one that can be computed statically prior to the start of execution with robustness guarantees and one that dynamically adjusts to opportunities and setbacks during execution. We show empirically that our dynamic approach outperforms all known approaches in terms of execution success rate.

A critical challenge in temporal planning is robustly dealing with non-determinism introduced by the environment, e.g., the durational uncertainty of an action taken by a robot in the physical world due to slippage or other unexpected influences. Recent advances show that robustness, which accounts for uncertainty in predicting schedule success, is a better measure of solution quality than traditional metrics such as flexibility. This paper introduces the Robust Execution Problem (REP) for finding maximally robust dispatch strategies for general probabilistic temporal planning problems. While the REP is generally intractable in practice, we introduce approximate solution techniques—one that can be computed statically prior to the start of execution while providing robustness guarantees and one that dynamically adjusts to opportunities and setbacks during execution. We show empirically that dynamically optimizing for robustness improves the likelihood of execution success.

Temporal uncertainty in large-scale logistics forces one to trade off between lost efficiency through built-in slack and costly replanning when deadlines are missed. Due to the difficulty of reasoning about such likelihoods and consequences, a computational framework is needed to quantify and bound the risk of violating scheduling requirements. This work addresses the chance-constrained scheduling problem, where actions' durations are modeled probabilistically. Our solution method uses conflict-directed risk allocation to efficiently compute a scheduling policy. The key insight, compared to previous work in probabilistic scheduling, is to decouple the reasoning about temporal and risk constraints. This decomposes the problem into a separate master and subproblem, which can be iteratively solved much quicker. Through a set of simulated car-sharing scenarios, it is empirically shown that conflict-directed risk allocation computes solutions nearly an order of magnitude faster than prior art, which considers all constraints in a single lump-sum optimization.

Scheduling under uncertainty is essential to many autonomous systems and logistics tasks. Probabilistic methods for solving temporal problems exist which quantify and attempt to minimize the probability of schedule failure. These methods are overly conservative, resulting in a loss in schedule utility. Chance constrained formalism address over-conservatism by imposing bounds on risk, while maximizing utility subject to these risk bounds. In this paper we present the probabilistic Simple Temporal Network (pSTN), a probabilistic formalism for representing temporal problems with bounded risk and a utility over event timing. We introduce a constrained optimisation algorithm for pSTNs that achieves compactness and efficiency through a problem encoding in terms of a parameterised STNU and its reformulation as a parameterised STN. We demonstrate through a car sharing application that our chance-constrained approach runs in the same time as the previous probabilistic approach, yields solutions with utility improvements of at least 5% over previous arts, while guaranteeing operation within the specified risk bound.