Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either lack scalability in solving larger problems or produce conservative plans. Recent advances in deep reinforcement learning improve scalability by learning policy networks as function approximators. In this paper, we propose an extension of soft actor critic model to estimate the execution risk of a plan through a risk critic and produce risk-bounded policies efficiently by adding an extra risk term in the loss function of the policy network. We define the execution risk in an accurate form, as opposed to approximating it through a summation of immediate risks at each time step that leads to conservative plans. Our proposed model is conditioned on a continuous spectrum of risk bounds, allowing the user to adjust the risk-averse level of the agent on the fly. Through a set of experiments, we show the advantage of our model in terms of both computational time and plan quality, compared to a state-of-the-art mathematical programming baseline, and validate its performance in more complicated scenarios, including nonlinear dynamics and larger state space.

This paper presents fast non-sampling based methods to assess the risk of trajectories for autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods address a wide range of representations for uncertain predictions including both Gaussian and non-Gaussian mixture models for predictions of both agent positions and controls. We show that the problem of risk assessment when Gaussian mixture models (GMMs) of agent positions are learned can be solved rapidly to arbitrary levels of accuracy with existing numerical methods. To address the problem of risk assessment for non-Gaussian mixture models of agent position, we propose finding upper bounds on risk using Chebyshev's Inequality and sums-of-squares (SOS) programming; they are both of interest as the former is much faster while the latter can be arbitrarily tight. These approaches only require statistical moments of agent positions to determine upper bounds on risk. To perform risk assessment when models are learned for agent controls as opposed to positions, we develop TreeRing, an algorithm analogous to tree search over the ring of polynomials that can be used to exactly propagate moments of control distributions into position distributions through nonlinear dynamics. The presented methods are demonstrated on realistic predictions from DNNs trained on the Argoverse and CARLA datasets and are shown to be effective for rapidly assessing the probability of low probability events.

In planning and scheduling, solving problems with both state and temporal constraints is hard since these constraints may be highly coupled. Judicious orderings of events enable solvers to efficiently make decisions over sequences of actions to satisfy complex hybrid specifications. The ordering problem is thus fundamental to planning. Promising recent works have explored the ordering problem as search, incorporating a special tree structure for efficiency. However, such approaches only reason over partial order specifications. Having observed that an ordering is inconsistent with respect to underlying constraints, prior works do not exploit the tree structure to efficiently generate orderings that resolve the inconsistency. In this paper, we present Conflict-directed Incremental Total Ordering (CDITO), a conflict-directed search method to incrementally and systematically generate event total orders given ordering relations and conflicts returned by sub-solvers. Due to its ability to reason over conflicts, CDITO is much more efficient than Incremental Total Ordering. We demonstrate this by benchmarking on temporal network configuration problems that involve routing network flows and allocating bandwidth resources over time.

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.

The state of the art practice in robotics planning is to script behaviors manually, where each behavior is typically generated using trajectory optimization. However, in order for robots to be able to act robustly and adapt to novel situations, they need to plan these activity sequences autonomously. Since the conditions and effects of these behaviors are tightly coupled through time, state and control variables, many problems require that the tasks of activity planning and trajectory optimization are considered together. There are two key issues underlying effective hybrid activity and trajectory planning: the sufficiently accurate modeling of robot dynamics and the capability of planning over long horizons. Hybrid activity and trajectory planners that employ mixed integer programming within a discrete time formulation are able to accurately model complex dynamics for robot vehicles, but are often restricted to relatively short horizons. On the other hand, current hybrid activity planners that employ continuous time formulations can handle longer horizons but they only allow actions to have continuous effects with constant rate of change, and restrict the allowed state constraints to linear inequalities. This is insufficient for many robotic applications and it greatly limits the expressivity of the problems that these approaches can solve. In this work we present the ScottyActivity planner, that is able to generate practical hybrid activity and motion plans over long horizons by employing recent methods in convex optimization combined with methods for planning with relaxed plan graphs and heuristic forward search. Unlike other continuous time planners, ScottyActivity can solve a broad class of robotic planning problems by supporting convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. In order to support planning over long horizons, ScottyActivity does not resort to time, state or control variable discretization. While straightforward formulations of consistency checks are not convex and do not scale, we present an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We also introduce several new realistic domains that demonstrate the capabilities and scalability of our approach, and their simplified linear versions, that we use to compare with other state of the art planners. This work demonstrates the power of integrating advanced convex optimization techniques with discrete search methods and paves the way for extensions dealing with non-convex disjoint constraints, such as obstacle avoidance.

