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In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper" problem) as a function of the parameters. Many existing approaches to bilevel optimization employ first-order sensitivity analysis, based on the implicit function theorem (IFT), for the lower problem to derive a gradient of the lower problem solution with respect to its parameters; this IFT gradient is then used in a first-order optimization method for the upper problem. This paper extends this sensitivity analysis to provide second-order derivative information of the lower problem (which we call the IFT Hessian), enabling the usage of faster-converging second-order optimization methods at the upper level. Our analysis shows that (i) much of the computation already used to produce the IFT gradient can be reused for the IFT Hessian, (ii) errors bounds derived for the IFT gradient readily apply to the IFT Hessian, (iii) computing IFT Hessians can significantly reduce overall computation by extracting more information from each lower level solve. We corroborate our findings and demonstrate the broad range of applications of our method by applying it to problem instances of least squares hyperparameter auto-tuning, multi-class SVM auto-tuning, and inverse optimal control., Comment: 16 pages, 6 figures

Reinforcement learning (RL) is capable of sophisticated motion planning and control for robots in uncertain environments. However, state-of-the-art deep RL approaches typically lack safety guarantees, especially when the robot and environment models are unknown. To justify widespread deployment, robots must respect safety constraints without sacrificing performance. Thus, we propose a Black-box Reachability-based Safety Layer (BRSL) with three main components: (1) data-driven reachability analysis for a black-box robot model, (2) a trajectory rollout planner that predicts future actions and observations using an ensemble of neural networks trained online, and (3) a differentiable polytope collision check between the reachable set and obstacles that enables correcting unsafe actions. In simulation, BRSL outperforms other state-of-the-art safe RL methods on a Turtlebot 3, a quadrotor, a trajectory-tracking point mass, and a hexarotor in wind with an unsafe set adjacent to the area of highest reward., Comment: This paper is accepted at IEEE Robotics and Automation Letters and International Conference on Robotics and Automation (ICRA)

Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With both fully-actuated and underactuated nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control., Comment: First published in Robotics: Science and Systems (RSS) 2021. This extended version is under review for a special issue in the International Journal of Robotics Research (IJRR). arXiv admin note: substantial text overlap with arXiv:2103.04490

In transportation networks, users typically choose routes in a decentralized and self-interested manner to minimize their individual travel costs, which, in practice, often results in inefficient overall outcomes for society. As a result, there has been a growing interest in designing road tolling schemes to cope with these efficiency losses and steer users toward a system-efficient traffic pattern. However, the efficacy of road tolling schemes often relies on having access to complete information on users' trip attributes, such as their origin-destination (O-D) travel information and their values of time, which may not be available in practice. Motivated by this practical consideration, we propose an online learning approach to set tolls in a traffic network to drive heterogeneous users with different values of time toward a system-efficient traffic pattern. In particular, we develop a simple yet effective algorithm that adjusts tolls at each time period solely based on the observed aggregate flows on the roads of the network without relying on any additional trip attributes of users, thereby preserving user privacy. In the setting where the O-D pairs and values of time of users are drawn i.i.d. at each period, we show that our approach obtains an expected regret and road capacity violation of $O(\sqrt{T})$, where $T$ is the number of periods over which tolls are updated. Our regret guarantee is relative to an offline oracle that has complete information on users' trip attributes. We further establish a $\Omega(\sqrt{T})$ lower bound on the regret of any algorithm, which establishes that our algorithm is optimal up to constants. Finally, we demonstrate the superior performance of our approach relative to several benchmarks on a real-world transportation network, thereby highlighting its practical applicability.

