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Artificial intelligence (AI) is interacting with people at an unprecedented scale, offering new avenues for immense positive impact, but also raising widespread concerns around the potential for individual and societal harm. Today, the predominant paradigm for human--AI safety focuses on fine-tuning the generative model's outputs to better agree with human-provided examples or feedback. In reality, however, the consequences of an AI model's outputs cannot be determined in isolation: they are tightly entangled with the responses and behavior of human users over time. In this paper, we distill key complementary lessons from AI safety and control systems safety, highlighting open challenges as well as key synergies between both fields. We then argue that meaningful safety assurances for advanced AI technologies require reasoning about how the feedback loop formed by AI outputs and human behavior may drive the interaction towards different outcomes. To this end, we introduce a unifying formalism to capture dynamic, safety-critical human--AI interactions and propose a concrete technical roadmap towards next-generation human-centered AI safety., Comment: Revised version with refined exposition and technical details. 12 pages + references, 5 figures

Despite the impressive recent advances in learning-based robot control, ensuring robustness to out-of-distribution conditions remains an open challenge. Safety filters can, in principle, keep arbitrary control policies from incurring catastrophic failures by overriding unsafe actions, but existing solutions for complex (e.g., legged) robot dynamics do not span the full motion envelope and instead rely on local, reduced-order models. These filters tend to overly restrict agility and can still fail when perturbed away from nominal conditions. This paper presents the gameplay filter, a new class of predictive safety filter that continually plays out hypothetical matches between its simulation-trained safety strategy and a virtual adversary co-trained to invoke worst-case events and sim-to-real error, and precludes actions that would cause it to fail down the line. We demonstrate the scalability and robustness of the approach with a first-of-its-kind full-order safety filter for (36-D) quadrupedal dynamics. Physical experiments on two different quadruped platforms demonstrate the superior zero-shot effectiveness of the gameplay filter under large perturbations such as tugging and unmodeled terrain.

We consider the multi-agent spatial navigation problem of computing the socially optimal order of play, i.e., the sequence in which the agents commit to their decisions, and its associated equilibrium in an N-player Stackelberg trajectory game. We model this problem as a mixed-integer optimization problem over the space of all possible Stackelberg games associated with the order of play's permutations. To solve the problem, we introduce Branch and Play (B&P), an efficient and exact algorithm that provably converges to a socially optimal order of play and its Stackelberg equilibrium. As a subroutine for B&P, we employ and extend sequential trajectory planning, i.e., a popular multi-agent control approach, to scalably compute valid local Stackelberg equilibria for any given order of play. We demonstrate the practical utility of B&P to coordinate air traffic control, swarm formation, and delivery vehicle fleets. We find that B&P consistently outperforms various baselines, and computes the socially optimal equilibrium., Comment: Robotics: Science and Systems (RSS) 2024

An outstanding challenge for the widespread deployment of robotic systems like autonomous vehicles is ensuring safe interaction with humans without sacrificing performance. Existing safety methods often neglect the robot's ability to learn and adapt at runtime, leading to overly conservative behavior. This paper proposes a new closed-loop paradigm for synthesizing safe control policies that explicitly account for the robot's evolving uncertainty and its ability to quickly respond to future scenarios as they arise, by jointly considering the physical dynamics and the robot's learning algorithm. We leverage adversarial reinforcement learning for tractable safety analysis under high-dimensional learning dynamics and demonstrate our framework's ability to work with both Bayesian belief propagation and implicit learning through large pre-trained neural trajectory predictors., Comment: Conference on Robot Learning 2023

Safety is a central requirement for autonomous system operation across domains. Hamilton-Jacobi (HJ) reachability analysis can be used to construct "least-restrictive" safety filters that result in infrequent, but often extreme, control overrides. In contrast, control barrier function (CBF) methods apply smooth control corrections to guard the system against an often conservative safety boundary. This paper provides an online scheme to construct an implicit CBF through HJ reach-avoid differential dynamic programming in a receding-horizon framework, enabling smooth safety filtering with infinite-time safety guarantees. Simulations with the Dubins car and 5D bicycle dynamics demonstrate the scheme's ability to preserve safety smoothly without the conservativeness of handcrafted CBFs., Comment: Accepted in IEEE Control Systems Letters (L-CSS)

