arXiv subjects

Meeko Oishi

Publications and source records attributed to Meeko Oishi.

At least 19 recordsLinked to original sources

arXiv2026

Characterizing Driver Interactions with Autonomous Vehicles via Response Maps

Understanding human responses to autonomous vehicle (AV) behaviors is essential for socially aware interaction, which is crucial for socially compatible navigation in shared traffic environments. We characterize human driving responses in interactions with AVs as feedback laws over the coupled state space of the human driven vehicle and the AV. We model the human driver's actions using a response map, a concept based in game theory, and employ a linear representation to capture driver behaviors as a function of AV behaviors, based on empirical data from a driving simulator study. Our results show that 1) human driver acceleration behavior can be captured using response maps, and 2) human driver responses differ significantly with respect to AV behaviors of yielding, non-yielding, and responsive to the human driver.

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arXiv2025

Characterizing Human Feedback-Based Control in Naturalistic Driving Interactions via Gaussian Process Regression with Linear Feedback

Understanding driver interactions is critical to designing autonomous vehicles to interoperate safely with human-driven cars. We consider the impact of these interactions on the policies drivers employ when navigating unsigned intersections in a driving simulator. The simulator allows the collection of naturalistic decision-making and behavior data in a controlled environment. Using these data, we model the human driver responses as state-based feedback controllers learned via Gaussian Process regression methods. We compute the feedback gain of the controller using a weighted combination of linear and nonlinear priors. We then analyze how the individual gains are reflected in driver behavior. We also assess differences in these controllers across populations of drivers. Our work in data-driven analyses of how drivers determine their policies can facilitate future work in the design of socially responsive autonomy for vehicles.

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arXiv2024

SAVER: A Toolbox for Sampling-Based, Probabilistic Verification of Neural Networks

We present a neural network verification toolbox to 1) assess the probability of satisfaction of a constraint, and 2) synthesize a set expansion factor to achieve the probability of satisfaction. Specifically, the tool box establishes with a user-specified level of confidence whether the output of the neural network for a given input distribution is likely to be contained within a given set. Should the tool determine that the given set cannot satisfy the likelihood constraint, the tool also implements an approach outlined in this paper to alter the constraint set to ensure that the user-defined satisfaction probability is achieved. The toolbox is comprised of sampling-based approaches which exploit the properties of signed distance function to define set containment.

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arXiv2024

The Impact of Social Value Orientation on Nash Equilibria of Two Player Quadratic Games

We consider two player quadratic games in a cooperative framework known as social value orientation, motivated by the need to account for complex interactions between humans and autonomous agents in dynamical systems. Social value orientation is a framework from psychology, that posits that each player incorporates the other player's cost into their own objective function, based on an individually pre-determined degree of cooperation. The degree of cooperation determines the weighting that a player puts on their own cost relative to the other player's cost. We characterize the Nash equilibria of two player quadratic games under social value orientation by creating expansions that elucidate the relative difference between this new equilibria (which we term the SVO-Nash equilibria) and more typical equilibria, such as the competitive Nash equilibria, individually optimal solutions, and the fully cooperative solution. Specifically, each expansion parametrizes the space of cooperative Nash equilibria as a family of one-dimensional curves where each curve is computed by solving an eigenvalue problem. We show that both bounded and unbounded equilibria may exist. For equilibria that are bounded, we can identify bounds as the intersection of various ellipses; for equilibria that are unbounded, we characterize conditions under which unboundedness will occur, and also compute the asymptotes that the unbounded solutions follow. We demonstrate these results in trajectory coordination scenario modeled as a linear time varying quadratic game.

