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We present a high-fidelity Mixed Reality sensor emulation framework for testing and evaluating the resilience of Unmanned Aerial Vehicles (UAVs) against false data injection (FDI) attacks. The proposed approach can be utilized to assess the impact of FDI attacks, benchmark attack detector performance, and validate the effectiveness of mitigation/reconfiguration strategies in single-UAV and UAV swarm operations. Our Mixed Reality framework leverages high-fidelity simulations of Gazebo and a Motion Capture system to emulate proprioceptive (e.g., GNSS) and exteroceptive (e.g., camera) sensor measurements in real-time. We propose an empirical approach to faithfully recreate signal characteristics such as latency and noise in these measurements. Finally, we illustrate the efficacy of our proposed framework through a Mixed Reality experiment consisting of an emulated GNSS attack on an actual UAV, which (i) demonstrates the impact of false data injection attacks on GNSS measurements and (ii) validates a mitigation strategy utilizing a distributed camera network developed in our previous work. Our open-source implementation is available at \href{https://github.com/CogniPilot/mixed\_sense}{\texttt{https://github.com/CogniPilot/mixed\_sense}}, Comment: 6 pages, 5 figures, IROS 2024

Human behavior modeling is important for the design and implementation of human-automation interactive control systems. In this context, human behavior refers to a human's control input to systems. We propose a novel method for human behavior modeling that uses human demonstrations for a given task to infer the unknown task objective and the variability. The task objective represents the human's intent or desire. It can be inferred by the inverse optimal control and improve the understanding of human behavior by providing an explainable objective function behind the given human behavior. Meanwhile, the variability denotes the intrinsic uncertainty in human behavior. It can be described by a Gaussian mixture model and capture the uncertainty in human behavior which cannot be encoded by the task objective. The proposed method can improve the prediction accuracy of human behavior by leveraging both task objective and variability. The proposed method is demonstrated through human-subject experiments using an illustrative quadrotor remote control example., Comment: 10 pages

Research in developing data-driven models for Air Traffic Management (ATM) has gained a tremendous interest in recent years. However, data-driven models are known to have long training time and require large datasets to achieve good performance. To address the two issues, this paper proposes a Multi-Agent Bidirectional Encoder Representations from Transformers (MA-BERT) model that fully considers the multi-agent characteristic of the ATM system and learns air traffic controllers' decisions, and a pre-training and fine-tuning transfer learning framework. By pre-training the MA-BERT on a large dataset from a major airport and then fine-tuning it to other airports and specific air traffic applications, a large amount of the total training time can be saved. In addition, for newly adopted procedures and constructed airports where no historical data is available, this paper shows that the pre-trained MA-BERT can achieve high performance by updating regularly with little data. The proposed transfer learning framework and MA-BERT are tested with the automatic dependent surveillance-broadcast data recorded in 3 airports in South Korea in 2019., Comment: 12 pages, 8 figures, submitted for IEEE Transactions on Intelligent Transportation System

The conventional solutions for fault-detection, identification, and reconstruction (FDIR) require centralized decision-making mechanisms which are typically combinatorial in their nature, necessitating the design of an efficient distributed FDIR mechanism that is suitable for multi-agent applications. To this end, we develop a general framework for efficiently reconstructing a sparse vector being observed over a sensor network via nonlinear measurements. The proposed framework is used to design a distributed multi-agent FDIR algorithm based on a combination of the sequential convex programming (SCP) and the alternating direction method of multipliers (ADMM) optimization approaches. The proposed distributed FDIR algorithm can process a variety of inter-agent measurements (including distances, bearings, relative velocities, and subtended angles between agents) to identify the faulty agents and recover their true states. The effectiveness of the proposed distributed multi-agent FDIR approach is demonstrated by considering a numerical example in which the inter-agent distances are used to identify the faulty agents in a multi-agent configuration, as well as reconstruct their error vectors.