The ability to accurately predict others' behavior is central to the safety and efficiency of interactive robotics. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as other agents' goals, attention, and willingness to cooperate. Dual control theory addresses this challenge by treating unknown parameters of a predictive model as stochastic hidden states and inferring their values at runtime using information gathered during system operation. While able to optimally and automatically trade off exploration and exploitation, dual control is computationally intractable for general interactive motion planning. In this paper, we present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of stochastic dynamic programming, leading to a model predictive control problem that can be readily solved by real-time gradient-based optimization methods. The resulting policy is shown to preserve the dual control effect for a broad class of predictive models with both continuous and categorical uncertainty. To ensure the safe operation of the interacting agents, we use a runtime safety filter (also referred to as a "shielding" scheme), which overrides the robot's dual control policy with a safety fallback strategy when a safety-critical event is imminent. We then augment the dual control framework with an improved variant of the recently proposed shielding-aware robust planning scheme, which proactively balances the nominal planning performance with the risk of high-cost emergency maneuvers triggered by low-probability agent behaviors. We demonstrate the efficacy of our approach with both simulated driving studies and hardware experiments using 1/10 scale autonomous vehicles., Comment: The International Journal of Robotics Research. arXiv admin note: text overlap with arXiv:2202.07720

The ability to accurately predict human behavior is central to the safety and efficiency of robot autonomy in interactive settings. Unfortunately, robots often lack access to key information on which these predictions may hinge, such as people's goals, attention, and willingness to cooperate. Dual control theory addresses this challenge by treating unknown parameters of a predictive model as stochastic hidden states and inferring their values at runtime using information gathered during system operation. While able to optimally and automatically trade off exploration and exploitation, dual control is computationally intractable for general interactive motion planning, mainly due to the fundamental coupling between robot trajectory optimization and human intent inference. In this paper, we present a novel algorithmic approach to enable active uncertainty reduction for interactive motion planning based on the implicit dual control paradigm. Our approach relies on sampling-based approximation of stochastic dynamic programming, leading to a model predictive control problem that can be readily solved by real-time gradient-based optimization methods. The resulting policy is shown to preserve the dual control effect for a broad class of predictive human models with both continuous and categorical uncertainty. The efficacy of our approach is demonstrated with simulated driving examples., Comment: Workshop on the Algorithmic Foundations of Robotics (WAFR) 2022

Safety is a critical component of autonomous systems and remains a challenge for learning-based policies to be utilized in the real world. In particular, policies learned using reinforcement learning often fail to generalize to novel environments due to unsafe behavior. In this paper, we propose Sim-to-Lab-to-Real to bridge the reality gap with a probabilistically guaranteed safety-aware policy distribution. To improve safety, we apply a dual policy setup where a performance policy is trained using the cumulative task reward and a backup (safety) policy is trained by solving the Safety Bellman Equation based on Hamilton-Jacobi (HJ) reachability analysis. In Sim-to-Lab transfer, we apply a supervisory control scheme to shield unsafe actions during exploration; in Lab-to-Real transfer, we leverage the Probably Approximately Correct (PAC)-Bayes framework to provide lower bounds on the expected performance and safety of policies in unseen environments. Additionally, inheriting from the HJ reachability analysis, the bound accounts for the expectation over the worst-case safety in each environment. We empirically study the proposed framework for ego-vision navigation in two types of indoor environments with varying degrees of photorealism. We also demonstrate strong generalization performance through hardware experiments in real indoor spaces with a quadrupedal robot. See https://sites.google.com/princeton.edu/sim-to-lab-to-real for supplementary material., Comment: Accepted to Special Issue on Risk-aware Autonomous Systems: Theory and Practice, Artificial Intelligence