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arXiv2023

Blameless and Optimal Control under Prioritized Safety Constraints

In many resource-limited optimal control problems, multiple constraints may be enforced that are jointly infeasible due to external factors such as subsystem failures, unexpected disturbances, or fuel limitations. In this manuscript, we introduce the concept of blameless optimality to characterize control actions that a) satisfy the highest prioritized and feasible constraints and b) remain optimal with respect to a mission objective. For a general optimal control problem with jointly infeasible constraints, we prove that a single optimization problem cannot find a blamelessly optimal control sequence. Instead, finding blamelessly optimal control actions requires sequentially solving at least two optimal control problems: one to determine the highest priority level of constraints that is feasible and another to determine the optimal control action with respect to these constraints. We apply our results to a rocket landing scenario in which violating at least one safety-induced landing constraint is unavoidable. Leveraging the concept of blameless optimality, we formulate blamelessly optimal controllers that can autonomously prioritize the constraints most critical to a mission.

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arXiv2023

Chance Constrained Stochastic Optimal Control for Linear Systems with a Time Varying Random Control Matrix

This work proposes an open-loop methodology to solve chance constrained stochastic optimal control problems for linear systems with a stochastic control matrix. We consider a joint chance constraint for polytopic time-varying target sets under moment and unimodality assumptions. We reformulate the chance constraint into individual biconvex constraints using the one-sided Vysochanskij-Petunin inequality. We demonstrate our methodology on two spacecraft rendezvous problems. We compare the proposed method with the scenario approach and moment-based methods based on Cantelli's inequality.

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arXiv2023

Chance Constrained Stochastic Optimal Control Based on Sample Statistics With Almost Surely Probabilistic Guarantees

While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample data in a manner that can provide almost surely guarantees of chance constraint satisfaction. In this paper, we develop a method for solving chance constrained stochastic optimal control problems for linear time-invariant systems with unknown but sampled additive disturbances. We propose an open-loop control scheme for multi-vehicle planning, with both target sets and collision avoidance constraints. To this end, we derive a concentration inequality to bound the tail probability of a random variable based on sample statistics. Using the derived concentration inequality, we reformulate each chance constraint in terms of the sample mean and sample standard deviation. While the reformulated bounds are conservative with respect to the original bounds, they have a simple and closed form, guarantee chance constraint satisfaction almost surely, and are amenable to difference of convex optimization techniques. We demonstrate our approach on two multi-satellite rendezvous problems.

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arXiv2023

Stochastic Optimal Control For Gaussian Disturbances with Unknown Mean and Variance Based on Sample Statistics

We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and covariance. We consider a joint chance constraint for time-varying polytopic target sets under assumptions that the disturbance has been sufficiently sampled. We derive two theorems that allow us to bound the probability of the state being more than some number of sample standard deviations away from the sample mean. We use these theorems to reformulate the chance constraint into a series of convex and linear constraints. Here, solutions guarantee chance constraint satisfaction. We demonstrate our method on a satellite rendezvous maneuver and provide comparisons with the scenario approach.

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arXiv2023

Chance Constrained Stochastic Optimal Control for Arbitrarily Disturbed LTI Systems Via the One-Sided Vysochanskij-Petunin Inequality

While many techniques have been developed for chance constrained stochastic optimal control with Gaussian disturbance processes, far less is known about computationally efficient methods to handle non-Gaussian processes. In this paper, we develop a method for solving chance constrained stochastic optimal control problems for linear time-invariant systems with general additive disturbances with finite moments and unimodal chance constraints. We propose an open-loop control scheme for multi-vehicle planning, with both target sets and collision avoidance constraints. Our method relies on the one-sided Vysochanskij-Petunin inequality, a tool from statistics used to bound tail probabilities of unimodal random variables. Using the one-sided Vysochanskij-Petunin inequality, we reformulate each chance constraint in terms of the expectation and standard deviation. While the reformulated bounds are conservative with respect to the original bounds, they have a simple and closed form, and are amenable to difference of convex optimization techniques. We demonstrate our approach on a multi-satellite rendezvous problem.

