Efficient Determination of Safety Requirements for Perception Systems

Perception systems operate as a subcomponent of the general autonomy stack, and perception system designers often need to optimize performance characteristics while maintaining safety with respect to the overall closed-loop system. For this reason, it is useful to distill high-level safety requirements into component-level requirements on the perception system. In this work, we focus on efficiently determining sets of safe perception system performance characteristics given a black-box simulator of the fully-integrated, closed-loop system. We combine the advantages of common black-box estimation techniques such as Gaussian processes and threshold bandits to develop a new estimation method, which we call smoothing bandits. We demonstrate our method on a vision-based aircraft collision avoidance problem and show improvements in terms of both accuracy and efficiency over the Gaussian process and threshold bandit baselines.

AVOIDDS: Aircraft Vision-based Intruder Detection Dataset and Simulator

Designing robust machine learning systems remains an open problem, and there is a need for benchmark problems that cover both environmental changes and evaluation on a downstream task. In this work, we introduce AVOIDDS, a realistic object detection benchmark for the vision-based aircraft detect-and-avoid problem. We provide a labeled dataset consisting of 72,000 photorealistic images of intruder aircraft with various lighting conditions, weather conditions, relative geometries, and geographic locations. We also provide an interface that evaluates trained models on slices of this dataset to identify changes in performance with respect to changing environmental conditions. Finally, we implement a fully-integrated, closed-loop simulator of the vision-based detect-and-avoid problem to evaluate trained models with respect to the downstream collision avoidance task. This benchmark will enable further research in the design of robust machine learning systems for use in safety-critical applications. The AVOIDDS dataset and code are publicly available at $\href{https://purl.stanford.edu/hj293cv5980}{purl.stanford.edu/hj293cv5980}$ and $\href{https://github.com/sisl/VisionBasedAircraftDAA}{github.com/sisl/VisionBasedAircraftDAA}$, respectively.

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify safe behavior. This paper presents a backward reachability approach for safety verification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While recent works have focused on forward reachability as a strategy for safety certification of NFLs, backward reachability offers advantages over the forward strategy, particularly in obstacle avoidance scenarios. Prior works have developed techniques for backward reachability analysis for systems without NNs, but the presence of NNs in the feedback loop presents a unique set of problems due to the nonlinearities in their activation functions and because NN models are generally not invertible. To overcome these challenges, we use existing forward NN analysis tools to efficiently find an over-approximation of the backprojection (BP) set, i.e., the set of states for which the NN control policy will drive the system to a given target set. We present frameworks for calculating BP over-approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.

Risk-Driven Design of Perception Systems

Modern autonomous systems rely on perception modules to process complex sensor measurements into state estimates. These estimates are then passed to a controller, which uses them to make safety-critical decisions. It is therefore important that we design perception systems to minimize errors that reduce the overall safety of the system. We develop a risk-driven approach to designing perception systems that accounts for the effect of perceptual errors on the performance of the fully-integrated, closed-loop system. We formulate a risk function to quantify the effect of a given perceptual error on overall safety, and show how we can use it to design safer perception systems by including a risk-dependent term in the loss function and generating training data in risk-sensitive regions. We evaluate our techniques on a realistic vision-based aircraft detect and avoid application and show that risk-driven design reduces collision risk by 37% over a baseline system.

Collision Risk and Operational Impact of Speed Change Advisories as Aircraft Collision Avoidance Maneuvers

Aircraft collision avoidance systems have long been a key factor in keeping our airspace safe. Over the past decade, the FAA has supported the development of a new family of collision avoidance systems called the Airborne Collision Avoidance System X (ACAS X), which model the collision avoidance problem as a Markov decision process (MDP). Variants of ACAS X have been created for both manned (ACAS Xa) and unmanned aircraft (ACAS Xu and ACAS sXu). The variants primarily differ in the types of collision avoidance maneuvers they issue. For example, ACAS Xa issues vertical collision avoidance advisories, while ACAS Xu and ACAS sXu allow for horizontal advisories due to reduced aircraft performance capabilities. Currently, a new variant of ACAS X, called ACAS Xr, is being developed to provide collision avoidance capability to rotorcraft and Advanced Air Mobility (AAM) vehicles. Due to the desire to minimize deviation from the prescribed flight path of these aircraft, speed adjustments have been proposed as a potential collision avoidance maneuver for aircraft using ACAS Xr. In this work, we investigate the effect of speed change advisories on the safety and operational efficiency of collision avoidance systems. We develop an MDP-based collision avoidance logic that issues speed advisories and compare its performance to that of horizontal and vertical logics through Monte Carlo simulation on existing airspace encounter models. Our results show that while speed advisories are able to reduce collision risk, they are neither as safe nor as efficient as their horizontal and vertical counterparts.