Reach-avoid optimal control problems, in which the system must reach certain goal conditions while staying clear of unacceptable failure modes, are central to safety and liveness assurance for autonomous robotic systems, but their exact solutions are intractable for complex dynamics and environments. Recent successes in reinforcement learning methods to approximately solve optimal control problems with performance objectives make their application to certification problems attractive; however, the Lagrange-type objective used in reinforcement learning is not suitable to encode temporal logic requirements. Recent work has shown promise in extending the reinforcement learning machinery to safety-type problems, whose objective is not a sum, but a minimum (or maximum) over time. In this work, we generalize the reinforcement learning formulation to handle all optimal control problems in the reach-avoid category. We derive a time-discounted reach-avoid Bellman backup with contraction mapping properties and prove that the resulting reach-avoid Q-learning algorithm converges under analogous conditions to the traditional Lagrange-type problem, yielding an arbitrarily tight conservative approximation to the reach-avoid set. We further demonstrate the use of this formulation with deep reinforcement learning methods, retaining zero-violation guarantees by treating the approximate solutions as untrusted oracles in a model-predictive supervisory control framework. We evaluate our proposed framework on a range of nonlinear systems, validating the results against analytic and numerical solutions, and through Monte Carlo simulation in previously intractable problems. Our results open the door to a range of learning-based methods for safe-and-live autonomous behavior, with applications across robotics and automation. See https://github.com/SafeRoboticsLab/safety_rl for code and supplementary material., Comment: Accepted in Robotics: Science and Systems (RSS), 2021

Safety-critical applications require controllers/policies that can guarantee safety with high confidence. The control barrier function is a useful tool to guarantee safety if we have access to the ground-truth system dynamics. In practice, we have inaccurate knowledge of the system dynamics, which can lead to unsafe behaviors due to unmodeled residual dynamics. Learning the residual dynamics with deterministic machine learning models can prevent the unsafe behavior but can fail when the predictions are imperfect. In this situation, a probabilistic learning method that reasons about the uncertainty of its predictions can help provide robust safety margins. In this work, we use a Gaussian process to model the projection of the residual dynamics onto a control barrier function. We propose a novel optimization procedure to generate safe controls that can guarantee safety with high probability. The safety filter is provided with the ability to reason about the uncertainty of the predictions from the GP. We show the efficacy of this method through experiments on Segway and Quadrotor simulations. Our proposed probabilistic approach is able to reduce the number of safety violations significantly as compared to the deterministic approach with a neural network., Comment: Presented at NeurIPS 2021 workshop - Safe and Robust Control of Uncertain Systems

Jointly achieving safety and efficiency in human-robot interaction (HRI) settings is a challenging problem, as the robot's planning objectives may be at odds with the human's own intent and expectations. Recent approaches ensure safe robot operation in uncertain environments through a supervisory control scheme, sometimes called "shielding", which overrides the robot's nominal plan with a safety fallback strategy when a safety-critical event is imminent. These reactive "last-resort" strategies (typically in the form of aggressive emergency maneuvers) focus on preserving safety without efficiency considerations; when the nominal planner is unaware of possible safety overrides, shielding can be activated more frequently than necessary, leading to degraded performance. In this work, we propose a new shielding-based planning approach that allows the robot to plan efficiently by explicitly accounting for possible future shielding events. Leveraging recent work on Bayesian human motion prediction, the resulting robot policy proactively balances nominal performance with the risk of high-cost emergency maneuvers triggered by low-probability human behaviors. We formalize Shielding-Aware Robust Planning (SHARP) as a stochastic optimal control problem and propose a computationally efficient framework for finding tractable approximate solutions at runtime. Our method outperforms the shielding-agnostic motion planning baseline (equipped with the same human intent inference scheme) on simulated driving examples with human trajectories taken from the recently released Waymo Open Motion Dataset.

