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With the rapid development of robotics swarm technology, there are more tasks that require the swarm to pass through complicated environments safely and efficiently. Virtual tube technology is a novel way to achieve this goal. Virtual tubes are free spaces connecting two places that provide safety boundaries and direction of motion for swarm robotics. How to determine the design quality of a virtual tube is a fundamental problem. For such a purpose, this paper presents a degree of flowability (DOF) for two-dimensional virtual tubes according to a minimum energy principle. After that, methods to calculate DOF are proposed with a feasibility analysis. Simulations of swarm robotics in different kinds of two-dimensional virtual tubes are performed to demonstrate the effectiveness of the proposed method of calculating DOF., Comment: 22 pages, 16 figures. This is a preprint, currently under review for publication in Robotics and Autonomous Systems, Elsevier. Version 2 is submitted to fix the rendering fault in HTML and correct spelling mistakes in the abstract and the references

In the Ramadge-Wonham supervisory control theory the only interaction mechanism between supervisor and plant is that the supervisor may enable/disable events from the plant and the plant makes a final decision about which of the enabled events is actually taking place. In this paper, the interaction between supervisor and plant is enriched by allowing the supervisor to force specific events (called forcible events) that are allowed to preempt uncontrollable events. A notion of forcible-controllability is defined that captures the interplay between controllability of a supervisor w.r.t. the uncontrollable events provided by a plant in the setting with event forcing. Existence of a maximally permissive, forcibly-controllable, nonblocking supervisor is shown and an algorithm is provided that computes such a supervisor. The approach is illustrated by two small case studies., Comment: 12 pages, 7 figures

In this paper, we study a security problem of protecting secrets in distributed systems. Specifically, we employ discrete-event systems to describe the structure and behaviour of distributed systems, in which global secret information is separated into pieces and stored in local component agents. The goal is to prevent such secrets from being exposed to intruders by imposing appropriate protection measures. This problem is formulated as to ensure that at least one piece of every distributed global secret is secured by a required number of protections, while the overall cost to apply protections is minimum. We first characterize the solvability of this security problem by providing a necessary and sufficient condition, and then develop an algorithm to compute a solution based on the supervisory control theory of discrete-event systems. Finally, we illustrate the effectiveness of our solution with an example system comprising distributed databases.

Recently an automaton property of quantitative nonblockingness was proposed in supervisory control of untimed discrete-event systems (DES), which quantifies the standard nonblocking property by capturing the practical requirement that all tasks be completed within a bounded number of steps. However, in practice tasks may be further required to be completed in specific time. To meet this new requirement, in this paper we introduce the concept of bounded-time nonblockingness, which extends the concept of quantitative nonblockingness from untimed DES to timed DES. This property requires that each task must be completed within a bounded time counted by the number of ticks, rather than bounded number of transition steps in quantitative nonblockingness. Accordingly, we formulate a new bounded-time nonblocking supervisory control problem (BTNSCP) of timed DES, and characterize its solvability in terms of a new concept of bounded-time language completability. Then we present an approach to compute the maximally permissive solution to the new BTNSCP., Comment: arXiv admin note: text overlap with arXiv:2108.00721

Supervisor localization can be applied to distribute a monolithic supervisor into local supervisors. Performing supervisor localization can be computationally costly. In this work, we consider systems that evolve over time. We study how to reuse the results from a previous supervisor localization, to more efficiently compute local supervisors when the system is adapted. We call this approach transformational supervisor localization, and present algorithms for the procedure. The efficiency of the procedure is experimentally evaluated., Comment: Accepted for IEEE Control Systems Letters (L-CSS) (2023)

This study proposes a uniform passive fault-tolerant control (FTC) method for a quadcopter that does not rely on fault information subject to one, two adjacent, two opposite, or three rotors failure. The uniform control implies that the passive FTC is able to cover the condition from quadcopter fault-free to rotor failure without controller switching. To achieve the purpose of the passive FTC, the rotors' fault is modeled as a disturbance acting on the virtual control of the quadcopter system. The disturbance estimate is used directly for the passive FTC with rotor failure. To avoid controller switching between normal control and FTC, a dynamic control allocation is used. In addition, the closed-loop stability has been analyzed and a virtual control feedback is adopted to achieve the passive FTC for the quadcopter with two and three rotor failure. To validate the proposed uniform passive FTC method, outdoor experiments are performed for the first time, which have demonstrated that the hovering quadcopter is able to recover from one rotor failure by the proposed controller and continue to fly even if two adjacent, two opposite, or three rotors fail, without any rotor fault information and controller switching., Comment: We found some important errors in the paper that need to be corrected

