Speed regulation in steering-based source seeking

The simplest strategy for extremum seeking-based source localization, for sources with unknown spatial distributions and nonholonomic unicycle vehicles without position measurement, employs a constant positive forward speed. Steering of the vehicle in the plane is performed using only the variation of the angular velocity. While keeping the forward speed constant is a reasonable strategy motivated by implementation with aerial vehicles, it leads to complexities in the asymptotic behavior of the vehicle, since the vehicle cannot settle—at best it can converge to a small-size attractor around the source. In this paper we regulate the forward velocity, with the intent of bringing the vehicle to a stop, or as close to a stop as possible. The vehicle speed is controlled using simple derivative-like feedback of the sensor measurement (the derivative is approximated with a washout filter) to which a speed bias parameter V_c is added. The angular velocity is tuned using standard extremum seeking. We prove two results. For V_c in a certain range around zero, we show that the vehicle converges to a ring around the source and on average the limit of the vehicle’s heading is either directly away or towards the source. For other values of V_c>0, the vehicle converges to a ring around the source and it revolves around the source. Interestingly, the average heading of this revolution around the source is more outward than inward—this is possible because the vehicle’s speed is not constant, it is lower during the outward steering intervals and higher during the inward steering intervals. The theoretical results are illustrated with simulations.     

Nonholonomic Source Seeking With Tuning of Angular Velocity

We consider the problem of seeking the source of a scalar signal using an autonomous vehicle modeled as the nonholonomic unicycle. The vehicle does not have the capability of sensing its position or the position of the source but is capable of sensing the scalar signal originating from the source. The signal field is assumed to decay away from the position of the source but the vehicle does not have the knowledge of the functional form of the field. We employ extremum seeking to steer the vehicle to the source. Our control strategy keeps the forward velocity constant and tunes the angular velocity, a setting suitable for most autonomous vehicles, including aerial ones. Because of the constant forward velocity constraint, after it has converged near the source, the vehicle exhibits extremely interesting and complex motions. Using averaging theory, we prove local exponential convergence to an ldquoorbit-likerdquo attractor around the source. We also present a thorough analysis of non-local behaviors and attractors that the vehicle can exhibit near the source. The richness and complexity of behaviors makes only some of them amenable to analysis, whereas others are illustrated through a carefully laid out simulation study.     

3-D Source Seeking for Underactuated Vehicles Without Position Measurement

Our past work introduced source seeking methods for GPS-denied autonomous vehicles using only local signal measurement and operating in two dimensions. In this paper, we extend these results to three dimensions. The 3-D extensions introduce many interesting challenges, including the choice of vehicle models in 3-D, sensor placement to allow probing-based gradient estimation of an unknown signal field in 3-D, the question of what type of pattern of vehicle motion can be produced in an underactuated 3-D vehicle to allow tuning by single-loop or multiloop extremum seeking, and the shape of attractors, which become very complex in 3-D. We present two control schemes that address these questions. The first scheme focuses on vehicles with a constant forward velocity and the ability to actuate pitch and yaw velocities. The second scheme employs vehicles with constant forward and pitch velocities and actuate only the roll velocity. Our results include convergence analysis and simulation results.      

Switching mode generation and optimal estimation with application to skid-steering

Skid-steered vehicles, by design, must skid in order to maneuver. The skidding causes the vehicle to behave discontinuously during a maneuver as well as introduces complications to the observation of the vehicle’s state, both of which affect a controller’s performance. This paper addresses estimation of contact state by applying switched system optimization to estimate skidding properties of the skid-steered vehicle.In order to treat the skid-steered vehicle as a switched system, the vehicle’s ground interaction is modeled using Coulomb friction, thereby partitioning the system dynamics into four distinct modes, one for each combination of the forward and back wheel pairs sticking or skidding. Thus, as the vehicle maneuvers, the system propagates over some mode sequence, transitioning between modes over some set of switching times. This paper presents second-order optimization algorithms for estimating these switching times. We emphasize the importance of the second-order algorithm because it exhibits quadratic convergence and because even for relatively simple examples, first-order methods fail to converge on time scales compatible with real-time operation. Furthermore, the paper presents a technique for estimating the mode sequence by optimizing a relaxation of the switched system.     