We study the so-called Gravitational Wave luminosity distance-redshift relation $d_L^{\,GW}(z)$ during cosmological eras driven by non-perfect fluids. In particular, we show that the presence of a shear viscosity in the energy momentum tensor turns out to be the most relevant effect. Within this scenario, a constant shear viscosity imprints the gravitational wave propagation through a friction term $\delta(z)$ with a uniquely given redshift dependence. This peculiar evolution predicts a specific shape for the ratio $d_{L}^{GW}/d_{L}^{EM}$ which tends to a constant value when the sources are at $z\gtrsim 1$, whereas scales linearly with the shear viscosity at lower redshifts, regardless of the value of $\Omega_{m0}$. According to our final discussion, the predicted redshift dependence $\delta(z)$ provided by a shear viscosity could be tested by upcoming surveys of multi-messenger sources against analogous scenarios provided by some widely studied theories of modified gravity., Comment: 19 pages, 4 figures. References and clarifications added. Conclusions unchanged. Accepted for publication in JCAP

Model Predictive Control (MPC) has become a popular framework in embedded control for high-performance autonomous systems. However, to achieve good control performance using MPC, an accurate dynamics model is key. To maintain real-time operation, the dynamics models used on embedded systems have been limited to simple first-principle models, which substantially limits their representative power. In contrast to such simple models, machine learning approaches, specifically neural networks, have been shown to accurately model even complex dynamic effects, but their large computational complexity hindered combination with fast real-time iteration loops. With this work, we present Real-time Neural MPC, a framework to efficiently integrate large, complex neural network architectures as dynamics models within a model-predictive control pipeline. Our experiments, performed in simulation and the real world onboard a highly agile quadrotor platform, demonstrate the capabilities of the described system to run learned models with, previously infeasible, large modeling capacity using gradient-based online optimization MPC. Compared to prior implementations of neural networks in online optimization MPC we can leverage models of over 4000 times larger parametric capacity in a 50Hz real-time window on an embedded platform. Further, we show the feasibility of our framework on real-world problems by reducing the positional tracking error by up to 82% when compared to state-of-the-art MPC approaches without neural network dynamics.

Autonomous systems and humans are increasingly sharing the same space. Robots work side by side or even hand in hand with humans to balance each other's limitations. Such cooperative interactions are ever more sophisticated. Thus, the ability to reason not just about a human's center of gravity position, but also its granular motion is an important prerequisite for human-robot interaction. Though, many algorithms ignore the multimodal nature of humans or neglect uncertainty in their motion forecasts. We present Motron, a multimodal, probabilistic, graph-structured model, that captures human's multimodality using probabilistic methods while being able to output deterministic maximum-likelihood motions and corresponding confidence values for each mode. Our model aims to be tightly integrated with the robotic planning-control-interaction loop; outputting physically feasible human motions and being computationally efficient. We demonstrate the performance of our model on several challenging real-world motion forecasting datasets, outperforming a wide array of generative/variational methods while providing state-of-the-art single-output motions if required. Both using significantly less computational power than state-of-the art algorithms., Comment: CVPR 2022

Verifying that input-output relationships of a neural network conform to prescribed operational specifications is a key enabler towards deploying these networks in safety-critical applications. Semidefinite programming (SDP)-based approaches to Rectified Linear Unit (ReLU) network verification transcribe this problem into an optimization problem, where the accuracy of any such formulation reflects the level of fidelity in how the neural network computation is represented, as well as the relaxations of intractable constraints. While the literature contains much progress on improving the tightness of SDP formulations while maintaining tractability, comparatively little work has been devoted to the other extreme, i.e., how to most accurately capture the original verification problem before SDP relaxation. In this work, we develop an exact, convex formulation of verification as a completely positive program (CPP), and provide analysis showing that our formulation is minimal -- the removal of any constraint fundamentally misrepresents the neural network computation. We leverage our formulation to provide a unifying view of existing approaches, and give insight into the source of large relaxation gaps observed in some cases.