Learning-based control policies are widely used in various tasks in the field of robotics and control. However, formal (Lyapunov) stability guarantees for learning-based controllers with nonlinear dynamical systems are difficult to obtain. We propose a novel control approach, namely Control with Patterns (CWP), to address the stability issue over data sets corresponding to nonlinear dynamical systems. For such data sets, we introduce a new definition, namely exponential attraction on data sets, to describe the nonlinear dynamical systems under consideration. The problem of exponential attraction on data sets is transformed into a problem of pattern classification one based on the data sets and parameterized Lyapunov functions. Furthermore, D-learning is proposed as a method to perform CWP without knowledge of the system dynamics. Finally, the effectiveness of CWP based on D-learning is demonstrated through simulations and real flight experiments. In these experiments, the position of the multicopter is stabilized using real-time images as feedback, which can be considered as an Image-Based Visual Servoing (IBVS) problem., Comment: Accepted for publication at 8th Conference on Robot Learning (CoRL), Munich, Germany. 2024

This paper focuses on the extreme-value problem for Shannon entropy of the joint distribution with given marginals. It is proved that the minimum-entropy coupling must be of order-preserving, while the maximum-entropy coupling coincides with the independent one. Note that in this sense, we interpret entropy as a measure of system disorder., Comment: 10 pages

This paper studies current-state opacity and initial-state opacity verification of distributed discrete event systems. The distributed system's global model is the parallel composition of multiple local systems: each of which represents a component. We propose sufficient conditions for verifying opacity of the global system model based only on the opacity of the local systems. We also present efficient approaches for the opacity verification problem that only rely on the intruder's observer automata of the local systems., Comment: 60th IEEE Conference on Decision and Control (CDC2021)

Unmanned Aerial Vehicles (UAVs) are now becoming increasingly accessible to amateur and com-mercial users alike. Several types of airspace structures are proposed in recent research, which include several structured free flight concepts. In this paper, for simplic-ity, distributed coordinating the motions of multicopters in structured airspace concepts is focused. This is formulated as a free flight problem, which includes convergence to destination lines and inter-agent collision avoidance. The destination line of each multicopter is known a priori. Further, Lyapunov-like functions are designed elaborately, and formal analysis and proofs of the proposed distributed control are made to show that the free flight control problem can be solved. What is more, by the proposed controller, a multicopter can keep away from another as soon as possible, once it enters into the safety area of another one. Simulations and experiments are given to show the effectiveness of the proposed method., Comment: arXiv admin note: text overlap with arXiv:2101.07578

In this paper, we propose two new nonblocking properties of automata as quantitative measures of maximal distances to marker states. The first property, called {\em quantitative nonblockingness}, captures the practical requirement that at least one of the marker states (representing e.g. task completion) be reachable within a prescribed number of steps from any non-marker state and following any trajectory of the system. The second property, called {\em heterogeneously quantitative nonblockingness}, distinguishes individual marker states and requires that each marker state be reached within a given bounded number of steps from any other state and following any trajectory of the system. Accordingly, we formulate two new problems of quantitatively nonblocking supervisory control and heterogeneously quantitatively nonblocking supervisory control, and characterize their solvabilities in terms of new concepts of quantitative language completability and heterogeneously quantitative language completability, respectively. It is proved that there exists the unique supremal (heterogeneously) quantitatively completable sublanguage of a given language, and we develop effective algorithms to compute the supremal sublanguages. Finally, combining with the algorithm of computing the supremal controllable sublanguage, we design algorithms to compute the maximally permissive solutions to the formulated (heterogeneously) quantitatively nonblocking supervisory control problems.

