Claire J. Tomlin

Andreas Doering, Marius Wiggert, Hanna Krasowski et al. · mit

Low-propulsion vessels can take advantage of powerful ocean currents to navigate towards a destination. Recent results demonstrated that vessels can reach their destination with high probability despite forecast errors. However, these results do not consider the critical aspect of safety of such vessels: because of their low propulsion which is much smaller than the magnitude of currents, they might end up in currents that inevitably push them into unsafe areas such as shallow areas, garbage patches, and shipping lanes. In this work, we first investigate the risk of stranding for free-floating vessels in the Northeast Pacific. We find that at least 5.04% would strand within 90 days. Next, we encode the unsafe sets as hard constraints into Hamilton-Jacobi Multi-Time Reachability (HJ-MTR) to synthesize a feedback policy that is equivalent to re-planning at each time step at low computational cost. While applying this policy closed-loop guarantees safe operation when the currents are known, in realistic situations only imperfect forecasts are available. We demonstrate the safety of our approach in such realistic situations empirically with large-scale simulations of a vessel navigating in high-risk regions in the Northeast Pacific. We find that applying our policy closed-loop with daily re-planning on new forecasts can ensure safety with high probability even under forecast errors that exceed the maximal propulsion. Our method significantly improves safety over the baselines and still achieves a timely arrival of the vessel at the destination.

Somil Bansal, Mo Chen, Sylvia Herbert et al.

Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools. The main challenge is addressing its exponential computational complexity with respect to the number of state variables. In this tutorial, we present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets. In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights.

Anil Aswani, Humberto Gonzalez, S. Shankar Sastry et al.

Controller design faces a trade-off between robustness and performance, and the reliability of linear controllers has caused many practitioners to focus on the former. However, there is renewed interest in improving system performance to deal with growing energy constraints. This paper describes a learning-based model predictive control (LBMPC) scheme that provides deterministic guarantees on robustness, while statistical identification tools are used to identify richer models of the system in order to improve performance; the benefits of this framework are that it handles state and input constraints, optimizes system performance with respect to a cost function, and can be designed to use a wide variety of parametric or nonparametric statistical tools. The main insight of LBMPC is that safety and performance can be decoupled under reasonable conditions in an optimization framework by maintaining two models of the system. The first is an approximate model with bounds on its uncertainty, and the second model is updated by statistical methods. LBMPC improves performance by choosing inputs that minimize a cost subject to the learned dynamics, and it ensures safety and robustness by checking whether these same inputs keep the approximate model stable when it is subject to uncertainty. Furthermore, we show that if the system is sufficiently excited, then the LBMPC control action probabilistically converges to that of an MPC computed using the true dynamics.

Matthias Killer, Marius Wiggert, Hanna Krasowski et al. · mit

Seaweed biomass presents a substantial opportunity for climate mitigation, yet to realize its potential, farming must be expanded to the vast open oceans. However, in the open ocean neither anchored farming nor floating farms with powerful engines are economically viable. Thus, a potential solution are farms that operate by going with the flow, utilizing minimal propulsion to strategically leverage beneficial ocean currents. In this work, we focus on low-power autonomous seaweed farms and design controllers that maximize seaweed growth by taking advantage of ocean currents. We first introduce a Dynamic Programming (DP) formulation to solve for the growth-optimal value function when the true currents are known. However, in reality only short-term imperfect forecasts with increasing uncertainty are available. Hence, we present three additional extensions. Firstly, we use frequent replanning to mitigate forecast errors. Second, to optimize for long-term growth, we extend the value function beyond the forecast horizon by estimating the expected future growth based on seasonal average currents. Lastly, we introduce a discounted finite-time DP formulation to account for the increasing uncertainty in future ocean current estimates. We empirically evaluate our approach with 30-day simulations of farms in realistic ocean conditions. Our method achieves 95.8\% of the best possible growth using only 5-day forecasts.This demonstrates that low-power propulsion is a promising method to operate autonomous seaweed farms in real-world conditions.

Kaylene C. Stocking, Zak Murez, Vijay Badrinarayanan et al.

Object-centric representations enable autonomous driving algorithms to reason about interactions between many independent agents and scene features. Traditionally these representations have been obtained via supervised learning, but this decouples perception from the downstream driving task and could harm generalization. In this work we adapt a self-supervised object-centric vision model to perform object decomposition using only RGB video and the pose of the vehicle as inputs. We demonstrate that our method obtains promising results on the Waymo Open perception dataset. While object mask quality lags behind supervised methods or alternatives that use more privileged information, we find that our model is capable of learning a representation that fuses multiple camera viewpoints over time and successfully tracks many vehicles and pedestrians in the dataset. Code for our model is available at https://github.com/wayveai/SOCS.

David Fridovich-Keil, Sylvia L. Herbert, Jaime F. Fisac et al.

Motion planning is an extremely well-studied problem in the robotics community, yet existing work largely falls into one of two categories: computationally efficient but with few if any safety guarantees, or able to give stronger guarantees but at high computational cost. This work builds on a recent development called FaSTrack in which a slow offline computation provides a modular safety guarantee for a faster online planner. We introduce the notion of "meta-planning" in which a refined offline computation enables safe switching between different online planners. This provides autonomous systems with the ability to adapt motion plans to a priori unknown environments in real-time as sensor measurements detect new obstacles, and the flexibility to maneuver differently in the presence of obstacles than they would in free space, all while maintaining a strict safety guarantee. We demonstrate the meta-planning algorithm both in simulation and in hardware using a small Crazyflie 2.0 quadrotor.

Mo Chen, Jaime F. Fisac, Shankar Sastry et al.

We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically, especially given the growing interest in utilizing unmanned aircraft systems for civil purposes. The direct solution of this problem by solving a single-obstacle Hamilton-Jacobi-Isaacs (HJI) variational inequality (VI) is numerically intractable due to the exponential scaling of computation complexity with problem dimensionality. Furthermore, the single-obstacle HJI VI cannot directly handle situations in which vehicles do not have a common scheduled arrival time. Instead, we perform sequential path planning by considering vehicles in order of priority, modeling higher-priority vehicles as time-varying obstacles for lower-priority vehicles. To do this, we solve a double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined as the set of states from which a vehicle can reach its target while staying within a time-varying state constraint set. From the solution of the double-obstacle HJI VI, we can also extract the latest start time and the optimal control for each vehicle. This is a first application of the double-obstacle HJI VI which can handle systems with time-varying dynamics, target sets, and state constraint sets, and results in computation complexity that scales linearly, as opposed to exponentially, with the number of vehicles in consideration.