Source seeking with non-holonomic unicycle without position measurement and with tuning of forward velocity

We consider the problem of seeking the source of a scalar signal using an autonomous vehicle modeled as the non-holonomic unicycle and equipped with a sensor of that scalar signal but not possessing the capability to sense either the position of the source nor its own position. We assume that the signal field is the strongest at the source and decays away from it. The functional form of the field is not available to our vehicle. We employ extremum seeking to estimate the gradient of the field in real time and steer the vehicle towards the point where the gradient is zero (the maximum of the field, i.e., the location of the source). We employ periodic forward–backward movement of the unicycle (implementable with mobile robots and some underwater vehicles but not with aircraft), where the forward velocity has a tunable bias term, which is appropriately combined with extremum seeking to produce a net effect of “drifting” towards the source. In addition to simulation results we present a local convergence proof via averaging, which exhibits a delicate periodic structure with two sinusoids of different frequencies—one related to the angular velocity of the unicycle and the other related to the probing frequency of extremum seeking.     

Stochastic consensus over noisy networks with Markovian and arbitrary switches

This paper considers stochastic consensus problems over lossy wireless networks. We first propose a measurement model with a random link gain, additive noise, and Markovian lossy signal reception, which captures uncertain operational conditions of practical networks. For consensus seeking, we apply stochastic approximation and derive a Markovian mode dependent recursive algorithm. Mean square and almost sure (i.e., probability one) convergence analysis is developed via a state space decomposition approach when the coefficient matrix in the algorithm satisfies a zero row and column sum condition. Subsequently, we consider a model with arbitrary random switching and a common stochastic Lyapunov function technique is used to prove convergence. Finally, our method is applied to models with heterogeneous quantizers and packet losses, and convergence results are proved.     

Influence of reentry turbulent plasma fluctuation on EM wave propagation

Electromagnetic wave propagation in turbulent plasma media during reentry is being investigated. Emphasis is placed on the effects of electron density fluctuations on electromagnetic wave propagation. The objective of this paper is to specify the source of noise in electromagnetic signal reception due to turbulence in the flow about a high velocity flight vehicle. A review of existing ground and flight test data is conducted, including electron density fluctuation measurements. Analytical algorithms deduced from first principles are being developed and validated with experimental measurements. A Navier-Stokes model, three-dimensional parabolized Navier-Stokes, and a coupled boundary-layer and inviscid flow codes are used to estimate the mean and variance of the electron density on the frustum and at the vehicle’s base region. Analytical and numerical solutions solving Maxwell’s equations and a commercial off the shelf code are used to estimate the phenomena of electromagnetic wave propagation in inhomogeneous plasma media. Results include the estimation of signal attenuation and phase shift induced by the mean electron density and by electron density fluctuations in the flowfield. Comparisons are made between the predictions and available data.     

Extremum seeking by a dynamic plant using mixed integral sliding mode controller with synchronous detection gradient estimation

This paper presents a continuous‐time optimization method for an unknown convex function restricted to a dynamic plant with an available output including a stochastic noise. For solving the problem, we propose an extremum seeking algorithm based on a modified synchronous detection method for computing a stochastic gradient descent approach. In order to reject from the beginning the undesirable uncertainties and perturbations of the dynamic plant, we employ the standard deterministic integral sliding mode control transforming the initial dynamic plant to the static one, and after (in fact, from the beginning of the process), we apply the gradient decedent technique. We consider time‐decreasing parameters for compensating the stochastic dynamics. We prove the stability and the mean‐square convergence of the method. To validate the exposition, we perform a numerical example simulation.     

Newton-based stochastic extremum seeking

In this paper, we introduce a Newton-based approach to stochastic extremum seeking and prove local stability of Newton-based stochastic extremum seeking algorithm in the sense of both almost sure convergence and convergence in probability. The convergence of the Newton algorithm is proved to be independent of the Hessian matrix and can be arbitrarily assigned, which is an advantage over the standard gradient-based stochastic extremum seeking. Simulation shows the effectiveness and advantage of the proposed algorithm over gradient-based stochastic extremum seeking.     