In the supervisory control framework of discrete-event systems (DES) with infinite behavior initiated by Thistle and Wonham, a supervisor satisfying the minimal acceptable specification and the maximal legal specification is synthesized. However, this supervisor may incur livelocks as it cannot ensure that the infinite behavior under supervision will always visit some marker states. To tackle this problem, we propose the definition of markability by requiring that all infinite cycles include at least one marker state. Then we formulate the problem of $\omega-$nonblocking supervisory control of DES with infinite behavior to synthesize an $\omega-$nonblocking (i.e. nonblocking, deadlock-free and livelock-free) supervisor. An algorithm is proposed to achieve $\omega-$nonblockingness by computing the supremal $*-$controllable, $*-$closed, $\omega-$controllable and markable sublanguage. We utilize the example of a robot as a running example.

In this paper we study a cybersecurity problem of protecting system's secrets with multiple protections and a required security level, while minimizing the associated cost due to implementation/maintenance of these protections as well as the affected system usability. The target system is modeled as a discrete-event system (DES) in which there are a subset of marker states denoting the services/functions provided to regular users, a subset of secret states, and multiple subsets of protectable events with different security levels. We first introduce usability-aware cost levels for the protectable events, and then formulate the security problem as to ensure that every system trajectory that reaches a secret state contains a specified number of protectable events with at least a certain security level, and the highest usability-aware cost level of these events is minimum. We first provide a necessary and sufficient condition under which this security problem is solvable, and when this condition holds we propose an algorithm to solve the problem based on the supervisory control theory of DES. Moreover, we extend the problem to the case of heterogeneous secrets with different levels of importance, and develop an algorithm to solve this extended problem. Finally, we demonstrate the effectiveness of our solutions with a network security example., Comment: 37 pages, 7 figures

Unmanned Aerial Vehicles (UAVs) are now becoming increasingly accessible to amateur and commercial users alike. An air traffic management (ATM) system is needed to help ensure that this newest entrant into the skies does not collide with others. In an ATM, airspace can be composed of airways, intersections and nodes. In this paper, for simplicity, distributed coordinating the motions of Vertical TakeOff and Landing (VTOL) UAVs to pass an airway is focused. This is formulated as a virtual tube passing problem, which includes passing a virtual tube, inter-agent collision avoidance and keeping within the virtual tube. Lyapunov-like functions are designed elaborately, and formal analysis based on invariant set theorem is made to show that all UAVs can pass the virtual tube without getting trapped, avoid collision and keep within the virtual tube. What is more, by the proposed distributed control, a VTOL UAV can keep away from another VTOL UAV or return back to the virtual tube as soon as possible, once it enters into the safety area of another or has a collision with the virtual tube during it is passing the virtual tube. Simulations and experiments are carried out to show the effectiveness of the proposed method and the comparison with other methods.

Unmanned Aerial Vehicles (UAVs) are now becoming increasingly accessible to amateur and commercial users alike. The main task for UAVs is to keep a prescribed separation with obstacles in the air. In this paper, a collision-avoidance control method for non-cooperative moving obstacles is proposed for a multicopter with the altitude hold mode by using a Lyapunov-like barrier function. Lyapunov-like functions are designed elaborately, based on which formal analysis and proofs of the proposed control are made to show that the collision-avoidance control problem can be solved if the moving obstacle is slower than the multicopter. The result can be extended to some cases of multiple obstacles. What is more, by the proposed control, a multicopter can keep away from obstacles as soon as possible, once obstacles enter into the safety area of the multicopter accidentally, and converge to the waypoint. Simulations and experiments are given to show the effectiveness of the proposed method by showing the distance between UAV and waypoint, obstacles respectively.

We investigate the real-time estimation protocols for the frequency shift of optically detected magnetic resonance (ODMR) of nitrogen-vacancy (NV) centers in nanodiamonds (NDs). Efficiently integrating multipoint ODMR measurements and ND particle tracking into fluorescence microscopy has recently demonstrated stable monitoring of the temperature inside living animals. We analyze the multipoint ODMR measurement techniques (3-, 4-, and 6-point methods) in detail and quantify the amount of measurement artifact owing to several systematic errors derived from instrumental errors of experimental hardware and ODMR spectral shape. We propose a practical approach to minimize the effect of these factors, which allows for measuring accurate temperatures of single NDs during dynamic thermal events. We also discuss integration of noise filters, data estimation protocols, and possible artifacts for further developments in real-time temperature estimation. The present study provides technical details of quantum diamond thermometry and discusses factors that may affect the temperature estimation in biological applications., Comment: 24 pages, 20 figures, 2 tables

The Langberg-M\'{e}dard multiple unicast conjecture claims that for a strongly reachable $k$-pair network, there exists a multi-flow with rate $(1,1,\dots,1)$. In this paper, we show that the conjecture holds true for {\em stable} $3$-pair networks.