Mo Chen, Jennifer C. Shih, Claire J. Tomlin

Multi-agent differential games are important and useful tools for analyzing many practical problems. With the recent surge of interest in using UAVs for civil purposes, the importance and urgency of developing tractable multi-agent analysis techniques that provide safety and performance guarantees is at an all-time high. Hamilton-Jacobi (HJ) reachability has successfully provided safety guarantees to small-scale systems and is flexible in terms of system dynamics. However, the exponential complexity scaling of HJ reachability prevents its direct application to large scale problems when the number of vehicles is greater than two. In this paper, we overcome the scalability limitations of HJ reachability by using a mixed integer program that exploits the properties of HJ solutions to provide higher-level control logic. Our proposed method provides safety guarantee for three-vehicle systems -- a previously intractable task for HJ reachability -- without incurring significant additional computation cost. Furthermore, our method is scalable beyond three vehicles and performs significantly better by several metrics than an extension of pairwise collision avoidance to multi-vehicle collision avoidance. We demonstrate our proposed method in simulations.

Mo Chen, Qie Hu, Casey Mackin et al.

Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations such as package delivery, firefighting, and fast disaster response. As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the airspace, in order to ensure their liveness and safety requirements are met. Hamilton-Jacobi (HJ) reachability is a powerful framework for providing conditions under which these requirements can be met, and for synthesizing the optimal controller for meeting them. However, due to the curse of dimensionality, HJ reachability is only tractable for a small number of vehicles if their set of maneuvers is unrestricted. In this paper, we define a platoon to be a group of UAVs in a single-file formation. We model each vehicle as a hybrid system with modes corresponding to its role in the platoon, and specify the set of allowed maneuvers in each mode to make the analysis tractable. We propose several liveness controllers based on HJ reachability, and wrap a safety controller, also based on HJ reachability, around the liveness controllers. For a single altitude range, our approach guarantees safety for one safety breach; in the unlikely event of multiple safety breaches, safety can be guaranteed over multiple altitude ranges. We demonstrate the satisfaction of liveness and safety requirements through simulations of three common scenarios.

Katie Kang, Paula Gradu, Jason Choi et al.

Learned models and policies can generalize effectively when evaluated within the distribution of the training data, but can produce unpredictable and erroneous outputs on out-of-distribution inputs. In order to avoid distribution shift when deploying learning-based control algorithms, we seek a mechanism to constrain the agent to states and actions that resemble those that it was trained on. In control theory, Lyapunov stability and control-invariant sets allow us to make guarantees about controllers that stabilize the system around specific states, while in machine learning, density models allow us to estimate the training data distribution. Can we combine these two concepts, producing learning-based control algorithms that constrain the system to in-distribution states using only in-distribution actions? In this work, we propose to do this by combining concepts from Lyapunov stability and density estimation, introducing Lyapunov density models: a generalization of control Lyapunov functions and density models that provides guarantees on an agent's ability to stay in-distribution over its entire trajectory.

Datong Zhou, Maximilian Balandat, Claire Tomlin

The large scale deployment of Advanced Metering Infrastructure among residential energy customers has served as a boon for energy systems research relying on granular consumption data. Residential Demand Response aims to utilize the flexibility of consumers to reduce their energy usage during times when the grid is strained. Suitable incentive mechanisms to encourage customers to deviate from their usual behavior have to be implemented to correctly control the bids into the wholesale electricity market as a Demand Response provider. In this paper, we present a framework for short term load forecasting on an individual user level, and relate nonexperimental estimates of Demand Response efficacy, i.e. the estimated reduction of consumption during Demand Response events, to the variability of user consumption. We apply our framework on a data set from a residential Demand Response program in the Western United States. Our results suggest that users with more variable consumption patterns are more likely to reduce their consumption compared to users with a more regular consumption behavior.

Sylvia L. Herbert, Shromona Ghosh, Somil Bansal et al.

Hamilton-Jacobi-Isaacs (HJI) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. This analysis is computationally intensive and typically performed offline. Online, however, the autonomous system may experience changes in system dynamics, external disturbances, and/or the surrounding environment, requiring updated safety guarantees. Rather than restarting the safety analysis, we propose a method of "warm-start" reachability, which uses a user-defined initialization (typically the previously computed solution). By starting with an HJI function that is closer to the solution than the standard initialization, convergence may take fewer iterations. In this paper we prove that warm-starting will result in guaranteed conservative solutions by over-approximating the states that must be avoided to maintain safety. We additionally prove that for many common problem formulations, warm-starting will result in exact solutions.We demonstrate our method on several illustrative examples with a double integrator, and also on a more practical example with a 10D quadcopter model that experiences changes in mass and disturbances and must update its safety guarantees accordingly. We compare our approach to standard reachability and a recently proposed "discounted" reachability method, and find for our examples that warm-starting is 1.6 times faster than standard and 6.2 times faster than (untuned) discounted reachability.

Thomas T. Zhang, Katie Kang, Bruce D. Lee et al.

We study representation learning for efficient imitation learning over linear systems. In particular, we consider a setting where learning is split into two phases: (a) a pre-training step where a shared $k$-dimensional representation is learned from $H$ source policies, and (b) a target policy fine-tuning step where the learned representation is used to parameterize the policy class. We find that the imitation gap over trajectories generated by the learned target policy is bounded by $\tilde{O}\left( \frac{k n_x}{HN_{\mathrm{shared}}} + \frac{k n_u}{N_{\mathrm{target}}}\right)$, where $n_x > k$ is the state dimension, $n_u$ is the input dimension, $N_{\mathrm{shared}}$ denotes the total amount of data collected for each policy during representation learning, and $N_{\mathrm{target}}$ is the amount of target task data. This result formalizes the intuition that aggregating data across related tasks to learn a representation can significantly improve the sample efficiency of learning a target task. The trends suggested by this bound are corroborated in simulation.