ZoPE: A Fast Optimizer for ReLU Networks with Low-Dimensional Inputs

Deep neural networks often lack the safety and robustness guarantees needed to be deployed in safety critical systems. Formal verification techniques can be used to prove input-output safety properties of networks, but when properties are difficult to specify, we rely on the solution to various optimization problems. In this work, we present an algorithm called ZoPE that solves optimization problems over the output of feedforward ReLU networks with low-dimensional inputs. The algorithm eagerly splits the input space, bounding the objective using zonotope propagation at each step, and improves computational efficiency compared to existing mixed integer programming approaches. We demonstrate how to formulate and solve three types of optimization problems: (i) minimization of any convex function over the output space, (ii) minimization of a convex function over the output of two networks in series with an adversarial perturbation in the layer between them, and (iii) maximization of the difference in output between two networks. Using ZoPE, we observe a $25\times$ speedup on property 1 of the ACAS Xu neural network verification benchmark and an $85\times$ speedup on a set of linear optimization problems. We demonstrate the versatility of the optimizer in analyzing networks by projecting onto the range of a generative adversarial network and visualizing the differences between a compressed and uncompressed network.

Verification of Image-based Neural Network Controllers Using Generative Models

Neural networks are often used to process information from image-based sensors to produce control actions. While they are effective for this task, the complex nature of neural networks makes their output difficult to verify and predict, limiting their use in safety-critical systems. For this reason, recent work has focused on combining techniques in formal methods and reachability analysis to obtain guarantees on the closed-loop performance of neural network controllers. However, these techniques do not scale to the high-dimensional and complicated input space of image-based neural network controllers. In this work, we propose a method to address these challenges by training a generative adversarial network (GAN) to map states to plausible input images. By concatenating the generator network with the control network, we obtain a network with a low-dimensional input space. This insight allows us to use existing closed-loop verification tools to obtain formal guarantees on the performance of image-based controllers. We apply our approach to provide safety guarantees for an image-based neural network controller for an autonomous aircraft taxi problem. We guarantee that the controller will keep the aircraft on the runway and guide the aircraft towards the center of the runway. The guarantees we provide are with respect to the set of input images modeled by our generator network, so we provide a recall metric to evaluate how well the generator captures the space of plausible images.

Preference-based Learning of Reward Function Features

Preference-based learning of reward functions, where the reward function is learned using comparison data, has been well studied for complex robotic tasks such as autonomous driving. Existing algorithms have focused on learning reward functions that are linear in a set of trajectory features. The features are typically hand-coded, and preference-based learning is used to determine a particular user's relative weighting for each feature. Designing a representative set of features to encode reward is challenging and can result in inaccurate models that fail to model the users' preferences or perform the task properly. In this paper, we present a method to learn both the relative weighting among features as well as additional features that help encode a user's reward function. The additional features are modeled as a neural network that is trained on the data from pairwise comparison queries. We apply our methods to a driving scenario used in previous work and compare the predictive power of our method to that of only hand-coded features. We perform additional analysis to interpret the learned features and examine the optimal trajectories. Our results show that adding an additional learned feature to the reward model enhances both its predictive power and expressiveness, producing unique results for each user.

Generating Probabilistic Safety Guarantees for Neural Network Controllers

Neural networks serve as effective controllers in a variety of complex settings due to their ability to represent expressive policies. The complex nature of neural networks, however, makes their output difficult to verify and predict, which limits their use in safety-critical applications. While simulations provide insight into the performance of neural network controllers, they are not enough to guarantee that the controller will perform safely in all scenarios. To address this problem, recent work has focused on formal methods to verify properties of neural network outputs. For neural network controllers, we can use a dynamics model to determine the output properties that must hold for the controller to operate safely. In this work, we develop a method to use the results from neural network verification tools to provide probabilistic safety guarantees on a neural network controller. We develop an adaptive verification approach to efficiently generate an overapproximation of the neural network policy. Next, we modify the traditional formulation of Markov decision process (MDP) model checking to provide guarantees on the overapproximated policy given a stochastic dynamics model. Finally, we incorporate techniques in state abstraction to reduce overapproximation error during the model checking process. We show that our method is able to generate meaningful probabilistic safety guarantees for aircraft collision avoidance neural networks that are loosely inspired by Airborne Collision Avoidance System X (ACAS X), a family of collision avoidance systems that formulates the problem as a partially observable Markov decision process (POMDP).

Learning an Urban Air Mobility Encounter Model from Expert Preferences

Airspace models have played an important role in the development and evaluation of aircraft collision avoidance systems for both manned and unmanned aircraft. As Urban Air Mobility (UAM) systems are being developed, we need new encounter models that are representative of their operational environment. Developing such models is challenging due to the lack of data on UAM behavior in the airspace. While previous encounter models for other aircraft types rely on large datasets to produce realistic trajectories, this paper presents an approach to encounter modeling that instead relies on expert knowledge. In particular, recent advances in preference-based learning are extended to tune an encounter model from expert preferences. The model takes the form of a stochastic policy for a Markov decision process (MDP) in which the reward function is learned from pairwise queries of a domain expert. We evaluate the performance of two querying methods that seek to maximize the information obtained from each query. Ultimately, we demonstrate a method for generating realistic encounter trajectories with only a few minutes of an expert's time.