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arXiv2023

Chance Constrained Stochastic Optimal Control for Linear Systems with Time Varying Random Plant Parameters

We propose an open loop control scheme for linear systems with time-varying random elements in the plant's state matrix. This paper focuses on joint chance constraints for potentially time-varying target sets. Under assumption of finite and known expectation and variance, we use the one-sided Vysochanskij-Petunin inequality to reformulate joint chance constraints into a tractable form. We demonstrate our methodology on a two-bus power system with stochastic load and wind power generation. We compare our method with situation approach. We show that the proposed method had superior solve times and favorable optimally considerations.

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arXiv2022

Approximate Stochastic Optimal Control for Linear Time Invariant Systems with Heavy-tailed Disturbances

We propose an open loop control scheme for linear time invariant systems perturbed by multivariate $t$ disturbances through the use of quantile reformulations. The multivariate $t$ disturbance is motivated by heavy tailed phenomena that arise in multi-vehicle planning planning problems through unmodeled perturbation forces, linearization effects, or faulty actuators. Our approach relies on convex quantile reformulations of the polytopic target sets and norm based collision avoidance constraints to enable fast computation. We embed quantile approximations of the Student's $t$ distribution and the beta prime distribution in a difference-of-convex function framework to compute provably safe but likely suboptimal controllers. We demonstrate our method with three satellite rendezvous examples and provide a comparison with particle control.

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arXiv2022

Approximate Quantiles for Stochastic Optimal Control of LTI Systems with Arbitrary Disturbances

We propose a method for open-loop stochastic optimal control of LTI systems based on Taylor approximations of quantile functions. This approach enables efficient computation of quantile functions that arise in chance constrained reformulations. We are motivated by multi-vehicle planning problems for LTI systems with norm-based collision avoidance constraints, and polytopic feasibility constraints. Respectively, these constraints can be posed as reverse-convex and convex chance constraints that are affine in the control and disturbance. We show for constraints of this form, piecewise affine approximations of the quantile function can be embedded in a difference-of-convex program that enables use of conic solvers. We demonstrate our method for multi-satellite coordination with Gaussian and Cauchy disturbances, and provide a comparison with particle control.

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arXiv2022

Characterizing Within-Driver Variability in Driving Dynamics During Obstacle Avoidance Maneuvers

Variability in human response creates non-trivial challenges for modeling and control of human-automation systems. As autonomy becomes pervasive, methods that can accommodate human variability will become paramount, to ensure efficiency, safety, and high levels of performance. We propose an easily computable modeling framework which takes advantage of a metric to assess variability in individual human response in a dynamic task that subjects repeat over several trials. Our approach is based in a transformation of observed trajectories to a reproducing kernel Hilbert space, which captures variability in human response as a distribution embedded within the Hilbert space. We evaluate the similarity across responses via the maximum mean discrepancy, which measures the distance between distributions within the Hilbert space. We apply this metric to a difficult driving task designed to elucidate differences across subjects. We conducted a pilot study with 6 subjects in an advanced driving simulator, in which subjects were tasked with collision avoidance of an obstacle in the middle of the road, around a blind corner, in a nighttime scenario, while steering only with the non-dominant hand.

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arXiv2019

Resilient Cyberphysical Systems and their Application Drivers: A Technology Roadmap

Cyberphysical systems (CPS) are ubiquitous in our personal and professional lives, and they promise to dramatically improve micro-communities (e.g., urban farms, hospitals), macro-communities (e.g., cities and metropolises), urban structures (e.g., smart homes and cars), and living structures (e.g., human bodies, synthetic genomes). The question that we address in this article pertains to designing these CPS systems to be resilient-from-the-ground-up, and through progressive learning, resilient-by-reaction. An optimally designed system is resilient to both unique attacks and recurrent attacks, the latter with a lower overhead. Overall, the notion of resilience can be thought of in the light of three main sources of lack of resilience, as follows: exogenous factors, such as natural variations and attack scenarios; mismatch between engineered designs and exogenous factors ranging from DDoS (distributed denial-of-service) attacks or other cybersecurity nightmares, so called "black swan" events, disabling critical services of the municipal electrical grids and other connected infrastructures, data breaches, and network failures; and the fragility of engineered designs themselves encompassing bugs, human-computer interactions (HCI), and the overall complexity of real-world systems. In the paper, our focus is on design and deployment innovations that are broadly applicable across a range of CPS application areas.

