Model-free Calibration Research Articles

A Robot Positional Error Compensation Method Based on Improved Kriging Interpolation and Kronecker Products

This paper proposes a stable and high-accuracy model-free calibration method for unopened robotic systems, which can significantly improve the robot positional accuracy. Two improvements are made to the existing kriging-based error compensation method to achieve robustness/practicality enhancement goals: (1) The semi-variogram model is solved using the sequential quadratic programming (SQP) algorithm, and the distance weight coefficients are added to the objective function. The accuracy of semi-variogram modeling is guaranteed, thereby improving the performance and stability of error compensation. (2) The hand-eye (the pose matrix between the robot base and the laser tracker) and the tool center point (TCP) position are calibrated based on Kronecker products without relying on the spatial analyzer (SA) software to construct the robot base coordinate system separately. Thus, the calibration accuracy and efficiency are significantly improved. Experiments have been conducted, and the results reveal that the proposed method can significantly reduce the robot positional error. Furthermore, the proposed approach performs better than the existing kriging-based error compensation method without Kronecker products. The maximum, mean, and root mean square (RMS) values of the absolute positional errors are reduced by 34.48%, 8.09%, and 10.05%, respectively.

Neural-Network-Based Model-Free Calibration Method for Stereo Fisheye Camera.

The fisheye camera has a field of view (FOV) of over 180°, which has advantages in the fields of medicine and precision measurement. Ordinary pinhole models have difficulty in fitting the severe barrel distortion of the fisheye camera. Therefore, it is necessary to apply a nonlinear geometric model to model this distortion in measurement applications, while the process is computationally complex. To solve the problem, this paper proposes a model-free stereo calibration method for binocular fisheye camera based on neural-network. The neural-network can implicitly describe the nonlinear mapping relationship between image and spatial coordinates in the scene. We use a feature extraction method based on three-step phase-shift method. Compared with the conventional stereo calibration of fisheye cameras, our method does not require image correction and matching. The spatial coordinates of the points in the common field of view of binocular fisheye camera can all be calculated by the generalized fitting capability of the neural-network. Our method preserves the advantage of the broad field of view of the fisheye camera. The experimental results show that our method is more suitable for fisheye cameras with significant distortion.

Efficient Model-Free Calibration of a 5-Degree of Freedom Hybrid Robot

Abstract The pose accuracy is a crucial issue that limits the application of hybrid robots. The model-free calibration instead of complex error modeling is investigated to improve the pose accuracy of a 5-degrees-of-freedom (DOF) hybrid robot efficiently. To overcome the difficult problem of model-free calibration in high-dimension joint space that the required measurement data for accurate prediction increase exponentially, a dimensionality reduction method is proposed to decompose high-dimension joint space into two low-dimension subspaces. Then the pose errors can be respectively measured in two subspaces based on the calibrated standard poses to train their corresponding pose error predicators. The standard poses ensure the measured pose errors in two subspaces do not affect each other. Thus, a merging operation obtained by kinematic analysis can finally merge the predicted pose errors of two subspaces into the complete pose error. The error predicators established by several regression methods including artificial neural network, extreme learning machine (ELM) and Twin Gaussian process regression are compared on multi aspects, and ELM stands out among them due to its outstanding prediction accuracy, good anti-noise ability, and low training data requirements. In addition, different representations of pose and pose error are adopted at different calibration stages to deal with the influence of parasitic motion of hybrid robot for the implementation of proposed calibration method. The compensation experiment is executed and the results show that position and orientation errors are reduced by 92.4% and 88.2% on average after calibration and the pose accuracy can meet application requirements.

Integrated Tool Set for Control, Calibration, and Characterization of Quantum Devices Applied to Superconducting Qubits

Efforts to scale-up quantum computation have reached a point where the principal limiting factor is not the number of qubits, but the entangling gate infidelity. However, the highly detailed system characterization required to understand the underlying error sources is an arduous process and impractical with increasing chip size. Open-loop optimal control techniques allow for the improvement of gates but are limited by the models they are based on. To rectify the situation, we provide an integrated open-source tool-set for Control, Calibration and Characterization, capable of open-loop pulse optimization, model-free calibration, model fitting and refinement. We present a methodology to combine these tools to find a quantitatively accurate system model, high-fidelity gates and an approximate error budget, all based on a high-performance, feature-rich simulator. We illustrate our methods using simulated fixed-frequency superconducting qubits for which we learn model parameters with less than 1% error and derive a coherence limited cross-resonance (CR) gate that achieves 99.6% fidelity without need for calibration.

A Model-Free Calibration Method of Inertial Navigation System and Doppler Sensors

The calibration of inertial navigation system (INS) and Doppler Velocity Log (DVL) is an essential task through which the positioning accuracy of the INS/DVL system can be improved significantly. Most existing calibration methods are dependent on the pre-established DVL error model and the hypothesis of small misalignment angles between DVL and INS. An integral calibration method without pre-established model is proposed, which utilizes Genetic Algorithm (GA) and Support Vector Regression (SVR) to construct regression predictor for integral calibration and consolidated compensation. GPS and pressure sensors are used to collect training data to construct the training target output. During underwater navigation, the output of GA-SVR predictor is regarded as the calibrated velocity to construct INS/DVL system. Simulation and semi-physical experiment results show that compared with other traditional calibration algorithms, the calibration accuracy of proposed algorithm is greatly improved. In addition, the limitations of other traditional algorithms can be overcome, which means proposed algorithm can perform smoothly when the misalignment angles are large.