Almost sure convergence of extremum seeking algorithm using stochastic perturbation

This paper presents an extremum seeking (ES) algorithm where the perturbation signal is a martingale difference sequence (m.d.s.) with a vanishing variance. The measurement noise at the plant output is modeled by a superposition of deterministic component, and a non-stationary colored noise signal. The optimizing set point of the uncertain reference-to-output equilibrium map is estimated by a stochastic approximation (SA)-type algorithm. The algorithm has a vanishing gain sequence dependent on the set point estimates. By utilizing powerful tools of the martingale convergence theory it is proved that with probability one the set point estimates converge to the optimizing equilibrium point, in spite of the presence of a measurement noise. This result is derived without requiring boundedness or any prior condition on the set point estimates.     

TMA: Trajectory-based Multi-Anycast forwarding for efficient multicast data delivery in vehicular networks

This paper describes Trajectory-based Multi-Anycast forwarding (TMA), tailored and optimized for the efficient multicast data delivery in vehicular networks in terms of transmission cost. To our knowledge, this is the first attempt to investigate the efficient multicast data delivery in vehicle networks, based on the trajectories of vehicles in the multicast group. Due to the privacy concern, we assume only a central server knows the trajectory of each vehicle and the estimated current location of the vehicle. Therefore, after receiving a request of multicast data delivery from a source vehicle, the central server has to figure out how the data has to be delivered to the moving vehicles in the multicast group. For each target vehicle in the multicast group, multiple packet-and-vehicle rendezvous points are computed as a set of relay nodes to temporarily hold the data, considering the vehicle’s trajectory. This set of rendezvous points can be considered an Anycast set for the target vehicle. We have formulated the multicast data delivery as the data delivery to the anycast sets of the multicast group vehicles. Through theoretical analysis and extensive simulation, it is shown that our design provides an efficient multicast for moving vehicles under a variety of vehicular traffic conditions.     

Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements

We remove the long standing restriction that plant dynamics in extremum seeking control must be stable and provide an extension that allows single integrators, double integrators, and moderately unstable single poles. An application of the result for single and double integrators is in control of autonomous vehicles. Extremum seeking is used for finding a source of a signal (chemical, electromagnetic, etc.) whose strength decays with the distance. This is achieved without the measurement of the position vector and using only the measurement of the scalar signal.     

Multivariable Newton-based extremum seeking

We present a Newton-based extremum seeking algorithm for the multivariable case. The design extends the recent Newton-based extremum seeking algorithms for the scalar case and introduces a dynamic estimator of the inverse of the Hessian matrix that removes the difficulty with the possible singularity of a possible direct estimate of the Hessian matrix. The estimator of the inverse of the Hessian has the form of a differential Riccati equation. We prove local stability of the new algorithm for general nonlinear dynamic systems using averaging and singular perturbations. In comparison with the standard gradient-based multivariable extremum seeking, the proposed algorithm removes the dependence of the convergence rate on the unknown Hessian matrix and makes the convergence rate, of both the parameter estimates and of the estimates of the Hessian inverse, user-assignable. In particular, the new algorithm allows all the parameters to converge with the same speed, yielding straight trajectories to the extremum even with maps that have highly elongated level sets, in contrast to curved “steepest descent” trajectories of the gradient algorithm. Simulation results show the advantage of the proposed approach over gradient-based extremum seeking, by assigning equal, desired convergence rates to all the parameters using Newton’s approach.     

Flow field eigenmode decompositions in aeroacoustics

In this paper an efficient method to study sound generation processes in low Mach number flows is presented. We apply the methodology on a two-dimensional flow over a cavity with smoothed corners. Instead of the full flow field obtained from, for example a Direct Numerical Simulation (DNS), we use a reduced model based on global modes to obtain the aeroacoustic sources. Global modes are eigenmodes to the Navier-Stokes equations, linearized about a steady base flow. In a reduced model the perturbations from a steady state are approximated by a linear combination of the eigenmodes. The time dependence is determined by the corresponding eigenvalues. Curle’s equation is used to calculate the acoustic field, and by studying the source terms in Curle’s equation, mechanisms for sources of sound are identified. Results of acoustic pressure in the far-field and source strengths for different superpositions of eigenmodes are presented.     

Robustness of c-velocity based methods for 3D moving plane detection

The Hough-like frame called c-velocity supports a surface detection from an image sequence, without calibration. A vehicle’s environment, set of 3D planes, can then be reconstructed exploiting isovelocity curves bound to an estimated optical flow. We show in this paper how the cumulative approach is robust against main perturbations.     