Wireless Sensor Network (WSN) localization refers to the problem of determining the position of each of the agents in a WSN using noisy measurement information. In many cases, such as in distance and bearing-based localization, the measurement model is a nonlinear function of the agents' positions, leading to pairwise interconnections between the agents. As the optimal solution for the WSN localization problem is known to be computationally expensive in these cases, an efficient approximation is desired. In this paper, we show that the inherent sparsity in this problem can be exploited to greatly reduce the computational effort of using an Extended Kalman Filter (EKF) for large-scale WSN localization. In the proposed method, which we call the Low-Bandwidth Extended Kalman Filter (LB-EKF), the measurement information matrix is converted into a banded matrix by relabeling (permuting the order of) the vertices of the graph. Using a combination of theoretical analysis and numerical simulations, it is shown that typical WSN configurations (which can be modeled as random geometric graphs) can be localized in a scalable manner using the proposed LB-EKF approach.

The Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is an almost exact closed-form approximation to the Bayes-optimal multi-target tracking algorithm. Due to its optimality guarantees and ease of implementation, it has been studied extensively in the literature. However, the challenges involved in implementing the GM-PHD filter efficiently in a distributed (multi-sensor) setting have received little attention. The existing solutions for distributed PHD filtering either have a high computational and communication cost, making them infeasible for resource-constrained applications, or are unable to guarantee the asymptotic convergence of the distributed PHD algorithm to an optimal solution. In this paper, we develop a distributed GM-PHD filtering recursion that uses a probabilistic communication rule to limit the communication bandwidth of the algorithm, while ensuring asymptotic optimality of the algorithm. We derive the convergence properties of this recursion, which uses weighted average consensus of Gaussian mixtures (GMs) to lower (and asymptotically minimize) the Cauchy-Schwarz divergence between the sensors' local estimates. In addition, the proposed method is able to avoid the issue of false positives, which has previously been noted to impact the filtering performance of distributed multi-target tracking. Through numerical simulations, it is demonstrated that our proposed method is an effective solution for distributed multi-target tracking in resource-constrained sensor networks.

A practical challenge which arises in the operation of sensor networks is the presence of sensor faults, biases, or adversarial attacks, which can lead to significant errors incurring in the localization of the agents, thereby undermining the security and performance of the network. We consider the problem of identifying and correcting the localization errors using inter-agent measurements, such as the distances or bearings from one agent to another, which can serve as a redundant source of information about the sensor network's configuration. The problem is solved by searching for a block sparse solution to an underdetermined system of equations, where the sparsity is introduced via the fact that the number of localization errors is typically much lesser than the total number of agents. Unlike the existing works, our proposed method does not require the knowledge of the identities of the anchors, i.e., the agents that do not have localization errors. We characterize the necessary and sufficient conditions on the sensor network configuration under which a given number of localization errors can be uniquely identified and corrected using the proposed method. The applicability of our results is demonstrated numerically by processing inter-agent distance measurements using a sequential convex programming (SCP) algorithm to identify the localization errors in a sensor network.

Motivated by the safety and security issues related to cyber-physical systems with potentially multi-rate, delayed, and nonuniformly sampled measurements, we investigate the attack detection and identification using the lifted system model in this paper. Attack detectability and identifiability based on the lifted system model are formally defined and rigorously characterized in a novel approach. The method of checking detectability is discussed, and a residual design problem for attack detection is formulated in a general way. For attack identification, we define and characterize it by generalizing the concept of mode discernibility for switched systems, and a method for identifying the attack is discussed based on the theoretical analysis. An illustrative example of an unmanned aircraft system (UAS) is provided to validate the main results., Comment: It is the preprint of a paper submitted to Automatica

One of the major errors affecting GNSS signals in urban canyons is GNSS multipath error. In this work, we develop a Gazebo plugin which utilizes a ray tracing technique to account for multipath effects in a virtual urban canyon environment using virtual satellites. This software plugin balances accuracy and computational complexity to run the simulation in real-time for both software-in-the-loop (SITL) and hardware-in-the-loop (HITL) testing. We also construct a 3D virtual environment of Hong Kong and compare the results from our plugin with the GNSS data in the publicly available Urban-Nav dataset, to validate the efficacy of the proposed Gazebo Plugin. The plugin is openly available to all the researchers in the robotics community. https://github.com/kpant14/multipath_sim, Comment: 13 pages, 8 figures