The Exact Implied Volatility Smile for Exponential Lévy Models

For any strictly positive martingale S=e^X for which X has an analytically tractable characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in log(K/S 0 ). We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Levy model (Merton), one infinite activity exponential Levy model (Variance Gamma), and one stochastic volatility model (Heston). We show how this technique can be extended to compute approximate forward implied volatilities and we implement this extension in the Heston setting. Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.

Model-free calibration of Raman measurements of reactive systems: Application to monoethanolamine/water/CO2

We present a method to calibrate Raman measurements of reactive systems without relying on thermodynamic models. Raman spectroscopy is able to detect multiple species even in reactive mixtures. Classical calibration methods require the knowledge of concentrations of all species as input. Typically, concentrations of intermediates cannot be prepared and fixed independently and are therefore calculated using thermodynamic models. The quality of the results thus depends on the accuracy of the thermodynamic model. In this paper, we present a method based only on stoichiometric balances and electroneutrality. By avoiding the use of thermodynamic models in the calibration step, the risk of overfitting spectroscopic data to a thermodynamic model is avoided. The presented method is demonstrated for the reactive system monoethanolamine, water, and CO2 and is validated by a thermodynamic model taken from the literature. While the model-free calibration is demonstrated for Raman spectroscopy in this work, the approach is generic should thus be applicable to most spectroscopic techniques.

From characteristic functions to implied volatility expansions

For any strictly positive martingale S = eX for which X has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log-strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model, Merton (1976), one infinite activity exponential Lévy model (variance gamma), and one stochastic volatility model, Heston (1993). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.

From characteristic functions to implied volatility expansions

For any strictly positive martingaleS= eXfor whichXhas a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log-strike. We illustrate the versatility of our expansion by computing the approximate implied volatility smile in three well-known martingale models: one finite activity exponential Lévy model, Merton (1976), one infinite activity exponential Lévy model (variance gamma), and one stochastic volatility model, Heston (1993). Finally, we illustrate how our expansion can be used to perform a model-free calibration of the empirically observed implied volatility surface.

Monitoring and repair of an impact damaged prestressed bridge

This paper details the monitoring and repair of an impact damaged prestressed concrete bridge. The repair was required following an impact from a low-loader carrying an excavator while passing underneath the bridge. The repair was carried out by preloading the bridge in the vicinity of the damage to relieve some prestressing. This preload was removed following the hardening and considerable strength gain of the repair material. The true behaviour of damaged prestressed concrete bridges during repair is difficult to estimate theoretically due to a lack of benchmarking and inadequacy of assumed damage models. A network of strain gauges at locations of interest was thus installed during the entire period of repair. Effects of various activities were qualitatively and quantitatively observed. The interaction and rapid, model-free calibration of damaged and undamaged beams, including identification of damaged gauges, were also probed. This full-scale experiment is expected to be of interest and benefit to the practising engineer and the researcher alike.

On the measurement of the real values of individual ionic activities: A chemical engineering perspective

This work demonstrates the perfect analogy between the standard method for determining activities in non-electrolyte mixtures and the method used for the determination of ionic activities in electrolyte solutions. For the case of electrolyte solutions, the general procedure of solving three equations with three unknowns is discussed and the reasons why this procedure failed to work for the case of KCl solutions are recapitulated. A modified iteration procedure implemented in this work gives convergence of the solution after three iterations. The crucial difference between eliminating the junction potential, by combination of independent equations, and the use of a proper estimate of its value is emphasized. A new model-free calibration procedure is proposed and sample calculations of K + and Cl − activities in KCl aqueous solutions are presented. Values of K + and Cl − activities in KCl aqueous solutions obtained by this new procedure and by a variety of other methods and researchers are compared.

Nonlinear Model Reduction for Dynamic and Automotive System Descriptions

The mathematical modeling of dynamic systems is an important task in the design, analysis, and implementation of advanced control systems. Although most vehicle control algorithms tend to use model-free calibration architectures, a need exists to migrate to model-based control algorithms which may offer greater operating performance. However, in many instances, the analytical descriptions are too complex for real-time powertrain and chassis model-based control algorithms. Thus, model reduction strategies may be applied to transform the original model into a simplified lower-order form while preserving the dynamic characteristics of the original high-order system. In this paper, an empirical gramian balanced nonlinear model reduction strategy is examined. The controllability gramian represents the energy needed to transport the system between states, while the observability gramian denotes the output energy transmitted. These gramians are then balanced and select system dynamics truncated. For comparison purposes, a Taylor Series linearization will also be introduced to linearize the original nonlinear system about an equilibrium operating point, and then a balanced realization linear reduction strategy applied to reduce the linearized model. To demonstrate the functionality of each model reduction strategy, a vehicle suspension system and exhaust gas recirculation valve are investigated, and respective transient performances are compared.