Delay robustness in consensus problems

We investigate the robustness of consensus schemes for linear Multi-Agent Systems (MAS) to feedback delays. To achieve this, we develop a unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor’s output, or affecting both the agent’s own and its neighbors’ output. This framework has the advantage of providing scalable, simple, and accurate set-valued conditions for consensus. Using these set-valued conditions, previous results on consensus in MAS with delays can be recovered and generalized. Moreover, we use them to derive conditions for the convergence rate of single integrator MAS with feedback delays. Finally, building on this framework, we propose a scalable delay-dependent design algorithm for consensus controllers for a large class of linear MAS.     

基于光电标签的火箭橇全程测速技术研究

火箭橇试验在兵器研制和性能测试上起着至关重要的作用,现有火箭橇测速方法均存在一些不足之处,针对火箭橇试验中全程速度测量难题,提出了一种基于光电标签的火箭橇全程速度测量方法;建立了光电标签的探测模型,对光电标签的原向反射特性进行研究,分析并仿真了传感器在动态测量中的信号变化过程,基于信号的频率特性对光电探测器件与信号处理电路进行选型,设计并搭建出硬件测量电路,对系统进行了测试与验证;实验结果表明：传感器对光电标签的探测距离可达40cm,系统速度测量范围满足了火箭橇试验在兵器靶场上的应用,与传统方法相比,光电标签法成本更低、易实现,在火箭橇全程速度测量中有更广泛的应用场景。     

Diagnosing and correcting design inconsistencies in source code with logical abduction

Correcting design decay in source code is not a trivial task. Diagnosing and subsequently correcting inconsistencies between a software system’s code and its design rules (e.g., database queries are only allowed in the persistence layer) and coding conventions can be complex, time-consuming and error-prone. Providing support for this process is therefore highly desirable, but of a far greater complexity than suggesting basic corrective actions for simplistic implementation problems (like the “declare a local variable for non-declared variable” suggested by Eclipse).We present an abductive reasoning approach to inconsistency correction that consists of (1) a means for developers to document and verify a system’s design and coding rules, (2) an abductive logic reasoner that hypothesizes possible causes of inconsistencies between the system’s code and the documented rules and (3) a library of corrective actions for each hypothesized cause. This work builds on our previous work, where we expressed design rules as equality relationships between sets of source code artifacts (e.g., the set of methods in the persistence layer is the same as the set of methods that query the database). In this paper, we generalize our approach to design rules expressed as user-defined binary relationships between two sets of source code artifacts (e.g., every state changing method should invoke a persistence method).We illustrate our approach on the design of IntensiVE, a tool suite that enables defining sets of source code artifacts intensionally (by means of logic queries) and verifying relationships between such sets.     

Stochastic contraction-based observer and controller design algorithm with application to a flight vehicle

This paper focuses on a stochastic version of contraction theory to construct observer-controller structure for a flight dynamic system with noisy velocity measurement. A nonlinear stochastic observer is designed to estimate the pitch rate, the pitch angle, and the velocity of an aircraft example model using stochastic contraction theory. Estimated states are used to compute feedback control for solving a tracking problem. The structure and gain selection of the observer is carried out using Itô's stochastic differential equations and the contraction theory. The contraction property of integrated observer-controller structure is derived to ensure the exponential convergence of the trajectories of closed-loop nonlinear system. The upper bound of the state estimation error is explicitly derived and the efficacy of the proposed observer-controller structure has been shown through the numerical simulations.     

A design methodology for switched discrete time linear systems with applications to automotive roll dynamics control

In this paper we consider the asymptotic stability of a class of discrete-time switching linear systems, where each of the constituent subsystems is Schur stable. We first present an example to motivate our study, which illustrates that the bilinear transform does not preserve the stability of a class of switched linear systems. Consequently, continuous time stability results cannot be transformed to discrete time analogs using this transformation. We then present a subclass of discrete-time switching systems that arise frequently in practical applications. We prove that global attractivity for this subclass can be obtained without requiring the existence of a common quadratic Lyapunov function (CQLF). Using this result, we present a synthesis procedure to construct switching stabilizing controllers for an automotive control problem, which is related to the stabilization of a vehicle’s roll dynamics subject to switches in the center of gravitys (CG) height.