Data-driven methodologies offer many exciting upsides, but they also introduce new challenges, particularly in the realm of user privacy. Specifically, the way data is collected can pose privacy risks to end users. In many routing services, a single entity (e.g., the routing service provider) collects and manages user trajectory data. When it comes to user privacy, these systems have a central point of failure since users have to trust that this entity will not sell or use their data to infer sensitive private information. Unfortunately, in practice many advertising companies offer to buy such data for the sake of targeted advertisements. With this as motivation, we study the problem of using location data for routing services in a privacy-preserving way. Rather than having users report their location to a central operator, we present a protocol in which users participate in a decentralized and privacy-preserving computation to estimate travel times for the roads in the network in a way that no individuals' location is ever observed by any other party. The protocol uses the Laplace mechanism in conjunction with secure multi-party computation to ensure that it is cryptogrpahically secure and that its output is differentially private. A natural question is if privacy necessitates degradation in accuracy or system performance. We show that if a road has sufficiently high capacity, then the travel time estimated by our protocol is provably close to the ground truth travel time. We validate the protocol through numerical experiments which show that using the protocol as a routing service provides privacy guarantees with minimal overhead to user travel time.

Autonomous Mobility-on-Demand (AMoD) systems represent an attractive alternative to existing transportation paradigms, currently challenged by urbanization and increasing travel needs. By centrally controlling a fleet of self-driving vehicles, these systems provide mobility service to customers and are currently starting to be deployed in a number of cities around the world. Current learning-based approaches for controlling AMoD systems are limited to the single-city scenario, whereby the service operator is allowed to take an unlimited amount of operational decisions within the same transportation system. However, real-world system operators can hardly afford to fully re-train AMoD controllers for every city they operate in, as this could result in a high number of poor-quality decisions during training, making the single-city strategy a potentially impractical solution. To address these limitations, we propose to formalize the multi-city AMoD problem through the lens of meta-reinforcement learning (meta-RL) and devise an actor-critic algorithm based on recurrent graph neural networks. In our approach, AMoD controllers are explicitly trained such that a small amount of experience within a new city will produce good system performance. Empirically, we show how control policies learned through meta-RL are able to achieve near-optimal performance on unseen cities by learning rapidly adaptable policies, thus making them more robust not only to novel environments, but also to distribution shifts common in real-world operations, such as special events, unexpected congestion, and dynamic pricing schemes., Comment: 11 pages, 4 figures

We study two-sided many-to-one matching markets with transferable utilities, e.g., labor and rental housing markets, in which money can exchange hands between agents, subject to distributional constraints on the set of feasible allocations. In such markets, we establish the efficiency of equilibrium arrangements, specified by an assignment and transfers between agents on the two sides of the market, and study the conditions on the distributional constraints and agent preferences under which equilibria exist and can be computed efficiently. To this end, we first consider the setting when the number of institutions (e.g., firms in a labor market) is one and show that equilibrium arrangements exist irrespective of the nature of the constraint structure or the agents' preferences. However, equilibrium arrangements may not exist in markets with multiple institutions even when agents on each side have linear (or additively separable) preferences over agents on the other side. Thus, for markets with linear preferences, we study sufficient conditions on the constraint structure that guarantee the existence of equilibria using linear programming duality. Our linear programming approach not only generalizes that of Shapley and Shubik (1971) in the one-to-one matching setting to the many-to-one matching setting under distributional constraints but also provides a method to compute market equilibria efficiently.

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment., Comment: Submitted to 4th Annual Learning for Dynamics & Control Conference (L4DC) 2022

There are spatio-temporal rules that dictate how robots should operate in complex environments, e.g., road rules govern how (self-driving) vehicles should behave on the road. However, seamlessly incorporating such rules into a robot control policy remains challenging especially for real-time applications. In this work, given a desired spatio-temporal specification expressed in the Signal Temporal Logic (STL) language, we propose a semi-supervised controller synthesis technique that is attuned to human-like behaviors while satisfying desired STL specifications. Offline, we synthesize a trajectory-feedback neural network controller via an adversarial training scheme that summarizes past spatio-temporal behaviors when computing controls, and then online, we perform gradient steps to improve specification satisfaction. Central to the offline phase is an imitation-based regularization component that fosters better policy exploration and helps induce naturalistic human behaviors. Our experiments demonstrate that having imitation-based regularization leads to higher qualitative and quantitative performance compared to optimizing an STL objective only as done in prior work. We demonstrate the efficacy of our approach with an illustrative case study and show that our proposed controller outperforms a state-of-the-art shooting method in both performance and computation time., Comment: Accepted to American Controls Conference 2022

