We study the problem of fitting a piecewise affine (PWA) function to input–output data. Our algorithm divides the input domain into finitely many regions whose shapes are specified by a user-provided template and such that the input–output data in each region are fit by an affine function within a user-provided error tolerance. We first prove that this problem is NP-hard. Then, we present a top-down algorithmic approach for solving the problem. The algorithm considers subsets of the data points in a systematic manner, trying to fit an affine function for each subset using linear regression. If regression fails on a subset, the algorithm extracts a minimal set of points from the subset (an unsatisfiable core) that is responsible for the failure. The identified core is then used to split the current subset into smaller ones. By combining this top-down scheme with a set-covering algorithm, we derive an overall approach that provides optimal PWA models for a given error tolerance, where optimality refers to minimizing the number of pieces of the PWA model. We demonstrate our approach on three numerical examples that include PWA approximations of a widely used nonlinear insulin–glucose regulation model and a double inverted pendulum with soft contacts.

In a Model Predictive Control (MPC) setting, the precise simulation of the behavior of the system over a finite time window is essential. This application-oriented benchmark study focuses on a robot arm that exhibits various nonlinear behaviors. For this arm, we have a physics-based model with approximate parameter values and an open benchmark dataset for system identification. However, the long-term simulation of this model quickly diverges from the actual arm’s measurements, indicating its inaccuracy. We compare the accuracy of black-box and purely physics-based approaches with several physics-informed approaches. These involve different combinations of a neural network’s output with information from the physics-based model or feeding the physics-based model’s information into the neural network. One of the physics-informed model structures can improve accuracy over a fully black-box model.

Large truss structures have many potential applications in space, such as antennas, telescopes and space solar power plants. In this scenario, a natural concern is the susceptibility of these lightweight structures to be damaged during their operational life, due to impacts, transient thermal states and fatigue phenomena. The inclusion of active elements, equipped with sensor/actuator systems capable of modulating their shape and strength, makes it possible to transform the truss into a smart structure capable of remedying the damage, once it is detected. In this paper, a procedure is described that is capable of restoring at least the basic functionality of a composite truss for space applications, starting with the observation that damage has occurred, regardless of its specific location. The system eigenstructure is used as a benchmark for damage detection, as well as a target characteristic for the subsequent restoration activity. The observer/Kalman filter identification algorithm (OKID), in cascade with the eigensystem realization algorithm (ERA), is adopted to reconstruct, from sensor recordings, the dynamic response of the truss in terms of system state-space representation and eigen-characteristics. Finally, a static output feedback control is developed to recover the low-frequency dynamic behaviour of the truss. The entire procedure is tested using finite element analysis. All activities are coordinated in an innovative procedure that, within a unique Python language code, automatically generates finite element (FE) models, launches finite element analysis (FEA), extracts output data, implements OKID-ERA, processes the control law and applies it to the final FE simulation.

This article is concerned with the problem of determining an unknown source of non-potential, external time-dependent perturbations of an incompressible fluid from large-scale observations on the flow field. A relaxation-based approach is proposed for accomplishing this, which makes use of a nonlinear property of the equations of motions to asymptotically enslave small scales to large scales. In particular, an algorithm is introduced that systematically produces approximations of the flow field on the unobserved scales in order to generate an approximation to the unknown force; the process is then repeated to generate an improved approximation of the unobserved scales, and so on. A mathematical proof of convergence of this algorithm is established in the context of the two-dimensional Navier–Stokes equations with periodic boundary conditions under the assumption that the force belongs to the observational subspace of phase space; at each stage in the algorithm, it is shown that the model error, represented as the difference between the approximating and true force, asymptotically decreases to zero in a geometric fashion provided that sufficiently many scales are observed and certain parameters of the algorithm are appropriately tuned.

