Chance-Constrained Probabilistic Simple Temporal Problems

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.National Science Foundation (U.S.) (Grant No. IIS-1017992

Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments

In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.Comment: 57th IEEE Conference on Decision and Control 201

Resolving Over-constrained Probabilistic Temporal Problems through Chance Constraint Relaxation

When scheduling tasks for field-deployable systems, our solutions must be robust to the uncertainty inherent in the real world. Although human intuition is trusted to balance reward and risk, humans perform poorly in risk assessment at the scale and complexity of real world problems. In this paper, we present a decision aid system that helps human operators diagnose the source of risk and manage uncertainty in temporal problems. The core of the system is a conflict-directed relaxation algorithm, called Conflict-Directed Chance-constraint Relaxation (CDCR), which specializes in resolving over-constrained temporal problems with probabilistic durations and a chance constraint bounding the risk of failure. Given a temporal problem with uncertain duration, CDCR proposes execution strategies that operate at acceptable risk levels and pinpoints the source of risk. If no such strategy can be found that meets the chance constraint, it can help humans to repair the over-constrained problem by trading off between desirability of solution and acceptable risk levels. The decision aid has been incorporated in a mission advisory system for assisting oceanographers to schedule activities in deep-sea expeditions, and demonstrated its effectiveness in scenarios with realistic uncertaintyBoeing Company (Grant MIT-BA-GTA-1

Chance-constrained Scheduling via Conflict-directed Risk Allocation

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 does, which considers all constraints in a single lump-sum optimization

A risk-aware architecture for resilient spacecraft operations

In this paper we discuss a resilient, risk-aware software architecture for onboard, real-time autonomous operations that is intended to robustly handle uncertainty in space-craft behavior within hazardous and unconstrained environments, without unnecessarily increasing complexity. This architecture, the Resilient Spacecraft Executive (RSE), serves three main functions: (1) adapting to component failures to allow graceful degradation, (2) accommodating environments, science observations, and spacecraft capabilities that are not fully known in advance, and (3) making risk-aware decisions without waiting for slow ground-based reactions. This RSE is made up of four main parts: deliberative, habitual, and reflexive layers, and a state estimator that interfaces with all three. We use a risk-aware goal-directed executive within the deliberative layer to perform risk-informed planning, to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Other state-of-the-art algorithms to be integrated into the RSE include correct-by-construction control synthesis and model-based estimation and diagnosis. We demonstrate the feasibility of the architecture in a simple implementation of the RSE for a simulated Mars rover scenario

Complexity Bounds for the Controllability of Temporal Networks with Conditions, Disjunctions, and Uncertainty

In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal constraints is consistent. While many of the simpler models have been well-studied from a computational complexity perspective, the algorithms developed for advanced models which combine features have very loose complexity bounds. In this paper, we provide tight completeness bounds for strong, weak, and dynamic controllability checking of temporal networks that have conditions, disjunctions, and temporal uncertainty. Our work exposes some of the subtle differences between these different structures and, remarkably, establishes a guarantee that all of these problems are computable in PSPACE

Reasoning and querying bounds on differences with layered preferences

Artificial intelligence largely relies on bounds on differences (BoDs) to model binary constraints regarding different dimensions, such as time, space, costs, and calories. Recently, some approaches have extended the BoDs framework in a fuzzy, \u201cnoncrisp\u201d direction, considering probabilities or preferences. While previous approaches have mainly aimed at providing an optimal solution to the set of constraints, we propose an innovative class of approaches in which constraint propagation algorithms aim at identifying the \u201cspace of solutions\u201d (i.e., the minimal network) with their preferences, and query answering mechanisms are provided to explore the space of solutions as required, for example, in decision support tasks. Aiming at generality, we propose a class of approaches parametrized over user\u2010defined scales of qualitative preferences (e.g., Low, Medium, High, and Very High), utilizing the resume and extension operations to combine preferences, and considering different formalisms to associate preferences with BoDs. We consider both \u201cgeneral\u201d preferences and a form of layered preferences that we call \u201cpyramid\u201d preferences. The properties of the class of approaches are also analyzed. In particular, we show that, when the resume and extension operations are defined such that they constitute a closed semiring, a more efficient constraint propagation algorithm can be used. Finally, we provide a preliminary implementation of the constraint propagation algorithms