We study the class of reach-avoid dynamic games in which multiple agents interact noncooperatively, and each wishes to satisfy a distinct target criterion while avoiding a failure criterion. Reach-avoid games are commonly used to express safety-critical optimal control problems found in mobile robot motion planning. Here, we focus on finding time-consistent solutions, in which future motion plans remain optimal even when a robot diverges from the plan early on due to, e.g., intrinsic dynamic uncertainty or extrinsic environment disturbances. Our main contribution is a computationally-efficient algorithm for multi-agent reach-avoid games which renders time-consistent solutions for all players. We demonstrate our approach in two- and three-player simulated driving scenarios, in which our method provides safe control strategies for all agents., Comment: accepted to ICRA 2022

Autonomous vehicles interacting with other traffic participants heavily rely on the perception and prediction of other agents' behaviors to plan safe trajectories. However, as occlusions limit the vehicle's perception ability, reasoning about potential hazards beyond the field of view is one of the most challenging issues in developing autonomous driving systems. This paper introduces a novel analytical approach that poses safe trajectory planning under occlusions as a hybrid zero-sum dynamic game between the autonomous vehicle (evader) and an initially hidden traffic participant (pursuer). Due to occlusions, the pursuer's state is initially unknown to the evader and may later be discovered by the vehicle's sensors. The analysis yields optimal strategies for both players as well as the set of initial conditions from which the autonomous vehicle is guaranteed to avoid collisions. We leverage this theoretical result to develop a novel trajectory planning framework for autonomous driving that provides worst-case safety guarantees while minimizing conservativeness by accounting for the vehicle's ability to actively avoid other road users as soon as they are detected in future observations. Our framework is agnostic to the driving environment and suitable for various motion planners. We demonstrate our algorithm on challenging urban and highway driving scenarios using the open-source CARLA simulator., Comment: To be appeared in Robotics: Science and Systems (RSS), 2021

Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified \textit{planning model} of the system. The plan is tracked by the system, represented by a more realistic, higher-dimensional \textit{tracking model}. We precompute the tracking error bound (TEB) due to mismatch between the two models and due to external disturbances. We also obtain the corresponding tracking controller used to stay within the TEB. The precomputation does not require prior knowledge of the environment. We demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and three different real-time trajectory planners with three different tracking-planning model pairs., Comment: Published in the IEEE Transactions on Automatic Control

Human input has enabled autonomous systems to improve their capabilities and achieve complex behaviors that are otherwise challenging to generate automatically. Recent work focuses on how robots can use such input - like demonstrations or corrections - to learn intended objectives. These techniques assume that the human's desired objective already exists within the robot's hypothesis space. In reality, this assumption is often inaccurate: there will always be situations where the person might care about aspects of the task that the robot does not know about. Without this knowledge, the robot cannot infer the correct objective. Hence, when the robot's hypothesis space is misspecified, even methods that keep track of uncertainty over the objective fail because they reason about which hypothesis might be correct, and not whether any of the hypotheses are correct. In this paper, we posit that the robot should reason explicitly about how well it can explain human inputs given its hypothesis space and use that situational confidence to inform how it should incorporate human input. We demonstrate our method on a 7 degree-of-freedom robot manipulator in learning from two important types of human input: demonstrations of manipulation tasks, and physical corrections during the robot's task execution., Comment: 20 pages. 12 figures, 1 table. IEEE Transactions on Robotics, 2020

Robots need models of human behavior for both inferring human goals and preferences, and predicting what people will do. A common model is the Boltzmann noisily-rational decision model, which assumes people approximately optimize a reward function and choose trajectories in proportion to their exponentiated reward. While this model has been successful in a variety of robotics domains, its roots lie in econometrics, and in modeling decisions among different discrete options, each with its own utility or reward. In contrast, human trajectories lie in a continuous space, with continuous-valued features that influence the reward function. We propose that it is time to rethink the Boltzmann model, and design it from the ground up to operate over such trajectory spaces. We introduce a model that explicitly accounts for distances between trajectories, rather than only their rewards. Rather than each trajectory affecting the decision independently, similar trajectories now affect the decision together. We start by showing that our model better explains human behavior in a user study. We then analyze the implications this has for robot inference, first in toy environments where we have ground truth and find more accurate inference, and finally for a 7DOF robot arm learning from user demonstrations., Comment: 9 pages, 7 figures

We evaluate the performance of Devito, a domain specific language (DSL) for finite differences on Arm ThunderX2 processors. Experiments with two common seismic computational kernels demonstrate that Arm processors can deliver competitive performance compared to other Intel Xeon processors., Comment: 2 pages, one figure, 2 tables

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk (CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set, and provide theoretical arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).