We present a first-principles investigation of the electronic and optical properties of hybrid organic-inorganic interfaces consisting of MoS$_2$ monolayer and the $\pi$-conjugate molecules pyrene and pyridine. For both hybrid systems, the quasi-particle band structure obtained from the $G_0W_0$ approximation shows -- in contrast to density-functional theory -- level alignment of type II, owing to the mutual dynamical screening of the interface constituents. $\textit{Ab initio}$ calculations of the absorption spectrum based on the Bethe-Salpeter equation reveal besides intra-layer excitons on the MoS$_2$ side, hybrid as well as charge-transfer excitons at the interface. These findings indicate that hybrid systems consisting of semiconducting transition-metal dichalcogenides and organic $\pi$-conjugate molecules can host a rich variety of optical excitations and thus provide a promising venue to explore many-body interactions and exciton physics in low dimensionality., Comment: 10 pages, 8 figures

In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of dynamical systems. By sampling inputs, evaluating their images in the true reachable set, and taking their $\epsilon$-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. Our main contribution is the derivation of asymptotic and finite-sample accuracy guarantees using random set theory. This analysis informs algorithmic design to obtain an $\epsilon$-close reachable set approximation with high probability, provides insights into which reachability problems are most challenging, and motivates safety-critical applications of the technique. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work. Informed by our analysis, we also design a robust model predictive controller that we demonstrate in hardware experiments., Comment: 4th Annual Learning for Dynamics & Control Conference (L4DC) 2022. Section V: added the assumption $\partial\mathcal{Y}\subseteq f(\partial\mathcal{X})$. If $\partial\mathcal{Y}\nsubseteq f(\partial\mathcal{X})$, then one should sample over the entire set $\mathcal{X}$ to obtain finite-sample bounds

Elastic and structural properties of $\beta$-Ga$_2$O$_3$ and $\alpha$-Ga$_2$O$_3$ are investigated from first principles. The full elastic tensors and elastic moduli of both phases at $0$ K are computed in the framework of semi-local density-functional theory. We determine mechanical instabilities of $\beta$-Ga$_2$O$_3$ by evaluating the full stiffness tensor under load for a range of hydrostatic pressure values. While a phase transition from the $\beta$ to $\alpha$ phase is found to be energetically favored at $2.6$ GPa, we show that the $\beta$ phase is only mechanically unstable for much higher pressures ($>30$ GPa), which agrees well with experimental results. Our employed approach is based on the Born stability criterion, is independent of crystal symmetry, and thus can be readily applied to different materials., Comment: 8 pages, 3 figures, 5 tables

Autonomous vehicles (AVs) must interact with a diverse set of human drivers in heterogeneous geographic areas. Ideally, fleets of AVs should share trajectory data to continually re-train and improve trajectory forecasting models from collective experience using cloud-based distributed learning. At the same time, these robots should ideally avoid uploading raw driver interaction data in order to protect proprietary policies (when sharing insights with other companies) or protect driver privacy from insurance companies. Federated learning (FL) is a popular mechanism to learn models in cloud servers from diverse users without divulging private local data. However, FL is often not robust -- it learns sub-optimal models when user data comes from highly heterogeneous distributions, which is a key hallmark of human-robot interactions. In this paper, we present a novel variant of personalized FL to specialize robust robot learning models to diverse user distributions. Our algorithm outperforms standard FL benchmarks by up to 2x in real user studies that we conducted where human-operated vehicles must gracefully merge lanes with simulated AVs in the standard CARLA and CARLO AV simulators.