Roel Dobbe, Werner van Westering, Stephan Liu et al.

Implementing state estimation in low and medium voltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to improve voltage predictions in real-time by leveraging a limited set of real-time measurements. The method relies on Bayesian estimation formulated as a linear least squares estimation problem, which resembles the classical weighted least-squares (WLS) approach for scenarios where full network observability is not available. We build on recently developed linear approximations for unbalanced three-phase power flow to construct voltage predictions as a linear mapping of load predictions constructed with Gaussian processes. The estimation step to update the voltage forecasts in real-time is a linear computation allowing fast high-resolution state estimate updates. The uncertainty in forecasts can be determined a priori and smoothed a posteriori, making the method useful for both planning, operation and post-hoc analysis. The method outperforms conventional WLS and is applied to different test feeders and validated on a real test feeder with the utility Alliander in The Netherlands.

Caroline Le Floch, Somil Bansal, Claire J. Tomlin et al.

This paper presents a predictive controller for handling plug-and-play (P&P) charging requests of flexible loads in a distribution system. We define two types of flexible loads: (i) deferrable loads that have a fixed power profile but can be deferred in time and (ii) shapeable loads that have flexible power profiles but fixed energy requests, such as Plug-in Electric Vehicles (PEVs). The proposed method uses a hierarchical control scheme based on a model predictive control (MPC) formulation for minimizing the global system cost. The first stage computes a reachable reference that trades off deviation from the nominal voltage with the required generation control. The second stage uses a price-based objective to aggregate flexible loads and provide load shaping services, while satisfying system constraints and users' preferences at all times. It is shown that the proposed controller is recursively feasible under specific conditions, i.e. the flexible load demands are satisfied and bus voltages remain within the desired limits. Finally, the proposed scheme is illustrated on a 55 bus radial distribution network.

Young Hwan Chang, Qie Hu, Claire J. Tomlin

Cyber-physical systems are found in many applications such as power networks, manufacturing processes, and air and ground transportation systems. Maintaining security of these systems under cyber attacks is an important and challenging task, since these attacks can be erratic and thus difficult to model. Secure estimation problems study how to estimate the true system states when measurements are corrupted and/or control inputs are compromised by attackers. The authors in [1] proposed a secure estimation method when the set of attacked nodes (sensors, controllers) is fixed. In this paper, we extend these results to scenarios in which the set of attacked nodes can change over time. We formulate this secure estimation problem into the classical error correction problem [2] and we show that accurate decoding can be guaranteed under a certain condition. Furthermore, we propose a combined secure estimation method with our proposed secure estimator and the Kalman Filter for improved practical performance. Finally, we demonstrate the performance of our method through simulations of two scenarios where an unmanned aerial vehicle is under adversarial attack.

Michael H. Lim, Tyler J. Becker, Mykel J. Kochenderfer et al.

Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are continuous or hybrid, which is often the case for physical systems. While recent online sampling-based POMDP algorithms that plan with observation likelihood weighting have shown practical effectiveness, a general theory characterizing the approximation error of the particle filtering techniques that these algorithms use has not previously been proposed. Our main contribution is bounding the error between any POMDP and its corresponding finite sample particle belief MDP (PB-MDP) approximation. This fundamental bridge between PB-MDPs and POMDPs allows us to adapt any sampling-based MDP algorithm to a POMDP by solving the corresponding particle belief MDP, thereby extending the convergence guarantees of the MDP algorithm to the POMDP. Practically, this is implemented by using the particle filter belief transition model as the generative model for the MDP solver. While this requires access to the observation density model from the POMDP, it only increases the transition sampling complexity of the MDP solver by a factor of $\mathcal{O}(C)$, where $C$ is the number of particles. Thus, when combined with sparse sampling MDP algorithms, this approach can yield algorithms for POMDPs that have no direct theoretical dependence on the size of the state and observation spaces. In addition to our theoretical contribution, we perform five numerical experiments on benchmark POMDPs to demonstrate that a simple MDP algorithm adapted using PB-MDP approximation, Sparse-PFT, achieves performance competitive with other leading continuous observation POMDP solvers.

Qie Hu, Frauke Oldewurtel, Maximilian Balandat et al.

The inter-temporal consumption flexibility of commercial buildings can be harnessed to improve the energy efficiency of buildings, or to provide ancillary service to the power grid. To do so, a predictive model of the building's thermal dynamics is required. In this paper, we identify a physics-based model of a multi-purpose commercial building including its heating, ventilation and air conditioning system during regular operation. We present our empirical results and show that large uncertainties in internal heat gains, due to occupancy and equipment, present several challenges in utilizing the building model for long-term prediction. In addition, we show that by learning these uncertain loads online and dynamically updating the building model, prediction accuracy is improved significantly.

Roel Dobbe, Ye Pu, Jingge Zhu et al.

Real-time data-driven optimization and control problems over networks may require sensitive information of participating users to calculate solutions and decision variables, such as in traffic or energy systems. Adversaries with access to coordination signals may potentially decode information on individual users and put user privacy at risk. We develop local differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have, for a larger family of convex distributed optimization problems. The mechanism allows agent to customize their own privacy level based on local needs and parameter sensitivities. We propose a general sampling based approach for determining sensitivity and derive analytical bounds for specific quadratic problems. We analyze inherent trade-offs between privacy and suboptimality and propose allocation schemes to divide the maximum allowable noise, a privacy budget, among all participating agents. Our algorithm is implemented to enable privacy in distributed optimal power flow for electric grids.

Anil Aswani, Neal Master, Jay Taneja et al.

Experimentally comparing the energy usage and comfort characteristics of different controllers in heating, ventilation, and air-conditioning (HVAC) systems is difficult because variations in weather and occupancy conditions preclude the possibility of establishing equivalent experimental conditions across the order of hours, days, and weeks. This paper is concerned with defining quantitative metrics of energy usage and occupant comfort, which can be computed and compared in a rigorous manner that is capable of determining whether differences between controllers are statistically significant in the presence of such environmental fluctuations. Experimental case studies are presented that compare two alternative controllers (a schedule controller and a hybrid system learning-based model predictive controller) to the default controller in a building-wide HVAC system. Lastly, we discuss how our proposed methodology may also be able to quantify the efficiency of other building automation systems.