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arXiv2018

Voronoi Partition-based Scenario Reduction for Fast Sampling-based Stochastic Reachability Computation of LTI Systems

In this paper, we address the stochastic reach-avoid problem for linear systems with additive stochastic uncertainty. We seek to compute the maximum probability that the states remain in a safe set over a finite time horizon and reach a target set at the final time. We employ sampling-based methods and provide a lower bound on the number of scenarios required to guarantee that our estimate provides an underapproximation. Due to the probabilistic nature of the sampling-based methods, our underapproximation guarantee is probabilistic, and the proposed lower bound can be used to satisfy a prescribed probabilistic confidence level. To decrease the computational complexity, we propose a Voronoi partition-based to check the reach-avoid constraints at representative partitions (cells), instead of the original scenarios. The state constraints arising from the safe and target sets are tightened appropriately so that the solution provides an underapproximation for the original sampling-based method. We propose a systematic approach for selecting these representative cells and provide the flexibility to trade-off the number of cells needed for accuracy with the computational cost.

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arXiv2015

Approximate Safety Verification and Control of Partially Observable Stochastic Hybrid Systems

Assuring safety in discrete time stochastic hybrid systems is particularly difficult when only noisy or incomplete observations of the state are available. We first review a formulation of the probabilistic safety problem under noisy hybrid observations as a dynamic program over an equivalent information state. Two methods for approximately solving the dynamic program are presented. The first method approximates the hybrid system as an equivalent finite state Markov decision process, so that the information state is a probability mass function. The second approach approximates an indicator function over the safe region using radial basis functions, to represent the information state as a Gaussian mixture. In both cases, we discretize the hybrid observation process and generate a sampled set of information states, then use point-based value iteration to under-approximate the safety probability and synthesize a suboptimal control policy. We obtain error bounds and convergence results in both cases, assuming switched affine dynamics and additive Gaussian noise on the continuous states and observations. We compare the performance of the finite state and Gaussian mixture approaches on a simple numerical example.

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arXiv2014

Computational Techniques for Reachability Analysis of Partially Observable Discrete Time Stochastic Hybrid Systems

Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been applied to stochastic hybrid systems, little work has been done on the equally important problem of reachability under incomplete or noisy measurements of the state. Further, there are currently no computational methods or results for reachability analysis of partially observable discrete time stochastic hybrid systems. We provide the first numerical results for solving this problem, by drawing upon existing literature on continuous state partially observable Markov decision processes (POMDPs). We first prove that the value function for the reachability problem (with a multiplicative cost structure) is piecewise-linear and convex, just as for discrete state POMDPs with an additive cost function. Because of these properties, we are able to extend existing point-based value iteration techniques to the reachability problem, demonstrating its applicability on a benchmark temperature regulation problem.

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arXiv2014

Reachability for Partially Observable Discrete Time Stochastic Hybrid Systems

When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must be taken into account in the controller's design in order to preserve its optimality. The same is true when performing reachability calculations. To estimate the probability that the state of a stochastic system reaches, or stays within, some set of interest in a given time horizon, it is necessary to find a controller (or at least prove one exists) that drives the system to that set with maximum probability. This controller, however, does not have access to the true state of the system. To date, little work has been done on stochastic reachability calculations with partially observable states. What work has been done relies on converting the reachability optimization problem to one with an additive cost function, for which theoretical results are well known. Our approach is to preserve the multiplicative cost structure when deriving a sufficient statistic that reduces the problem to one of perfect state information. Our transformation includes a change of measure that simplifies the distribution of the sufficient statistic conditioned on its previous value. We develop a dynamic programming recursion for the solution of the equivalent perfect information problem, proving that the recursion is valid, an optimal solution exists, and results in the same solution as to the original problem. We also show that our results are equivalent to those for the reformulated additive cost problem, and so such a reformulation is not required.

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