A stochastic reach-avoid problem with random obstacles

Summers, Sean; Kamgarpour, Maryam; Lygeros, John; Tomlin, Claire J.

doi:10.1145/1967701.1967738

Cited by 40 publications

(34 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These formulations feature a control whose objective is to achieve either a probabilistic safety or reach-avoid objective, and an adversarial disturbance whose objective is assumed to be opposed to that of the control. Our analysis of these formulations generalizes the stochastic optimal control argument used by Amin et al (2006), Abate et al (2006), and Summers et al (2011) for the single player case, while also adapting results from the literature on additive cost stochastic games (see for example Kumar and Shiau, 1981;Nowak, 1985;Gonzalez-Trejo et al, 2002) to the multiplicative payoff structure of the safety and reach-avoid problems. For a feedback Stackelberg formulation, with an asymmetric information pattern favoring the disturbance, a dynamic programming algorithm is given for the computation of the max-min probability of satisfying either the safety or the reach-avoid specifications, as the Stackelberg value.…”

Section: Discussionmentioning

confidence: 98%

“…Based upon prior work by Amin et al (2006), Abate et al (2006), and Summers et al (2011) on probabilistic reachability problems for DTSHS, we considered two extensions to account for different models of uncertainty. In the first extension, two-player stochastic game formulations of the probability reachability problem are analyzed, in terms of a model which we referred to as a discrete-time stochastic hybrid game (DTSHG).…”

Section: Discussionmentioning

confidence: 99%

“…These results are generalized in Summers and Lygeros (2010) to address the reach-avoid problem, in which the control objective is to reach a desired target set, while remaining within a safe set. Considerations for time-varying and stochastic sets are discussed in Abate et al (2006) and Summers et al (2011) respectively.…”

Section: Overview and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Methods for Reachability-based Hybrid Controller Design

Ding¹

2012

View full text Add to dashboard Cite

With the increasing complexity of systems found in practical applications, the problem of controller design is often approached in a hierarchical fashion, with discrete abstractions and design methods used to satisfy high level task specifications, and continuous abstractions and design techniques used to satisfy low level control objectives. Although such a separation allows the application of mature theoretical and computational tools from the realms of computer science and control theory, the task of ensuring desired closed-loop behaviors, which results from the composition between discrete and continuous designs, often requires costly and time consuming verification and validation. This problem becomes especially acute in safety-critical applications, in which design specifications are often subject to rigorous industry standards and government regulations. Hybrid systems, which feature state trajectories evolving on a combination of discrete and continuous state spaces, have been proposed as a possible approach to reconcile the analysis and design techniques from the discrete and continuous domains under a rigorous theoretical framework. However, designing controllers for general classes of hybrid systems is a highly nontrivial task, as such a design problem inherits both the difficulty of nonlinear control, as well as the range of theoretical and computational issues introduced by the consideration of discrete switching.This dissertation describes several efforts aimed towards the development of theoretical analysis tools and computational synthesis techniques to facilitate the systematic design of feedback control policies satisfying safety and target attainability specifications with respect to subclasses of hybrid system models. The main types of problems we consider are safety/invariance problems, which involve keeping the closed-loop state trajectory within a safe set in the hybrid state space, and reach-avoid problems, which involve driving the state trajectory into a target set subject to a safety constraint. These problems are addressed within the context of continuous time switched nonlinear systems and discrete time stochastic hybrid systems, as motivated by application scenarios arising in autonomous vehicle control and air traffic management.First, we provide several design techniques and synthesis algorithms for deterministic reachability problems formulated in the setting of switched nonlinear systems, with controlled switches between discrete modes, and bounded continuous disturbances. For scenarios in which the mode transitions proceed in a known sequence, a method is discussed for designing controllers to satisfy 1 sequential reachability specifications, consisting of a temporally ordered sequence of invariance and reach-avoid objectives. In particular, we use continuous time reachable sets to inform choices of feedback control policies within each discrete mode to satisfy both individual reachability objectives and compatibility conditions between successive modes. This technique is illus...