Network Control Systems (NCSs) pose unique vulnerabilities to cyberattacks due to a heavy reliance on communication channels. These channels can be susceptible to eavesdropping, false data injection (FDI), and denial of service (DoS). As a result, smarter cyberattacks can employ a combination of techniques to cause degradation of the considered NCS performance. We consider a white-box cyberattack synthesis technique in which the attacker initially eavesdrops to gather system data, and constructs equivalent system model. We utilize the equivalent model to synthesize hybrid cyberattacks -- a combination of FDI and DoS attacks against the NCS. Reachable sets for the equivalent NCS model provide rapid, real-time directives towards selecting NCS agents to be attacked. The devised method provides a significantly more realistic approach toward cyberattack synthesis against NCSs with unknown parameters. We demonstrate the proposed method using a multi-aerial vehicle formation control scenario., Comment: 10 pages, 5 figures

In this paper, we present a data-driven framework for real-time estimation of reachable sets for control systems where the plant is modeled using neural networks (NNs). We utilize a running example of a quadrotor model that is learned using trajectory data via NNs. The NN learned offline, can be excited online to obtain linear approximations for reachability analysis. We use a dynamic mode decomposition based approach to obtain linear liftings of the NN model. The linear models thus obtained can utilize optimal control theory to obtain polytopic approximations to the reachable sets in real-time. The polytopic approximations can be tuned to arbitrary degrees of accuracy. The proposed framework can be extended to other nonlinear models that utilize NNs to estimate plant dynamics. We demonstrate the effectiveness of the proposed framework using an illustrative simulation of quadrotor dynamics., Comment: 14 pages, 11 figures, journal paper that has been conditionally accepted

In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie groups. Additionally, we design a log-linear dynamic inversion-based control law to remove the nonlinearities due to spatial curvature and enhance the robustness of the controller. We apply Linear Matrix Inequalities (LMIs) to bound the tracking error given a bounded disturbance amplified by the distortion matrix and leverage the tracking error bound to create flow pipes. To demonstrate the usefulness of our method, we show its application with Urban Air Mobility (UAM) scenarios using a simplified kinematic aircraft model and polynomial-based path planning methods., Comment: 7 pages, 5 figures. Revision is submitted to IEEE TAC

Motivated by the increasing need to monitor safety-critical systems subject to uncertainties, a novel set-membership approach is proposed to estimate the state of a dynamical system with unknown-but-bounded exogenous inputs. The proposed method decomposes the system into the strongly observable and weakly unobservable subsystem in which an unknown input observer and an ellipsoidal set-membership observer are designed for each subsystem, respectively. The conditions for the boundedness of the proposed set estimate are discussed, and the proposed set-membership observer is also tested numerically using illustrative examples.

In this paper, we present a provably convergent Model-Free ${Q}$-Learning algorithm that learns a stabilizing control policy for an unknown Bilinear System from a single online run. Given an unknown bilinear system, we study the interplay between its equivalent control-affine linear time-varying and linear time-invariant representations to derive i) from Pontryagin's Minimum Principle, a pair of point-to-point model-free policy improvement and evaluation laws that iteratively solves for an optimal state-dependent control policy; and ii) the properties under which the state-input data is sufficient to characterize system behavior in a model-free manner. We demonstrate the performance of the proposed algorithm via illustrative numerical examples and compare it to the model-based case., Comment: 7 pages, 1 figure, Submitted to IEEE Control Systems Letters (L-CSS)