We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but uncertain parameters (a source of epistemic uncertainty) with a model subject to external disturbances modeled as a Brownian motion (corresponding to aleatoric uncertainty).

Robots are widely deployed in space environments because of their versatility and robustness. However, adverse gravity conditions and challenging terrain geometry expose the limitations of traditional robot designs, which are often forced to sacrifice one of mobility or manipulation capabilities to attain the other. Prospective climbing operations in these environments reveals a need for small, compact robots capable of versatile mobility and manipulation. We propose a novel robotic concept called ReachBot that fills this need by combining two existing technologies: extendable booms and mobile manipulation. ReachBot leverages the reach and tensile strength of extendable booms to achieve an outsized reachable workspace and wrench capability. Through their lightweight, compactable structure, these booms also reduce mass and complexity compared to traditional rigid-link articulated-arm designs. Using these advantages, ReachBot excels in mobile manipulation missions in low gravity or that require climbing, particularly when anchor points are sparse. After introducing the ReachBot concept, we discuss modeling approaches and strategies for increasing stability and robustness. We then develop a 2D analytical model for ReachBot's dynamics inspired by grasp models for dexterous manipulators. Next, we introduce a waypoint-tracking controller for a planar ReachBot in microgravity. Our simulation results demonstrate the controller's robustness to disturbances and modeling error. Finally, we briefly discuss next steps that build on these initially promising results to realize the full potential of ReachBot., Comment: 12 pages, 13 figures

Recently, there has been tremendous progress in developing each individual module of the standard perception-planning robot autonomy pipeline, including detection, tracking, prediction of other agents' trajectories, and ego-agent trajectory planning. Nevertheless, there has been less attention given to the principled integration of these components, particularly in terms of the characterization and mitigation of cascading errors. This paper addresses the problem of cascading errors by focusing on the coupling between the tracking and prediction modules. First, by using state-of-the-art tracking and prediction tools, we conduct a comprehensive experimental evaluation of how severely errors stemming from tracking can impact prediction performance. On the KITTI and nuScenes datasets, we find that predictions consuming tracked trajectories as inputs (the typical case in practice) can experience a significant (even order of magnitude) drop in performance in comparison to the idealized setting where ground truth past trajectories are used as inputs. To address this issue, we propose a multi-hypothesis tracking and prediction framework. Rather than relying on a single set of tracking results for prediction, our framework simultaneously reasons about multiple sets of tracking results, thereby increasing the likelihood of including accurate tracking results as inputs to prediction. We show that this framework improves overall prediction performance over the standard single-hypothesis tracking-prediction pipeline by up to 34.2% on the nuScenes dataset, with even more significant improvements (up to ~70%) when restricting the evaluation to challenging scenarios involving identity switches and fragments -- all with an acceptable computation overhead., Comment: Project page: https://www.xinshuoweng.com/projects/MTP

We address the problem of routing a team of drones and trucks over large-scale urban road networks. To conserve their limited flight energy, drones can use trucks as temporary modes of transit en route to their own destinations. Such coordination can yield significant savings in total vehicle distance traveled, i.e., truck travel distance and drone flight distance, compared to operating drones and trucks independently. But it comes at the potentially prohibitive computational cost of deciding which trucks and drones should coordinate and when and where it is most beneficial to do so. We tackle this fundamental trade-off by decoupling our overall intractable problem into tractable sub-problems that we solve stage-wise. The first stage solves only for trucks, by computing paths that make them more likely to be useful transit options for drones. The second stage solves only for drones, by routing them over a composite of the road network and the transit network defined by truck paths from the first stage. We design a comprehensive algorithmic framework that frames each stage as a multi-agent path-finding problem and implement two distinct methods for solving them. We evaluate our approach on extensive simulations with up to $100$ agents on the real-world Manhattan road network containing nearly $4500$ vertices and $10000$ edges. Our framework saves on more than $50\%$ of vehicle distance traveled compared to independently solving for trucks and drones, and computes solutions for all settings within $5$ minutes on commodity hardware., Comment: Accepted to Autonomous Agents and Multiagent Systems, 2022