In this work, a three degrees-of-freedom (3-DoF) static quadcopter unmanned aerial vehicle (UAV) test-rig of a pendulum-type configuration is custom-designed, developed, instrumented, and interfaced with a PC. The rig serves as a test bed to develop high-fidelity mathematical models as well as to investigate autopilot designs and real-time closed-loop controllers’ performances. The Simulink Desktop Real-Time software is employed for the quadcopter’s attitude signals acquisition and real-time implementation of closed-loop controllers on a target microcontroller hardware. The mathematical models for pitch, roll, and yaw axes are derived via the first principle and validated with the experimental linear system identification (SI) techniques. Subsequently, employing the multi-parameter root contour technique, the classical proportional integral derivative (PID) controllers are designed and implemented in real-time on the quadcopter UAV test rig. This served as a benchmark controller for comparing it with an integral-based linear quadratic regulator (LQR) controller. Further, to improve the transient response of the LQR controller, a novel robust integral-based LQR controller with a feedforward term (LQR-FF) is implemented, which shows much superior performance than the benchmark and basic LQR controller. This work thus will act as a precursor for a more complex 3-DoF autopilot design of an untethered quadcopter.

In the present work, a folding wing system (FWS) was developed for guided ammunitions, so that the swept-back angle could be adjusted during both gliding and diving phases. Unlike previous designs, the FWS does not have any fixing mechanisms or brake elements, and it provides folding functionality to reduce the drag force during the terminal phase. We conducted mechanism design, manufactured the FWS, performed system identification and designed various controllers including linear quadratic regulator (LQR), linear quadratic integrator (LQI), sliding mode control (SMC) and second-order sliding mode control (SOSMC) to adjust and hold the desired swept-back angles. Then, the performance of the FWS was tested experimentally under two different flight scenarios, with and without aerodynamic loads. While all controllers operated with almost zero steady-state error (SSE) in the absence of aerodynamic loads, the SOSMC was the most effective controller under aerodynamic loads, considering SSE, delay, chattering, and energy consumption.

This article presents the results of the first AIAA Stability and Control Prediction Workshop obtained at the U.S. Air Force Academy using the kCFD flow solver of the ${\rm{HPCMP}}\;{\rm{CREAT}}{{\rm{E}}^{{\rm{TM}}}}$ -AV Kestrel simulation tools. The test case considered is a large-scale Common Research Model (CRM) tested at the ONERA S1MA wind tunnel at different transonic speeds and fixed lift coefficient values at zero and non-zero side-slip angles. The computational results include a grid sensitivity analysis and validation with available experimental data. In addition, the Mach number and sting effects on the predicted stability and control values of the test case are investigated. Finally, a system identification method using a regression model is developed and used for prediction of stability and control data. The regression coefficients are estimated from an input signal with varying-frequency changes in the angle-of-attack, pitch rate, and side-slip angle. Once the model was created, it was used to predict the static and dynamic aerodynamic data of the test cases. The results show that the model predictions match very well with calculated CFD data at discrete flow conditions.

Mathematical models are essential to analyze and understand the dynamics of complex systems. Recently, data-driven methodologies have gotten a lot of attention which is leveraged by advancements in sensor technology. However, the quality of obtained data plays a vital role in learning a good and reliable model. Therefore, in this paper, we propose an efficient heuristic methodology to collect data both in the frequency domain and the time domain, aiming at having more information gained from limited experimental data than equidistant points. In the frequency domain, the interpolation points are restricted to the imaginary axis as the transfer function can be estimated easily on the imaginary axis. The efficiency of the proposed methodology is illustrated by means of several examples, and its robustness in the presence of noisy data is shown.

This paper aims to accurately estimate the lateral directional aerodynamic parameters in real time irrespective of the variations in the process and measurement covariance matrices. The proposed algorithm for parameter estimation is based on the integration of adaptive techniques into a stochastic nonlinear filter. The proposed adaptive estimation algorithm is applied to flight test data, and the lateral directional derivatives are estimated in real time. The estimates are compared with those obtained from the Filter Error Method (FEM), an offline parameter estimation method accounting for process noise. The estimation results are observed to be very comparable, and the supremacy of the adaptive filter is illustrated by varying the covariance matrices of both process and measurement noises. The parameters estimated by the adaptive filter are found to converge to their actual values, whereas the estimates of the regular filter are observed to diverge from the actual values when changing the noise covariance matrices. The proposed adaptive algorithm can estimate the lateral directional aerodynamic derivatives more accurately without prior knowledge of either process or measurement noise covariance matrices. Hence, it is of great value in online implementations.