Jingqi Li, Donggun Lee, Somayeh Sojoudi et al.

In this paper, we consider the infinite-horizon reach-avoid zero-sum game problem, where the goal is to find a set in the state space, referred to as the reach-avoid set, such that the system starting at a state therein could be controlled to reach a given target set without violating constraints under the worst-case disturbance. We address this problem by designing a new value function with a contracting Bellman backup, where the super-zero level set, i.e., the set of states where the value function is evaluated to be non-negative, recovers the reach-avoid set. Building upon this, we prove that the proposed method can be adapted to compute the viability kernel, or the set of states which could be controlled to satisfy given constraints, and the backward reachable set, or the set of states that could be driven towards a given target set. Finally, we propose to alleviate the curse of dimensionality issue in high-dimensional problems by extending Conservative Q-Learning, a deep reinforcement learning technique, to learn a value function such that the super-zero level set of the learned value function serves as a (conservative) approximation to the reach-avoid set. Our theoretical and empirical results suggest that the proposed method could learn reliably the reach-avoid set and the optimal control policy even with neural network approximation.

Qie Hu, Dariush Fooladivanda, Young Hwan Chang et al.

This paper focuses on securely estimating the state of a nonlinear dynamical system from a set of corrupted measurements. In particular, we consider two broad classes of nonlinear systems, and propose a technique which enables us to perform secure state estimation for such nonlinear systems. We then provide guarantees on the achievable state estimation error against arbitrary corruptions, and analytically characterize the number of errors that can be perfectly corrected by a decoder. To illustrate how the proposed nonlinear estimation approach can be applied to practical systems, we focus on secure estimation for the wide area control of an interconnected power system under cyber-physical attacks and communication failures, and propose a secure estimator for the power system. Finally, we numerically show that the proposed secure estimation algorithm enables us to reconstruct the attack signals accurately.

Fernando Castañeda, Jason J. Choi, Wonsuhk Jung et al.

Learning-based control has recently shown great efficacy in performing complex tasks for various applications. However, to deploy it in real systems, it is of vital importance to guarantee the system will stay safe. Control Barrier Functions (CBFs) offer mathematical tools for designing safety-preserving controllers for systems with known dynamics. In this article, we first introduce a model-uncertainty-aware reformulation of CBF-based safety-critical controllers using Gaussian Process (GP) regression to close the gap between an approximate mathematical model and the real system, which results in a second-order cone program (SOCP)-based control design. We then present the pointwise feasibility conditions of the resulting safety controller, highlighting the level of richness that the available system information must meet to ensure safety. We use these conditions to devise an event-triggered online data collection strategy that ensures the recursive feasibility of the learned safety controller. Our method works by constantly reasoning about whether the current information is sufficient to ensure safety or if new measurements under active safe exploration are required to reduce the uncertainty. As a result, our proposed framework can guarantee the forward invariance of the safe set defined by the CBF with high probability, even if it contains a priori unexplored regions. We validate the proposed framework in two numerical simulation experiments.

Mo Chen, Somil Bansal, Ken Tanabe et al.

Provably safe and scalable multi-vehicle path planning is an important and urgent problem due to the expected increase of automation in civilian airspace in the near future. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several small-scale problems. However, a direct application of HJ reachability to large scale systems is often intractable because of its exponentially-scaling computation complexity with respect to system dimension, also known as the "curse of dimensionality". To overcome this problem, the sequential path planning (SPP) method, which assigns strict priorities to vehicles, was previously proposed; SPP allows multi-vehicle path planning to be done with a linearly-scaling computation complexity. In this work, we demonstrate the potential of SPP algorithm for large-scale systems. In particular, we simulate large-scale multi-vehicle systems in two different urban environments, a city environment and a multi-city environment, and use the SPP algorithm for trajectory planning. SPP is able to efficiently design collision-free trajectories in both environments despite the presence of disturbances in vehicles' dynamics. To ensure a safe transition of vehicles to their destinations, our method automatically allocates space-time reservations to vehicles while accounting for the magnitude of disturbances such as wind in a provably safe way. Our simulation results show an intuitive multi-lane structure in airspace, where the number of lanes and the distance between the lanes depend on the size of disturbances and other problem parameters.

Qie Hu, Young Hwan Chang, Claire J. Tomlin

In the coming years, usage of Unmanned Aerial Vehicles (UAVs) is expected to grow tremendously. Maintaining security of UAVs under cyber attacks is an important yet challenging task, as these attacks are often erratic and difficult to predict. Secure estimation problems study how to estimate the states of a dynamical system from a set of noisy and maliciously corrupted sensor measurements. The fewer assumptions that an estimator makes about the attacker, the larger the set of attacks it can protect the system against. In this paper, we focus on sensor attacks on UAVs and attempt to design a secure estimator for linear time-invariant systems based on as few assumptions about the attackers as possible. We propose a computationally efficient estimator that protects the system against arbitrary and unbounded attacks, where the set of attacked sensors can also change over time. In addition, we propose to combine our secure estimator with a Kalman Filter for improved practical performance and demonstrate its effectiveness through simulations of two scenarios where an UAV is under adversarial cyber attack.

Datong Zhou, Qie Hu, Claire J. Tomlin

Commercial buildings are responsible for a large fraction of energy consumption in developed countries, and therefore are targets of energy efficiency programs. Motivated by the large inherent thermal inertia of buildings, the power consumption can be flexibly scheduled without compromising occupant comfort. This temporal flexibility offers opportunities for the provision of frequency regulation to support grid stability. To realize energy savings and frequency regulation, it is of prime importance to identify a realistic model for the temperature dynamics of a building. We identify a low- dimensional data-driven model and a high-dimensional physics- based model for different spatial granularities and temporal seasons based on a case study of an entire floor of Sutardja Dai Hall, an office building on the University of California, Berkeley campus. A comparison of these contrasting models shows that, despite the higher forecasting accuracy of the physics-based model, both models perform almost equally well for energy efficient control. We conclude that the data-driven model is more amenable to controller design due to its low complexity, and could serve as a substitution for highly complex physics- based models with an insignificant loss of prediction accuracy for many applications. On the other hand, our physics-based approach is more suitable for modeling buildings with finer spatial granularities.