Detecting other agents and forecasting their behavior is an integral part of the modern robotic autonomy stack, especially in safety-critical scenarios entailing human-robot interaction such as autonomous driving. Due to the importance of these components, there has been a significant amount of interest and research in perception and trajectory forecasting, resulting in a wide variety of approaches. Common to most works, however, is the use of the same few accuracy-based evaluation metrics, e.g., intersection-over-union, displacement error, log-likelihood, etc. While these metrics are informative, they are task-agnostic and outputs that are evaluated as equal can lead to vastly different outcomes in downstream planning and decision making. In this work, we take a step back and critically assess current evaluation metrics, proposing task-aware metrics as a better measure of performance in systems where they are deployed. Experiments on an illustrative simulation as well as real-world autonomous driving data validate that our proposed task-aware metrics are able to account for outcome asymmetry and provide a better estimate of a model's closed-loop performance., Comment: 8 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:2107.10297

Uncertainty pervades through the modern robotic autonomy stack, with nearly every component (e.g., sensors, detection, classification, tracking, behavior prediction) producing continuous or discrete probabilistic distributions. Trajectory forecasting, in particular, is surrounded by uncertainty as its inputs are produced by (noisy) upstream perception and its outputs are predictions that are often probabilistic for use in downstream planning. However, most trajectory forecasting methods do not account for upstream uncertainty, instead taking only the most-likely values. As a result, perceptual uncertainties are not propagated through forecasting and predictions are frequently overconfident. To address this, we present a novel method for incorporating perceptual state uncertainty in trajectory forecasting, a key component of which is a new statistical distance-based loss function which encourages predicting uncertainties that better match upstream perception. We evaluate our approach both in illustrative simulations and on large-scale, real-world data, demonstrating its efficacy in propagating perceptual state uncertainty through prediction and producing more calibrated predictions., Comment: IEEE International Conference on Robotics and Automation (ICRA) 2022 -- 8 pages, 6 figures, 4 tables

Sharing forecasts of network timeseries data, such as cellular or electricity load patterns, can improve independent control applications ranging from traffic scheduling to power generation. Typically, forecasts are designed without knowledge of a downstream controller's task objective, and thus simply optimize for mean prediction error. However, such task-agnostic representations are often too large to stream over a communication network and do not emphasize salient temporal features for cooperative control. This paper presents a solution to learn succinct, highly-compressed forecasts that are co-designed with a modular controller's task objective. Our simulations with real cellular, Internet-of-Things (IoT), and electricity load data show we can improve a model predictive controller's performance by at least $25\%$ while transmitting $80\%$ less data than the competing method. Further, we present theoretical compression results for a networked variant of the classical linear quadratic regulator (LQR) control problem., Comment: Accepted by 35th Conference on Neural Information Processing Systems (NeurIPS 2021)

Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical success, these controllers still lack theoretical guarantees on their performance, such as Lyapunov stability (i.e., all trajectories of the closed-loop system are guaranteed to converge to a goal state under the control policy). This is in stark contrast to traditional model-based controller design, where principled approaches (like LQR) can synthesize stable controllers with provable guarantees. To address this gap, we propose a generic method to synthesize a Lyapunov-stable neural-network controller, together with a neural-network Lyapunov function to simultaneously certify its stability. Our approach formulates the Lyapunov condition verification as a mixed-integer linear program (MIP). Our MIP verifier either certifies the Lyapunov condition, or generates counter examples that can help improve the candidate controller and the Lyapunov function. We also present an optimization program to compute an inner approximation of the region of attraction for the closed-loop system. We apply our approach to robots including an inverted pendulum, a 2D and a 3D quadrotor, and showcase that our neural-network controller outperforms a baseline LQR controller. The code is open sourced at \url{https://github.com/StanfordASL/neural-network-lyapunov}., Comment: Published at Robotics: Science and Systems (RSS) in July, 2021