In this paper, forward/inverse dynamics of a continuum robotic arm is developed using a data-driven approach, which could tackle uncertainties and extreme nonlinearities to obtain reliable solutions. By establishing a direct mapping between the actuator and task spaces, the unnecessary mappings of actuator-to-configuration then configuration-to-task are eliminated, to reduce extra computational cost. The proposed approach is validated through simulation (based on Cosserat rod theory) and experimental tests on RoboArm. Next, path tracking in the presence/absence of obstacles as well as load carrying maneuver are investigated. Finally, the obtained results concerning repeatability, scalability, and disturbance rejection performance of the approach are discussed.

Adding active toe joints to a humanoid robot structure has lots of difficulties such as mounting a small motor and an encoder on the robot feet. Conversely, adding passive toe joints is simple, since it only consists of a spring and a damper. Due to lots of benefits of implementing passive toe joints, mentioned in the literature, the goal of this study is to add passive toe joints to the SURENA III humanoid robot which was designed and fabricated at the Center of Advanced Systems and Technologies (CAST), University of Tehran. To this end, a simple passive toe joint is designed and fabricated, at first. Then, stiffness and damping coefficients are calculated using a vision-based measurement. Afterwards, a gait planning routine for humanoid robots equipped with passive toe joints is implemented. The tip-over stability of the gait is studied, considering the vibration of the passive toe joints in swing phases. The multi-body dynamics of the robot equipped with passive toe joints are presented using the Lagrange approach. Furthermore, system identification routine is adopted to model the dynamic behaviors of the power transmission system. By adding the calculated actuating torques for these two models, the whole dynamic model of the robot is computed. Finally, the performance of the proposed approach is evaluated by several simulations and experimental results. Results show that using passive toe joints reduces energy consumption of ankle and knee joints by 15.3% and 9.0%, respectively. Moreover, with relatively large values of stiffness coefficients, the required torque and power of the knee and hip joints during heel-off motion reduces as the ankle joint torque and power increases.

Two methods have been compared for the determination of the inertial properties of a small, fixed-wing un-manned aerial vehicle. The first method uses the standard single degree of freedom pendulum method and the second method implements a novel, potentially easier, 3 degrees of freedom pendulum method, which yields the entire inertia tensor from a single swing test. Both methods are using system identification of the pendulum motion to estimate the inertial properties. Substantial corrections (up to 25%) have to be applied to the experimental results. These corrections are caused by the acceleration of the pendulum being immersed in the surrounding air, also called the added mass effect. It has been found that the methods presented in literature to determine the corrections for full-scale aircraft do not give the correct results for the small-scale un-manned aerial vehicle under consideration. The only feasible, cost-effective method to generate these corrections utilise swing tests with a geometrically similar object of known inertial properties. It has also been found that the corrections are unique with respect to the experimental methods. Several benchmarking methods, including the innovative use of static and dynamic wind-tunnel test data, give high confidence in the results.

This study aims to create a prediction model for state-space estimation and to elucidate the required information processing for identifying an external space in prism adaptation. Subjects were 57 healthy students. The subjects were instructed to rapidly perform reaching movements to one of the randomly illuminating light-emitting diode lights. Their movements were measured while wearing prism glasses and after removing that. We provided the following four conditions and control. In target condition, reaching error distance was visually fed back to the subject. In trajectory condition, the trajectory of fingertip movement could be seen, and the final reaching error was not fed back. Two restricted visual feedback conditions were prepared based on a different presentation timing (on-time and late-time conditions). We set up a linear parametric model and an estimation model using Kalman filtering. The goodness of fit between the estimated and observed values in each model was examined using Akaike information criterion (AIC). AIC would be one way to evaluate two models with different number of parameters. In the control, the value of AIC was 179.0 and 154.0 for the linear model and Kalman filtering, respectively, while these values were 173.6 and 161.1 for the target condition, 202.8 and 159.7 for the trajectory condition, 192.7 and 180.8 for the on-time condition, and 206.9 and 174.0 for the late-time condition. Kalman gain in the control was 0.07–0.26. Kalman gain relies on the prior estimation distribution when its value is below 0.5. Kalman gain in the trajectory and late-time conditions was 0.03–0.60 and 0.08–0.95, respectively. The Kalman filter, a state estimation model based on Bayesian theory, expressed the dynamics of the internal model under uncertain feedback information better than the linear parametric model. The probabilistic estimation model can clearly simulate state estimation according to the reliability of the visual feedback.