Over-subscription, that is, being assigned too many things to do, is commonly encountered in temporal scheduling problems. As human beings, we often want to do more than we can actually do, and underestimate how long it takes to perform each task. Decision makers can benefit from aids that identify when these failure situations are likely, the root causes of these failures, and resolutions to these failures. In this paper, we present a decision assistant that helps users resolve over-subscribed temporal problems. The system works like an experienced advisor that can quickly identify the cause of failure underlying temporal problems and compute resolutions. The core of the decision assistant is the Best-first Conflict-Directed Relaxation (BCDR) algorithm, which can detect conflicting sets of constraints within temporal problems, and computes continuous relaxations for them that weaken constraints to the minimum extent, instead of removing them completely. BCDR is an extension to the Conflict-Directed A* algorithm, first developed in the model-based reasoning community to compute most likely system diagnoses or reconfigurations. It generalizes the discrete conflicts and relaxations, to hybrid conflicts and relaxations, which denote minimal inconsistencies and minimal relaxations to both discrete and continuous relaxable constraints. In addition, BCDR is capable of handling temporal uncertainty, expressed as either set-bounded or probabilistic durations, and can compute preferred trade-offs between the risk of violating a schedule requirement, versus the loss of utility by weakening those requirements. BCDR has been applied to several decision support applications in different domains, including deep-sea exploration, urban travel planning and transit system management. It has demonstrated its effectiveness in helping users resolve over-subscribed scheduling problems and evaluate the robustness of existing solutions. In our benchmark experiments, BCDR has also demonstrated its efficiency on solving large-scale scheduling problems in the aforementioned domains. Thanks to its conflict-driven approach for computing relaxations, BCDR achieves one to two orders of magnitude improvements on runtime performance when compared to state-of-the-art numerical solvers.

Robots operating in the real world must be able to handle both discrete and continuous change. Many robot behaviors can be controlled through numeric parameters (called control variables), which affect the rate of the continuous change. Previous approaches capable of reasoning efficiently with control variables impose severe restrictions that limit the expressivity of the problems that can be solved. A broad class of robotic applications require, for example, convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. However, extensions to prior approaches are not straightforward, since these characteristics are non-linear and hard to scale. We introduce cqScotty, a heuristic forward search planner that solves these problems efficiently. While naive formulations of consistency checks are not convex and do not scale, cqScotty uses an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We demonstrate the scalability of our approach on three new realistic domains.

We extend chance-constrained path planning with direct method into continuous time. Chance-constrained path planning is a method to obtain the optimal path satisfying a specified risk (or probability of failure) value. Previous work expects trajectories' states as discrete information with respect to time. This discretized encoding makes the conversion from probabilistic path planning to deterministic path planning easy. However, risk guarantees are only produced for the discrete time model. The probability of constraints violation in continuous time could be larger than the discretized risk values. To address this problem, we modified the constraint encoding and risk assessment method. First, we introduce a computationally efficient mean path securing method, which uses fewer binary variables as compared with prior work. Second, we note that the deviation of the actual trajectory from the mean trajectory can be considered as a Brownian motion, for which the reflection principle holds in general. Therefore, we take advantage of the reflection principle to bound the probability of the constraint violation in continuous time. In numerical simulations, we confirmed faster solution generation, and the probability guarantees of the path in the continuous time model, with deterioration in the objective function.

Autonomous agents operating in partially observable stochastic environments often face the problem of optimizing expected performance while bounding the risk of violating safety constraints. Such problems can be modeled as chance-constrained POMDP's (CC-POMDP's). Our first contribution is a systematic derivation of execution risk in POMDP domains, which improves upon how chance constraints are handled in the constrained POMDP literature. Second, we present RAO*, a heuristic forward search algorithm producing optimal, deterministic, finite-horizon policies for CC-POMDP's. In addition to the utility heuristic, RAO* leverages an admissible execution risk heuristic to quickly detect and prune overly-risky policy branches. Third, we demonstrate the usefulness of RAO* in two challenging domains of practical interest: power supply restoration and autonomous science agents.

The future will see autonomous machines acting in the same environment as humans, in areas as diverse as driving, assistive technology, and health care. Think of self-driving cars, companion robots, and medical diagnosis support systems. We also believe that humans and machines will often need to work together and agree on common decisions. Thus hybrid collective decision making systems will be in great need. In this scenario, both machines and collective decision making systems should follow some form of moral values and ethical principles (appropriate to where they will act but always aligned to humans'), as well as safety constraints. In fact, humans would accept and trust more machines that behave as ethically as other humans in the same environment. Also, these principles would make it easier for machines to determine their actions and explain their behavior in terms understandable by humans. Moreover, often machines and humans will need to make decisions together, either through consensus or by reaching a compromise. This would be facilitated by shared moral values and ethical principles.