show abstract

Section: Discussionmentioning

confidence: 98%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Methods for Reachability-based Hybrid Controller Design

Ding¹

2012

View full text Add to dashboard Cite

show abstract

“…This problem has been well-studied in the literature. 9,13 We will consider the motion of the aircraft as a discrete-time stochastic system. The stochasticity stems from the uncertainty in the trajectory evolution, due to potential wind and process noise, and in the convective weather cell characterization.…”

Section: Reach-avoid Methodologymentioning

confidence: 99%

“…The obstacle set is modeled as a time-indexed sequence of random closed sets. 9 The stochastic reach-avoid problem is cast as a discrete time, finite horizon stochastic optimal control problem 10 with a sum-multiplicative cost-to-go function. The optimal Markov control policy is computed using dynamic programming.…”

Section: Introductionmentioning

confidence: 99%

Optimal Aircraft Trajectory Planning in the Presence of Stochastic Convective Weather Cells

González-Arribas

Hentzen

Sanjurjo-Rivo

et al. 2017

17th AIAA Aviation Technology, Integration, and Operations Conference

Self Cite

View full text Add to dashboard Cite

The Air Traffic Management system is heavily influenced by meteorological uncertainty, and convective weather cells represent one of the most relevant uncertain meteorological phenomena. They are weather hazards that must be avoided through tactical trajectory modifications. As a consequence of the existence in uncertainty in meteorological forecasts and nowcasts, it is important to consider the convective weather cells to be avoided as a stochastic, time-dependent process. In this paper we present a comparative analysis of two methodologies for handling stochastic storms in trajectory planning: one based on stochastic reachability and a second one, based on robust optimal control. In the former, the thunderstorm avoidance problem is modelled as a stochastic reach-avoid problem, consid-ering the motion of the aircraft as a discrete-time stochastic system and the weather haz-ards as random set-valued obstacles. Dynamic programming is used to compute a Markov feedback policy that maximizes the probability of reaching the target before entering the unsafe set, i.e., the hazardous weather zones. For the latter, the stochastic dynamics of the storms are modeled in continuous time. We implement an optimal control formulation that allows different possible realizations of the stochastic process to be considered.The resulting problem is then transcribed to a nonlinear programming (NLP) problem through the use of direct numerical methods. A benchmark case study is presented, in which the effectiveness of the two proposed approaches are analyzed.

show abstract

Perception simplex: Verifiable collision avoidance in autonomous vehicles amidst obstacle detection faults

Bansal,

Kim,

et al. 2024

Software Testing Verif & Rel

View full text Add to dashboard Cite

Advances in deep learning have revolutionized cyber‐physical applications, including the development of autonomous vehicles. However, real‐world collisions involving autonomous control of vehicles have raised significant safety concerns regarding the use of deep neural networks (DNNs) in safety‐critical tasks, particularly perception. The inherent unverifiability of DNNs poses a key challenge in ensuring their safe and reliable operation. In this work, we propose perception simplex (), a fault‐tolerant application architecture designed for obstacle detection and collision avoidance. We analyse an existing LiDAR‐based classical obstacle detection algorithm to establish strict bounds on its capabilities and limitations. Such analysis and verification have not been possible for deep learning‐based perception systems yet. By employing verifiable obstacle detection algorithms, identifies obstacle existence detection faults in the output of unverifiable DNN‐based object detectors. When faults with potential collision risks are detected, appropriate corrective actions are initiated. Through extensive analysis and software‐in‐the‐loop simulations, we demonstrate that provides deterministic fault tolerance against obstacle existence detection faults, establishing a robust safety guarantee.

show abstract

A stochastic reach-avoid problem with random obstacles

Cited by 40 publications

References 22 publications

Methods for Reachability-based Hybrid Controller Design

Methods for Reachability-based Hybrid Controller Design

Optimal Aircraft Trajectory Planning in the Presence of Stochastic Convective Weather Cells

Perception simplex: Verifiable collision avoidance in autonomous vehicles amidst obstacle detection faults

Contact Info

Product

Resources

About