Datong P. Zhou, Mardavij Roozbehani, Munther A. Dahleh et al.

This paper analyzes stability conditions for wholesale electricity markets under real-time retail pricing and realistic consumption models with memory, which explicitly take into account previous electricity prices and consumption levels. By passing on the current retail price of electricity from supplier to consumer and feeding the observed consumption back to the supplier, a closed-loop dynamical system for electricity prices and consumption arises whose stability is to be investigated. Under mild assumptions on the generation cost of electricity and consumers' backlog disutility functions, we show that, for consumer models with price memory only, market stability is achieved if the ratio between the consumers' marginal backlog disutility and the suppliers' marginal cost of supply remains below a fixed threshold. Further, consumer models with price and consumption memory can result in greater stability regions and faster convergence to the equilibrium compared to models with price memory alone, if consumption deviations from nominal demand are adequately penalized.

Jason J. Choi, Donggun Lee, Boyang Li et al.

Control invariant sets are crucial for various methods that aim to design safe control policies for systems whose state constraints must be satisfied over an indefinite time horizon. In this article, we explore the connections among reachability, control invariance, and Control Barrier Functions (CBFs). Unlike prior formulations based on backward reachability concepts, we establish a strong link between these three concepts by examining the inevitable Forward Reachable Tube (FRT), which is the set of states such that every trajectory reaching the FRT must have passed through a given initial set of states. First, our findings show that the inevitable FRT is a robust control invariant set if it has a continuously differentiable boundary. If the boundary is not differentiable, the FRT may lose invariance. We also show that any robust control invariant set including the initial set is a superset of the FRT if the boundary of the invariant set is differentiable. Next, we formulate a differential game between the control and disturbance, where the inevitable FRT is characterized by the zero-superlevel set of the value function. By incorporating a discount factor in the cost function of the game, the barrier constraint of the CBF naturally arises in the Hamilton-Jacobi (HJ) equation and determines the optimal policy. The resulting FRT value function serves as a CBF-like function, and conversely, any valid CBF is also a forward reachability value function. We further prove that any $C^1$ supersolution of the HJ equation for the FRT value functions is a valid CBF and characterizes a robust control invariant set that outer-approximates the FRT. Building on this property, finally, we devise a novel method that learns neural control barrier functions, which learn an control invariant superset of the FRT of a given initial set.

Anil Aswani, Claire Tomlin

Buildings are a large consumer of energy, and reducing their energy usage may provide financial and societal benefits. One challenge in achieving efficient building operation is the fact that few financial motivations exist for encouraging low energy configuration and operation of buildings. As a result, incentive schemes for managers of large buildings are being proposed for the purpose of saving energy. This paper focuses on incentive design for the configuration and operation of building-wide heating, ventilation, and air-conditioning (HVAC) systems, because these systems constitute the largest portion of energy usage in most buildings. We begin with an empirical model of a building-wide HVAC system, which describes the tradeoffs between energy consumption, quality of service (as defined by occupant satisfaction), and the amount of work required for maintenance and configuration. The model has significant non-convexities, and so we derive some results regarding qualitative properties of non-convex optimization problems with certain partial-ordering features. These results are used to show that "baselining" incentive schemes suffer from moral hazard problems, and they also encourage energy reductions at the expense of also decreasing occupant satisfaction. We propose an alternative incentive scheme that has the interpretation of a performance-based bonus. A theoretical analysis shows that this encourages energy and monetary savings and modest gains in occupant satisfaction and quality of service, which is confirmed by our numerical simulations.

Alonso Marco, Elias Morley, Claire J. Tomlin

In order for robots to safely navigate in unseen scenarios using learning-based methods, it is important to accurately detect out-of-training-distribution (OoD) situations online. Recently, Gaussian process state-space models (GPSSMs) have proven useful to discriminate unexpected observations by comparing them against probabilistic predictions. However, the capability for the model to correctly distinguish between in- and out-of-training distribution observations hinges on the accuracy of these predictions, primarily affected by the class of functions the GPSSM kernel can represent. In this paper, we propose (i) a novel approach to embed existing domain knowledge in the kernel and (ii) an OoD online runtime monitor, based on receding-horizon predictions. Domain knowledge is provided in the form of a dataset, collected either in simulation or by using a nominal model. Numerical results show that the informed kernel yields better regression quality with smaller datasets, as compared to standard kernel choices. We demonstrate the effectiveness of the OoD monitor on a real quadruped navigating an indoor setting, which reliably classifies previously unseen terrains.

Datong P. Zhou, Munther A. Dahleh, Claire J. Tomlin

Load-serving entities which procure electricity from the wholesale electricity market to service end-users face significant quantity and price risks due to the volatile nature of electricity demand and quasi-fixed residential tariffs at which electricity is sold. This paper investigates strategies for load serving entities to hedge against such price risks. Specifically, we compute profit-maximizing portfolios of forward contract and call options as a function of the uncertain aggregate user demand. We compare the profit to the case of Demand Response, where users are offered monetary incentives to temporarily reduce their consumption during periods of supply shortages. Using smart meter data of residential customers in California, we simulate optimal portfolios and derive conditions under which Demand Response outperforms call options and forward contracts.

Somil Bansal, Mo Chen, Claire J. Tomlin

Provably safe and scalable multi-vehicle trajectory planning is an important and urgent problem. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several small-scale problems. However, a direct application of HJ reachability to multi-vehicle trajectory planning is often intractable due to the "curse of dimensionality." To overcome this problem, the sequential trajectory planning (STP) method, which assigns strict priorities to vehicles, was proposed, STP allows multi-vehicle trajectory planning to be done with a linearly-scaling computation complexity. However, if a vehicle not in the set of STP vehicles enters the system, or even worse, if this vehicle is an adversarial intruder, the previous formulation requires the entire system to perform replanning, an intractable task for large-scale systems. In this paper, we make STP more practical by providing a new algorithm where replanning is only needed only for a fixed number of vehicles, irrespective of the total number of STP vehicles. Moreover, this number is a design parameter, which can be chosen based on the computational resources available during run time. We demonstrate this algorithm in a representative simulation of an urban airspace environment.