La cyclostationnarité, propriété propre aux processus dont les caractéristiques évoluentcycliquement au cours du temps, offre un cadre particulièrement adapté à l’analyse denombreux signaux acoustiques et vibratoires. Après avoir rappelé les spécificités del’approche cyclostationnaire dans le contexte mécanique, nous montrons à travers plusieursexemples les possibilités qu’elle autorise dans des domaines d’application liés audiagnostic des machines, à l’identification des systèmes mécaniques et à la séparation desources vibro-acoustiques.

This paper examines three methods of adaptive output feedback control for robotic manipulators. Implementing output feedback control allows use of only the position information, which can be measured quite accurately. Velocity and acceleration measurements can get corrupted by noise. A method proposed by K. W. Lee and H. K. Khalil [Adaptive output feedback control of robot manipulators using high-gain observer, Int. J. Control, 6, 869–886 (1997)] using a high-gain observer, one proposed by J. J. Craig, P. Hsu and S. S. Sastry [Adaptive control of mechanical manipulators, Int. J. Robot. Res., 6(2), 16–27 (1987)] with the addition of a linear observer that we propose, and a method proposed by R. Gourdeau and H. M. Schwartz [Adaptive control of robotic manipulators: Experimental results, Proceedings of the 1991 IEEE International Conference on Robotics and Automation (Apr. 1991) pp. 8–15] using an Extended Kalman Filter are examined. The methods are implemented in simulation and experimentally on a direct-drive robot. The performance of each of the algorithms is compared.

Multifocal VEP (mfVEP) responses were obtained from 13 normal human subjects for nine test conditions, covering three viewing conditions (dichoptic and left and right monocular), and three different temporal stimulation forms (rapid contrast reversal, rapid pattern pulse presentation, and slow pattern pulse presentation). The rapid contrast reversal stimulus had pseudorandomized reversals of checkerboards in each visual field region at a mean rate of 25 reversals/s, similar to most mfVEP studies to date. The rapid pattern pulse presentation had pseudorandomized presentations of a checkerboard for one frame, interspersed with uniform grey frames, with a mean rate of 25 presentations/s per region per eye. The slow pattern pulse stimulus had six presentations/s per region per eye. Recording time was 5.3 min/condition. For dichoptic presentation slow pattern pulse responses were 4.6 times larger in amplitude than the contrast reversal responses. Binocular suppression was greatest for the contrast reversal stimulus. Consideration of the signal-to-noise ratios indicated that to achieve a given level of reliability, slow pattern pulse stimuli would require half the recording time of contrast reversal stimuli for monocular viewing, and 0.4 times the recording time for dichoptically presented stimuli. About half the responses to the slow pattern pulse stimuli had peak value exceeding five times their estimated standard error. Responses were about 20% smaller in the upper visual field locations. Space–time decomposition showed that responses to slow pattern pulse were more consistent across visual field locations. We conclude that the pattern pulse stimuli, which we term temporally sparse, maintain the visual system in a high contrast gain state. This more than compensates for the smaller number of presentations in the run, and provides signal-to-noise advantages that may be valuable in clinical application.

This paper develops a method to re-evaluate the reliability of a structure after a period of service. System identification is performed on the structure to identify the current properties of the structure. The Bayesian approach is adopted to modify the prior distributions of the properties based on the identification results. Then, reliability analysis is performed on the structure using the updated distributions of the properties. Sensitivity analysis is also performed to attain the maintenance strategy.

This paper presents a virtual headstick system as an alternative to the conventional passive headstick for persons with limited upper extremity function. The system is composed of a pair of kinematically dissimilar master-slave robots with the master robot being operated by the user's head. At the remote site, the end-effector of the slave robot moves as if it were at the tip of an imaginary headstick attached to the user's head. A unique feature of this system is that through force-reflection, the virtual headstick provides the user with proprioceptive information as in a conventional headstick, but with an augmentation of workspace volume and additional mechanical power. This paper describes the test-bed development, system identification, bilateral control implementation, and system performance evaluation.