Optimising Flexibility of Temporal Problems with Uncertainty

Temporal networks have been applied in many autonomous systems. In real situations, we cannot ignore the uncertain factors when using those autonomous systems. Achieving robust schedules and temporal plans by optimising flexibility to tackle the uncertainty is the motivation of the thesis. This thesis focuses on the optimisation problems of temporal networks with uncertainty and controllable options in the field of Artificial Intelligence Planning and Scheduling. The goal of this thesis is to construct flexibility and robustness metrics for temporal networks under the constraints of different levels of controllability. Furthermore, optimising flexibility for temporal plans and schedules to achieve robust solutions with flexible executions. When solving temporal problems with uncertainty, postponing decisions according to the observations of uncertain events enables flexible strategies as the solutions instead of fixed schedules or plans. Among the three levels of controllability of the Simple Temporal Problem with Uncertainty (STPU), a problem is dynamically controllable if there is a successful dynamic strategy such that every decision in it is made according to the observations of past events. In the thesis, we make the following contributions. (1) We introduce an optimisation model for STPU based on the existing dynamic controllability checking algorithms. Some flexibility and robustness measures are introduced based on the model. (2) We extend the definition and verification algorithm of dynamic controllability to temporal problems with controllable discrete variables and uncertainty, which is called Controllable Conditional Temporal Problems with Uncertainty (CCTPU). An entirely dynamically controllable strategy of CCTPU consists of both temporal scheduling and variable assignments being dynamically decided, which maximize the flexibility of the execution. (3) We introduce optimisation models of CCTPU under fully dynamic controllability. The optimisation models aim to answer the questions how flexible, robust or controllable a schedule or temporal plan is. The experiments show that making decisions dynamically can achieve better objective values than doing statically. The thesis also contributes to the field of AI planning and scheduling by introducing robustness metrics of temporal networks, proposing an envelope-based algorithm that can check dynamic controllability of temporal networks with uncertainty and controllable discrete decisions, evaluating improvements from making decisions strongly controllable to temporally dynamically controllable and fully dynamically controllable and comparing the runtime of different implementations to present the scalability of dynamically controllable strategies

Belief Space Scheduling

This thesis develops the belief space scheduling framework for scheduling under uncertainty in Stochastic Collection and Replenishment (SCAR) scenarios. SCAR scenarios involve the transportation of a resource such as fuel to agents operating in the field. Key characteristics of this scenario are persistent operation of the agents, and consideration of uncertainty. Belief space scheduling performs optimisation on probability distributions describing the state of the system. It consists of three major components---estimation of the current system state given uncertain sensor readings, prediction of the future state given a schedule of tasks, and optimisation of the schedule of the replenishing agents. The state estimation problem is complicated by a number of constraints that act on the state. A novel extension of the truncated Kalman Filter is developed for soft constraints that have uncertainty described by a Gaussian distribution. This is shown to outperform existing estimation methods, striking a balance between the high uncertainty of methods that ignore the constraints and the overconfidence of methods that ignore the uncertainty of the constraints. To predict the future state of the system, a novel analytical, continuous-time framework is proposed. This framework uses multiple Gaussian approximations to propagate the probability distributions describing the system state into the future. It is compared with a Monte Carlo framework and is shown to provide similar discrimination performance while computing, in most cases, orders of magnitude faster. Finally, several branch and bound tree search methods are developed for the optimisation problem. These methods focus optimisation efforts on earlier tasks within a model predictive control-like framework. Combined with the estimation and prediction methods, these are shown to outperform existing approaches