Datong P. Zhou, Maximilian Balandat, Claire J. Tomlin

We evaluate the causal effect of hour-ahead price interventions on the reduction in residential electricity consumption using a data set from a large-scale experiment on 7,000 households in California. By estimating user-level counterfactuals using time-series prediction, we estimate an average treatment effect of ~0.10 kWh (11%) per intervention and household. Next, we leverage causal decision trees to detect treatment effect heterogeneity across users by incorporating census data. These decision trees depart from classification and regression trees, as we intend to estimate a causal effect between treated and control units rather than perform outcome regression. We compare the performance of causal decision trees with a simpler, yet more inaccurate k-means clustering approach that naively detects heterogeneity in the feature space, confirming the superiority of causal decision trees. Lastly, we comment on how our methods to detect heterogeneity can be used for targeting households to improve cost efficiency.

Katie Kang, Amrith Setlur, Claire Tomlin et al. · cmu

Conventional wisdom suggests that neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. Our work reassesses this assumption for neural networks with high-dimensional inputs. Rather than extrapolating in arbitrary ways, we observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. Moreover, we find that this value often closely approximates the optimal constant solution (OCS), i.e., the prediction that minimizes the average loss over the training data without observing the input. We present results showing this phenomenon across 8 datasets with different distributional shifts (including CIFAR10-C and ImageNet-R, S), different loss functions (cross entropy, MSE, and Gaussian NLL), and different architectures (CNNs and transformers). Furthermore, we present an explanation for this behavior, which we first validate empirically and then study theoretically in a simplified setting involving deep homogeneous networks with ReLU activations. Finally, we show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.

Roel Dobbe, Stephan Liu, Ye Yuan et al.

Discrete-time linear time-varying (LTV) systems form a powerful class of models to approximate complex dynamical systems with nonlinear dynamics for the purpose of analysis, design and control. Motivated by inference of spatio-temporal dynamics in breast cancer research, we propose a method to efficiently solve an identification problem for a specific class of discrete-time LTV systems, in which the states are fully observed and there is no access to system inputs. In addition, it is assumed that we do not know on which states the inputs act, which can change between time steps, and that the total number of inputs is sparse over all states and over time. The problem is formulated as a compressive sensing problem, which incorporates the effect of measurement noise and which has a solution with a partially sparse support. We derive sufficient conditions for the unique recovery of the system model and input values, which lead to practical conditions on the number of experiments and rank conditions on system outputs. Synthetic experiments analyze the method's sensitivity to noise for randomly generated models.

Sampada Deglurkar, Ebonye Smith, Jingqi Li et al.

Reachability computations that rely on learned or estimated models require calibration in order to uphold confidence about their guarantees. Calibration generally involves sampling scenarios inside the reachable set. However, producing reasonable probabilistic guarantees may require many samples, which can be costly. To remedy this, we propose that calibration of reachable sets be performed using active learning strategies. In order to produce a probabilistic guarantee on the active learning, we adapt the Pick-to-Learn algorithm, which produces generalization bounds for standard supervised learning, to the active learning setting. Our method, Approximate Pick-to-Learn, treats the process of choosing data samples as maximizing an approximate error function. We can then use conformal prediction to ensure that the approximate error is close to the true model error. We demonstrate our technique for a simulated drone racing example in which learning is used to provide an initial guess of the reachable tube. Our method requires fewer samples to calibrate the model and provides more accurate sets than the baselines. We simultaneously provide tight generalization bounds.

Xingpeng Xia, Jason J. Choi, Ayush Agrawal et al.

Learning-based approaches have recently shown notable success in legged locomotion. However, these approaches often lack accountability, necessitating empirical tests to determine their effectiveness. In this work, we are interested in designing a learning-based locomotion controller whose stability can be examined and guaranteed. This can be achieved by verifying regions of attraction (RoAs) of legged robots to their stable walking gaits. This is a non-trivial problem for legged robots due to their hybrid dynamics. Although previous work has shown the utility of Hamilton-Jacobi (HJ) reachability to solve this problem, its practicality was limited by its poor scalability. The core contribution of our work is the employment of a deep learning-based HJ reachability solution to the hybrid legged robot dynamics, which overcomes the previous work's limitation. With the learned reachability solution, first, we can estimate a library of RoAs for various gaits. Second, we can design a one-step predictive controller that effectively stabilizes to an individual gait within the verified RoA. Finally, we can devise a strategy that switches gaits, in response to external perturbations, whose feasibility is guided by the RoA analysis. We demonstrate our method in a two-link walker simulation, whose mathematical model is well established. Our method achieves improved stability than previous model-based methods, while ensuring transparency that was not present in the existing learning-based approaches.

Sara Pohland, Claire Tomlin

While deep neural network (DNN)-based perception models are useful for many applications, these models are black boxes and their outputs are not yet well understood. To confidently enable a real-world, decision-making system to utilize such a perception model without human intervention, we must enable the system to reason about the perception model's level of competency and respond appropriately when the model is incompetent. In order for the system to make an intelligent decision about the appropriate action when the model is incompetent, it would be useful for the system to understand why the model is incompetent. We explore five novel methods for identifying regions in the input image contributing to low model competency, which we refer to as image cropping, segment masking, pixel perturbation, competency gradients, and reconstruction loss. We assess the ability of these five methods to identify unfamiliar objects, recognize regions associated with unseen classes, and identify unexplored areas in an environment. We find that the competency gradients and reconstruction loss methods show great promise in identifying regions associated with low model competency, particularly when aspects of the image that are unfamiliar to the perception model are causing this reduction in competency. Both of these methods boast low computation times and high levels of accuracy in detecting image regions that are unfamiliar to the model, allowing them to provide potential utility in decision-making pipelines. The code for reproducing our methods and results is available on GitHub: https://github.com/sarapohland/explainable-competency.

Sara Pohland, Alvin Tan, Prabal Dutta et al.