Reachability analysis is a widely used method to analyze the safety of a Human-in-the-Loop Cyber Physical System (HiLCPS). This strategy allows the HiLCPS to respond against an imminent threat in advance by predicting reachable states of the system. However, it could lead to an unnecessarily conservative reachable set if the prediction only relies on the system dynamics without explicitly considering human behavior, and thus the risk might be overestimated. To reduce the conservativeness of the reachability analysis, we present a state prediction method which takes into account a stochastic human behavior model represented as a Gaussian Mixture Model (GMM). In this paper, we focus on the multi-rotor in a near-collision situation. The stochastic human behavior model is trained using experimental data to represent human operators' evasive maneuver. Then, we can retrieve a human control input probability distribution from the trained stochastic human behavior model using the Gaussian Mixture Regression (GMR). The proposed algorithm predicts the probability distribution of the multi-rotor's future state based on the given dynamics and the retrieved human control input probability distribution. Besides, the proposed state prediction method considers the uncertainty of the initial state modeled as a GMM, which yields more robust performance. Human subject experiment results are provided to demonstrate the effectiveness of the proposed algorithm., Comment: This work has been submitted to IFAC for possible publication

Due to the rapid development technologies for small unmanned aircraft systems (sUAS), the supply and demand market for sUAS is expanding globally. With the great number of sUAS ready to fly in civilian airspace, an sUAS aircraft traffic management system that can guarantee the safe and efficient operation of sUAS is still at absence. In this paper, we propose a control protocol design and analysis method for sUAS traffic management (UTM) which can safely manage a large number of sUAS. The benefits of our approach are two folds: at the top level, the effort for monitoring sUAS traffic (authorities) and control/planning for each sUAS (operator/pilot) are both greatly reduced under our framework; and at the low level, the behavior of individual sUAS is guaranteed to follow the restrictions. Mathematical proofs and numerical simulations are presented to demonstrate the proposed method.

Model-based reinforcement learning (RL) has emerged as a promising tool for developing controllers for real world systems (e.g., robotics, autonomous driving, etc.). However, real systems often have constraints imposed on their state space which must be satisfied to ensure the safety of the system and its environment. Developing a verification tool for RL algorithms is challenging because the non-linear structure of neural networks impedes analytical verification of such models or controllers. To this end, we present a novel safety verification framework for model-based RL controllers using reachable set analysis. The proposed frame-work can efficiently handle models and controllers which are represented using neural networks. Additionally, if a controller fails to satisfy the safety constraints in general, the proposed framework can also be used to identify the subset of initial states from which the controller can be safely executed.

Several works have addressed the problem of incorporating constraints in the reinforcement learning (RL) framework, however majority of them can only guarantee the satisfaction of soft constraints. In this work, we address the problem of satisfying hard state constraints in a model-free RL setting with the deterministic system dynamics. The proposed algorithm is developed for the discrete state and action space and utilizes a multi-class support vector machine (SVM) to represent the policy. The state constraints are incorporated in the SVM optimization framework to derive an analytical solution for determining the policy parameters. This final policy converges to a solution which is guaranteed to satisfy the constraints. Additionally, the proposed formulation adheres to the Q-learning framework and thus, also guarantees convergence to the optimal solution. The algorithm is demonstrated with multiple example problems.

Knowing the similarity between sets of data has a number of positive implications in training an effective model, such as assisting an informed selection out of known datasets favorable to model transfer or data augmentation problems with an unknown dataset. Common practices to estimate the similarity between data include comparing in the original sample space, comparing in the embedding space from a model performing a certain task, or fine-tuning a pretrained model with different datasets and evaluating the performance changes therefrom. However, these practices would suffer from shallow comparisons, task-specific biases, or extensive time and computations required to perform comparisons. We present SimEx, a new method for early prediction of inter-dataset similarity using a set of pretrained autoencoders each of which is dedicated to reconstructing a specific part of known data. Specifically, our method takes unknown data samples as input to those pretrained autoencoders, and evaluate the difference between the reconstructed output samples against their original input samples. Our intuition is that, the more similarity exists between the unknown data samples and the part of known data that an autoencoder was trained with, the better chances there could be that this autoencoder makes use of its trained knowledge, reconstructing output samples closer to the originals. We demonstrate that our method achieves more than 10x speed-up in predicting inter-dataset similarity compared to common similarity-estimating practices. We also demonstrate that the inter-dataset similarity estimated by our method is well-correlated with common practices and outperforms the baselines approaches of comparing at sample- or embedding-spaces, without newly training anything at the comparison time., Comment: 12 pages