This paper proposes a distributed dual gradient tracking algorithm (DDGT) to solve resource allocation problems over an unbalanced network, where each node in the network holds a private cost function and computes the optimal resource by interacting only with its neighboring nodes. Our key idea is the novel use of the distributed push-pull gradient algorithm (PPG) to solve the dual problem of the resource allocation problem. To study the convergence of the DDGT, we first establish the sublinear convergence rate of PPG for non-convex objective functions, which advances the existing results on PPG as they require the strong-convexity of objective functions. Then we show that the DDGT converges linearly for strongly convex and Lipschitz smooth cost functions, and sublinearly without the Lipschitz smoothness. Finally, experimental results suggest that DDGT outperforms existing algorithms., Comment: Accepted by IEEE Transactions on Signal Processing. This version fixed some typos in the accepted version

The traditional multicopter design method usually requires a long iterative process to find the optimal design based on given performance requirements. The method is uneconomical and inefficient. In this paper, a practical method is proposed to automatically calculate the optimal multicopter design according to the given design requirements including flight time, altitude, payload capacity, and maneuverability. The proposed method contains two algorithms: an offline algorithm and an online algorithm. The offline algorithm finds the optimal components (propeller and electronic speed controller) for each motor to establish its component combination, and subsequently, these component combinations and their key performance parameters are stored in a combination database. The online algorithm obtains the multicopter design results that satisfy the given requirements by searching through the component combinations in the database and calculating the optimal parameters for the battery and airframe. Subsequently, these requirement-satisfied multicopter design results are obtained and sorted according to an objective function that contains evaluation indexes including size, weight, performance, and practicability. The proposed method has the advantages of high precision and quick calculating speed because parameter calibrations and time-consuming calculations are completed offline. Experiments are performed to validate the effectiveness and practicality of the proposed method. Comparisons with the brutal search method and other design methods demonstrate the efficiency of the proposed method.

In this paper we study a security problem of protecting secrets with multiple protections and minimum costs. The target system is modeled as a discrete-event system (DES) in which a few states are secrets, and there are multiple subsets of protectable events with different cost levels. We formulate the problem as to ensure that every string that reaches a secret state (from the initial state) contains a specified number of protectable events and the highest cost level of these events is minimum. We first provide a necessary and sufficient condition under which this security problem is solvable, and then propose an algorithm to solve the problem based on the supervisory control theory of DES. The resulting solution is a protection policy which specifies at each state which events to protect and the highest cost level of protecting these events is minimum. Finally, we demonstrate the effectiveness of our solution with a network security example., Comment: 8 pages, 9 figures

Control systems on unmanned vehicles are safety-critical systems whose requirements on reliability and safety are ever-increasing. Currently, testing a complex autonomous control system is an expensive and time-consuming process, which requires massive repeated experimental testing during the whole development stage. This paper presents a unified simulation and test platform for vehicle autonomous control systems aiming to significantly improve the development speed and safety level of unmanned vehicles. First, a unified modular modeling framework compatible with different types of vehicles is proposed with methods to ensure modeling credibility. Then, the simulation software system is developed by the model-based design framework, whose modular programming methods and automatic code generation functions ensure the efficiency, credibility, and standardization of the system development process. Finally, an FPGA-based real-time hardware-in-the-loop simulation platform is proposed to ensure the comprehensiveness and credibility of the simulation and test results. In the end, the proposed platform is applied to a multicopter control system. By comparing with experimental results, the accuracy and credibility of the simulation testing results are verified by using the simulation credibility assessment method proposed in our previous work. To verify the practicability of the proposed platform, several successful applications are presented for the multicopter rapid prototyping, estimation algorithm verification, autonomous flight testing, and automatic safety testing with automatic fault injection and result evaluation of unmanned vehicles.