When deploying machine learning models in high-stakes robotics applications, the ability to detect unsafe situations is crucial. Early warning systems can provide alerts when an unsafe situation is imminent (in the absence of corrective action). To reliably improve safety, these warning systems should have a provable false negative rate; i.e. of the situations that are unsafe, fewer than $\epsilon$ will occur without an alert. In this work, we present a framework that combines a statistical inference technique known as conformal prediction with a simulator of robot/environment dynamics, in order to tune warning systems to provably achieve an $\epsilon$ false negative rate using as few as $1/\epsilon$ data points. We apply our framework to a driver warning system and a robotic grasping application, and empirically demonstrate guaranteed false negative rate while also observing low false detection (positive) rate., Comment: International Journal of Robotics Research, 2023

Over the past decade, GPS enabled traffic applications, such as Google Maps and Waze, have become ubiquitous and have had a significant influence on billions of daily commuters' travel patterns. A consequence of the online route suggestions of such applications, e.g., via greedy routing, has often been an increase in traffic congestion since the induced travel patterns may be far from the system optimum. Spurred by the widespread impact of traffic applications on travel patterns, this work studies online traffic routing in the context of capacity-constrained parallel road networks and analyzes this problem from two perspectives. First, we perform a worst-case analysis to identify the limits of deterministic online routing and show that the ratio between the total travel cost of the online solution of any deterministic algorithm and that of the optimal offline solution is unbounded, even in simple settings. This result motivates us to move beyond worst-case analysis. Here, we consider algorithms that exploit knowledge of past problem instances and show how to design data-driven algorithms whose performance can be quantified and formally generalized to unseen future instances. We present numerical experiments based on an application case for the San Francisco Bay Area to evaluate the performance of our approach. Our results show that the data-driven algorithms we develop outperform commonly used greedy online-routing algorithms.

This paper presents an approach towards guaranteed trajectory tracking for nonlinear control-affine systems subject to external disturbances based on robust control contraction metrics (CCM) that aims to minimize the $\mathcal L_\infty$ gain from the disturbances to nominal-actual trajectory deviations. The guarantee is in the form of invariant tubes, computed offline and valid for any nominal trajectories, in which the actual states and inputs of the system are guaranteed to stay despite disturbances. Under mild assumptions, we prove that the proposed robust CCM (RCCM) approach yields tighter tubes than an existing approach based on CCM and input-to-state stability analysis. We show how the RCCM-based tracking controller together with tubes can be incorporated into a feedback motion planning framework to plan safe trajectories for robotic systems. Simulation results illustrate the effectiveness of the proposed method and empirically demonstrate reduced conservatism compared to the CCM-based approach., Comment: Extended version of a paper published in IEEE Robotics and Automation Letters (2022). 13 pages, 6 figures

Cities worldwide struggle with overloaded transportation systems and their externalities. The emerging autonomous transportation technology has the potential to alleviate these issues, but the decisions of profit-maximizing operators running large autonomous fleets could negatively impact other stakeholders and the transportation system. An analysis of these tradeoffs requires modeling the modes of transportation in a unified framework. In this paper, we propose such a framework, which allows us to study the interplay among mobility service providers (MSPs), public transport authorities, and customers. Our framework combines a graph-theoretic network model for the transportation system with a game-theoretic market model in which MSPs are profit maximizers while customers select individually-optimal transportation options. We apply our framework to data for the city of Berlin and present sensitivity analyses to study parameters that MSPs or municipalities can strategically influence. We show that autonomous ride-hailing systems may cannibalize a public transportation system, serving between 7% and 80% of all customers, depending on market conditions and policy restrictions., Comment: Accepted for publication in the IEEE Transactions on Control of Network Systems