Reinforcement learning (RL) methods for social robot navigation show great success navigating robots through large crowds of people, but the performance of these learning-based methods tends to degrade in particularly challenging or unfamiliar situations due to the models' dependency on representative training data. To ensure human safety and comfort, it is critical that these algorithms handle uncommon cases appropriately, but the low frequency and wide diversity of such situations present a significant challenge for these data-driven methods. To overcome this challenge, we propose modifications to the learning process that encourage these RL policies to maintain additional caution in unfamiliar situations. Specifically, we improve the Socially Attentive Reinforcement Learning (SARL) policy by (1) modifying the training process to systematically introduce deviations into a pedestrian model, (2) updating the value network to estimate and utilize pedestrian-unpredictability features, and (3) implementing a reward function to learn an effective response to pedestrian unpredictability. Compared to the original SARL policy, our modified policy maintains similar navigation times and path lengths, while reducing the number of collisions by 82% and reducing the proportion of time spent in the pedestrians' personal space by up to 19 percentage points for the most difficult cases. We also describe how to apply these modifications to other RL policies and demonstrate that some key high-level behaviors of our approach transfer to a physical robot.

Bear Häon, Kaylene Stocking, Ian Chuang et al.

Vision-Language-Action (VLA) models are a promising path to realizing generalist embodied agents that can quickly adapt to new tasks, modalities, and environments. However, methods for interpreting and steering VLAs fall far short of classical robotics pipelines, which are grounded in explicit models of kinematics, dynamics, and control. This lack of mechanistic insight is a central challenge for deploying learned policies in real-world robotics, where robustness and explainability are critical. Motivated by advances in mechanistic interpretability for large language models, we introduce the first framework for interpreting and steering VLAs via their internal representations, enabling direct intervention in model behavior at inference time. We project feedforward activations within transformer layers onto the token embedding basis, identifying sparse semantic directions - such as speed and direction - that are causally linked to action selection. Leveraging these findings, we introduce a general-purpose activation steering method that modulates behavior in real time, without fine-tuning, reward signals, or environment interaction. We evaluate this method on two recent open-source VLAs, Pi0 and OpenVLA, and demonstrate zero-shot behavioral control in simulation (LIBERO) and on a physical robot (UR5). This work demonstrates that interpretable components of embodied VLAs can be systematically harnessed for control - establishing a new paradigm for transparent and steerable foundation models in robotics.

Kai-Chieh Hsu, Vicenç Rubies-Royo, Claire J. Tomlin et al.

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.

Anil Aswani, Patrick Bouffard, Xiaojing Zhang et al.

Learning-based control methods are an attractive approach for addressing performance and efficiency challenges in robotics and automation systems. One such technique that has found application in these domains is learning-based model predictive control (LBMPC). An important novelty of LBMPC lies in the fact that its robustness and stability properties are independent of the type of online learning used. This allows the use of advanced statistical or machine learning methods to provide the adaptation for the controller. This paper is concerned with providing practical comparisons of different optimization algorithms for implementing the LBMPC method, for the special case where the dynamic model of the system is linear and the online learning provides linear updates to the dynamic model. For comparison purposes, we have implemented a primal-dual infeasible start interior point method that exploits the sparsity structure of LBMPC. Our open source implementation (called LBmpcIPM) is available through a BSD license and is provided freely to enable the rapid implementation of LBMPC on other platforms. This solver is compared to the dense active set solvers LSSOL and qpOASES using a quadrotor helicopter platform. Two scenarios are considered: The first is a simulation comparing hovering control for the quadrotor, and the second is on-board control experiments of dynamic quadrotor flight. Though the LBmpcIPM method has better asymptotic computational complexity than LSSOL and qpOASES, we find that for certain integrated systems (like our quadrotor testbed) these methods can outperform LBmpcIPM. This suggests that actual benchmarks should be used when choosing which algorithm is used to implement LBMPC on practical systems.

Katie Kang, Eric Wallace, Claire Tomlin et al.

Large language models are known to hallucinate when faced with unfamiliar queries, but the underlying mechanism that govern how models hallucinate are not yet fully understood. In this work, we find that unfamiliar examples in the models' finetuning data -- those that introduce concepts beyond the base model's scope of knowledge -- are crucial in shaping these errors. In particular, we find that an LLM's hallucinated predictions tend to mirror the responses associated with its unfamiliar finetuning examples. This suggests that by modifying how unfamiliar finetuning examples are supervised, we can influence a model's responses to unfamiliar queries (e.g., say ``I don't know''). We empirically validate this observation in a series of controlled experiments involving SFT, RL, and reward model finetuning on TriviaQA and MMLU. Our work further investigates RL finetuning strategies for improving the factuality of long-form model generations. We find that, while hallucinations from the reward model can significantly undermine the effectiveness of RL factuality finetuning, strategically controlling how reward models hallucinate can minimize these negative effects. Leveraging our previous observations on controlling hallucinations, we propose an approach for learning more reliable reward models, and show that they improve the efficacy of RL factuality finetuning in long-form biography and book/movie plot generation tasks.

Sara Pohland, Claire Tomlin

Perception-based navigation systems are useful for unmanned ground vehicle (UGV) navigation in complex terrains, where traditional depth-based navigation schemes are insufficient. However, these data-driven methods are highly dependent on their training data and can fail in surprising and dramatic ways with little warning. To ensure the safety of the vehicle and the surrounding environment, it is imperative that the navigation system is able to recognize the predictive uncertainty of the perception model and respond safely and effectively in the face of uncertainty. In an effort to enable safe navigation under perception uncertainty, we develop a probabilistic and reconstruction-based competency estimation (PaRCE) method to estimate the model's level of familiarity with an input image as a whole and with specific regions in the image. We find that the overall competency score can correctly predict correctly classified, misclassified, and out-of-distribution (OOD) samples. We also confirm that the regional competency maps can accurately distinguish between familiar and unfamiliar regions across images. We then use this competency information to develop a planning and control scheme that enables effective navigation while maintaining a low probability of error. We find that the competency-aware scheme greatly reduces the number of collisions with unfamiliar obstacles, compared to a baseline controller with no competency awareness. Furthermore, the regional competency information is very valuable in enabling efficient navigation.

Will Lavanakul, Jason J. Choi, Koushil Sreenath et al.