Electronic control systems are becoming more and more complicated, which makes it difficult to test them sufficiently only through experiments. Simulation is an efficient way in the development and testing of complex electronic systems, but the simulation results are always doubtful by people due to the lack of credible simulation platforms and assessment methods. This paper proposes a credible simulation platform based on real-time FPGA-based hardware-in-the-loop (HIL) simulation, and then an assessment method is proposed to quantitatively assess its simulation credibility. By using the FPGA to simulate all sensor chips, the simulation platform can ensure that the tested electronic system maintains the same hardware and software operating environment in both simulations and experiments, which makes it possible to perform the same tests in the simulation platform and the real experiment to compare and analyze the simulation errors. Then, the testing methods and assessment indices are proposed to assess the simulation platform from various perspectives, such as performance, time-domain response, and frequency-domain response. These indices are all normalized to the same scale (from 0 to 1) and mapped to a uniform assessment criterion, which makes it convenient to compare and synthesize different assessment indices. Finally, an overall assessment index is proposed by combining all assessment indices obtained from different tests to assess the simulation credibility of the whole simulation platform. The simulation platform and the proposed assessment method are applied to a multicopter system, where the effectiveness and practicability are verified by simulations and experiments., Comment: 8 pages, 10 figures

We present a 3D hydrodynamics study of gravitational instabilities (GIs) in a 0.14 M$_{\odot}$ circumbinary protoplanetary disc orbiting a 1 M$_{\odot}$ star and a 0.02 M$_{\odot}$ brown dwarf companion. We examine the thermodynamical state of the disc and determine the strengths of GI-induced density waves, nonaxisymmetric density structures, mass inflow and outflow, and gravitational torques. Results are compared with a parallel simulation of a protoplanetary disc without the brown dwarf binary companion. Simulations are performed using CHYMERA, a radiative 3D hydrodynamics code. The onset of GIs in the circumbinary disc is much more violent due to the stimulation of a strong one-armed density wave by the brown dwarf. Despite this early difference, detailed analyses show that both discs relax to a very similar quasi-steady phase by 2,500 years after the beginning of the simulations. Similarities include the thermodynamics of the quasi-steady phase, the final surface density distribution, radial mass influx, and nonaxisymmetric power and torques for spiral arm multiplicities of two or more. Effects of binarity in the disc are evident in gravitational torque profiles, temperature profiles in the inner discs, and radial mass transport. After 3,800 years, the semimajor axis of the binary decreases by about one percentage and the eccentricity roughly doubles. The mass transport in the outer circumbinary disc associated with the one-armed wave may influence planet formation.

Multicopters are becoming increasingly important in both civil and military fields. Currently, most multicopter propulsion systems are designed by experience and trial-and-error experiments, which are costly and ineffective. This paper proposes a simple and practical method to help designers find the optimal propulsion system according to the given design requirements. First, the modeling methods for four basic components of the propulsion system including propellers, motors, electric speed controls, and batteries are studied respectively. Secondly, the whole optimization design problem is simplified and decoupled into several sub-problems. By solving these sub-problems, the optimal parameters of each component can be obtained respectively. Finally, based on the obtained optimal component parameters, the optimal product of each component can be quickly located and determined from the corresponding database. Experiments and statistical analyses demonstrate the effectiveness of the proposed method.

The Langberg-M\'edard multiple unicast conjecture claims that for any strongly reachable $k$-pair network, there exists a multi-flow with rate $(1,1,\dots,1)$. In a previous work, through combining and concatenating the so-called elementary flows, we have constructed a multi-flow with rate at least $(\frac{8}{9}, \frac{8}{9}, \dots, \frac{8}{9})$ for any $k$. In this paper, we examine an optimization problem arising from this construction framework. We first show that our previous construction yields a sequence of asymptotically optimal solutions to the aforementioned optimization problem. And furthermore, based on this solution sequence, we propose a perturbation framework, which not only promises a better solution for any $k \mod 4 \neq 2$ but also solves the optimization problem for the cases $k=3, 4, \dots, 10$, accordingly yielding multi-flows with the largest rate to date.

This paper studies the model of the probe-drogue aerial refueling system under aerodynamic disturbances, and proposes a docking control method based on terminal iterative learning control to compensate for the docking errors caused by aerodynamic disturbances. The designed controller works as an additional unit for the trajectory generation function of the original autopilot system. Simulations based on our previously published simulation environment show that the proposed control method has a fast learning speed to achieve a successful docking control under aerodynamic disturbances including the bow wave effect., Comment: Accepted by Journal of Guidance, Control, and Dynamics