Learning-based approaches are emerging as an effective approach for safety filters for black-box dynamical systems. Existing methods have relied on certificate functions like Control Barrier Functions (CBFs) and Hamilton-Jacobi (HJ) reachability value functions. The primary motivation for our work is the recognition that ultimately, enforcing the safety constraint as a control input constraint at each state is what matters. By focusing on this constraint, we can eliminate dependence on any specific certificate function-based design. To achieve this, we define a discriminating hyperplane that shapes the half-space constraint on control input at each state, serving as a sufficient condition for safety. This concept not only generalizes over traditional safety methods but also simplifies safety filter design by eliminating dependence on specific certificate functions. We present two strategies to learn the discriminating hyperplane: (a) a supervised learning approach, using pre-verified control invariant sets for labeling, and (b) a reinforcement learning (RL) approach, which does not require such labels. The main advantage of our method, unlike conventional safe RL approaches, is the separation of performance and safety. This offers a reusable safety filter for learning new tasks, avoiding the need to retrain from scratch. As such, we believe that the new notion of the discriminating hyperplane offers a more generalizable direction towards designing safety filters, encompassing and extending existing certificate-function-based or safe RL methodologies.

Katie Kang, Amrith Setlur, Dibya Ghosh et al. · berkeley, cmu

Despite the remarkable capabilities of modern large language models (LLMs), the mechanisms behind their problem-solving abilities remain elusive. In this work, we aim to better understand how the learning dynamics of LLM finetuning shapes downstream generalization. Our analysis focuses on reasoning tasks, whose problem structure allows us to distinguish between memorization (the exact replication of reasoning steps from the training data) and performance (the correctness of the final solution). We find that a model's generalization behavior can be effectively characterized by a training metric we call pre-memorization train accuracy: the accuracy of model samples on training queries before they begin to copy the exact reasoning steps from the training set. On the dataset level, this metric is able to reliably predict test accuracy, achieving $R^2$ of around or exceeding 0.9 across various models (Llama3 8, Gemma2 9B), datasets (GSM8k, MATH), and training configurations. On a per-example level, this metric is also indicative of whether individual model predictions are robust to perturbations in the training query. By connecting a model's learning behavior to its generalization, pre-memorization train accuracy can guide targeted improvements to training strategies. We focus on data curation as an example, and show that prioritizing examples with low pre-memorization accuracy leads to 1.5-2x improvements in data efficiency compared to i.i.d. data scaling, and outperforms other standard data curation techniques.

Sara Pohland, Claire Tomlin

Convolutional neural networks (CNNs) are extremely popular and effective for image classification tasks but tend to be overly confident in their predictions. Various works have sought to quantify uncertainty associated with these models, detect out-of-distribution (OOD) inputs, or identify anomalous regions in an image, but limited work has sought to develop a holistic approach that can accurately estimate perception model confidence across various sources of uncertainty. We develop a probabilistic and reconstruction-based competency estimation (PaRCE) method and compare it to existing approaches for uncertainty quantification and OOD detection. We find that our method can best distinguish between correctly classified, misclassified, and OOD samples with anomalous regions, as well as between samples with visual image modifications resulting in high, medium, and low prediction accuracy. We describe how to extend our approach for anomaly localization tasks and demonstrate the ability of our approach to distinguish between regions in an image that are familiar to the perception model from those that are unfamiliar. We find that our method generates interpretable scores that most reliably capture a holistic notion of perception model confidence.

Sara Pohland, Claire Tomlin

There exist many methods to explain how an image classification model generates its decision, but very little work has explored methods to explain why a classifier might lack confidence in its prediction. As there are various reasons the classifier might lose confidence, it would be valuable for this model to not only indicate its level of uncertainty but also explain why it is uncertain. Counterfactual images have been used to visualize changes that could be made to an image to generate a different classification decision. In this work, we explore the use of counterfactuals to offer an explanation for low model competency--a generalized form of predictive uncertainty that measures confidence. Toward this end, we develop five novel methods to generate high-competency counterfactual images, namely Image Gradient Descent (IGD), Feature Gradient Descent (FGD), Autoencoder Reconstruction (Reco), Latent Gradient Descent (LGD), and Latent Nearest Neighbors (LNN). We evaluate these methods across two unique datasets containing images with six known causes for low model competency and find Reco, LGD, and LNN to be the most promising methods for counterfactual generation. We further evaluate how these three methods can be utilized by pre-trained Multimodal Large Language Models (MLLMs) to generate language explanations for low model competency. We find that the inclusion of a counterfactual image in the language model query greatly increases the ability of the model to generate an accurate explanation for the cause of low model competency, thus demonstrating the utility of counterfactual images in explaining low perception model competency.

Marsalis Gibson, David Babazadeh, Claire Tomlin et al.

Adversarial attacks on learning-based multi-modal trajectory predictors have already been demonstrated. However, there are still open questions about the effects of perturbations on inputs other than state histories, and how these attacks impact downstream planning and control. In this paper, we conduct a sensitivity analysis on two trajectory prediction models, Trajectron++ and AgentFormer. The analysis reveals that between all inputs, almost all of the perturbation sensitivities for both models lie only within the most recent position and velocity states. We additionally demonstrate that, despite dominant sensitivity on state history perturbations, an undetectable image map perturbation made with the Fast Gradient Sign Method can induce large prediction error increases in both models, revealing that these trajectory predictors are, in fact, susceptible to image-based attacks. Using an optimization-based planner and example perturbations crafted from sensitivity results, we show how these attacks can cause a vehicle to come to a sudden stop from moderate driving speeds.

Jason J. Choi, Ayush Agrawal, Koushil Sreenath et al.

Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, the stability analysis and region-of-attraction computation for these systems are often challenging because of the discontinuous state changes upon contact (also referred to as state resets). In this work, we cast the computation of region-ofattraction as a Hamilton-Jacobi (HJ) reachability problem. This enables us to leverage HJ reachability tools that are compatible with general nonlinear system dynamics, and can formally deal with state and input constraints as well as bounded disturbances. Our main contribution is the generalization of HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions for several underactuated walking robots and demonstrate that the proposed approach can (a) recover a bigger region-of-attraction than state-of-the-art approaches, (b) handle state resets, nonlinear dynamics, external disturbances, and input constraints, and (c) also provides a stabilizing controller for the system that can leverage the state resets for enhancing system stability.