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1. Parameter Identification of Spatial–Temporal Varying Processes by a Multi-Robot System in Realistic Diffusion Fields

   https://doi.org/10.1017/S0263574720000788  

   Wu, Wencen; You, Jie; Zhang, Yufei; Li, Mingchen; Su, Kun (May 2021, Robotica)

   null (Ed.)

   SUMMARY In this article, we investigate the problem of parameter identification of spatial–temporal varying processes described by a general nonlinear partial differential equation and validate the feasibility and robustness of the proposed algorithm using a group of coordinated mobile robots equipped with sensors in a realistic diffusion field. Based on the online parameter identification method developed in our previous work using multiple mobile robots, in this article, we first develop a parameterized model that represents the nonlinear spatially distributed field, then develop a parameter identification scheme consisting of a cooperative Kalman filter and recursive least square method. In the experiments, we focus on the diffusion field and consider the realistic scenarios that the diffusion field contains obstacles and hazard zones that the robots should avoid. The identified parameters together with the located source could potentially assist in the reconstruction and monitoring of the field. To validate the proposed methods, we generate a controllable carbon dioxide (CO 2 ) field in our laboratory and build a static CO 2 sensor network to measure and calibrate the field. With the reconstructed realistic diffusion field measured by the sensor network, a multi-robot system is developed to perform the parameter identification in the field. The results of simulations and experiments show satisfactory performance and robustness of the proposed algorithms. 

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2. Cooperative Filtering and Parameter Identification for Advection–Diffusion Processes Using a Mobile Sensor Network

   https://doi.org/10.1109/TCST.2022.3183585  

   You, Jie; Zhang, Ziqiao; Zhang, Fumin; Wu, Wencen (June 2022, IEEE Transactions on Control Systems Technology)

   This article presents an online parameter identification scheme for advection-diffusion processes using data collected by a mobile sensor network. The advection-diffusion equation is incorporated into the information dynamics associated with the trajectories of the mobile sensors. A constrained cooperative Kalman filter is developed to provide estimates of the field values and gradients along the trajectories of the mobile sensors so that the temporal variations in the field values can be estimated. This leads to a co-design scheme for state estimation and parameter identification for advection-diffusion processes that is different from comparable schemes using sensors installed at fixed spatial locations. Using state estimates from the constrained cooperative Kalman filter, a recursive least-square (RLS) algorithm is designed to estimate unknown model parameters of the advection-diffusion processes. Theoretical justifications are provided for the convergence of the proposed cooperative Kalman filter by deriving a set of sufficient conditions regarding the formation shape and the motion of the mobile sensor network. Simulation and experimental results show satisfactory performance and demonstrate the robustness of the algorithm under realistic uncertainties and disturbances. 

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3. Distributed Cooperative Kalman Filter Constrained by Discretized Poisson Equation for Mobile Sensor Networks

   https://doi.org/10.23919/ACC55779.2023.10156161  

   Zhang, Ziqiao; Mayberry, Scott T.; Wu, Wencen; Zhang, Fumin (May 2023, 2023 American Control Conference)

   This paper proposes cooperative Kalman filters for distributed mobile sensor networks where the mobile sensors are organized into cells that resemble a mesh grid to cover a spatial area. The mobile sensor networks are deployed to map an underlying spatial-temporal field modeled by the Poisson equation. After discretizing the Poisson equation with finite volume method, we found that the cooperative Kalman filters for the cells are subjected to a set of distributed constraints. The field value and gradient information at each cell center can be estimated by the constrained cooperative Kalman filter using measurements within each cell and information from neighboring cells. We also provide convergence analysis for the distributed constrained cooperative Kalman filter. Simulation results with a five cell network validates the proposed distributed filtering method. 

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4. Development and Preliminary Evaluation of a RANSAC Algorithm for Dynamical Model Identification in the Presence of Unmodeled Dynamics

   https://doi.org/10.23919/ACC53348.2022.9867353  

   Dimmig, Cora A.; Moore, Joseph; Whitcomb, Louis L. (June 2022, 2022 American Control Conference)

   This paper reports a novel Random Sample Consensus (RANSAC) algorithm for robust identification of second-order plant dynamical model parameters in the presence of unmodeled plant dynamics and noisy experimental data. Accurate plant dynamical models are essential to model-based control system design and for accurate numerical simulation of plant response. Studies of RANSAC approaches for plant model identification have been extremely limited and have not explored performance improvements in the presence of unmodeled dynamics. The performance of the proposed approach, evaluated in a preliminary simulation study of a planar aerial rotorcraft model, is found to be significantly more robust to the effects of unmodeled vehicle dynamics and outlier noise than conventional least squares parameter identification. We conjecture that the proposed approach may be broadly applicable to robust model parameter identification for a wide variety of plants that exhibit noisy sensor data and/or unmodeled dynamics. 

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5. Nonlinear techniques for few-mode wavefront sensors

   https://doi.org/10.1364/AO.537925  

   Lin, Jonathan; Fitzgerald, Michael_P (November 2024, Applied Optics)

   We present several nonlinear wavefront sensing techniques for few-mode sensors, all of which are empirically calibrated and agnostic to the choice of wavefront sensor. The first class of techniques involves a straightforward extension of the linear phase retrieval scheme to higher order; the resulting Taylor polynomial can then be solved using the method of successive approximations, though we discuss alternate methods such as homotopy continuation. In the second class of techniques, a model of the WFS intensity response is created using radial basis function interpolation. We consider both forward models, which map phase to intensity and can be solved with nonlinear least-squares methods such as the Levenberg-Marquardt algorithm, as well as backwards models, which directly map intensity to phase and do not require a solver. We provide demonstrations for both types of techniques in simulation using a quad-cell sensor and a photonic lantern wavefront sensor as examples. Next, we demonstrate how the nonlinearity of an arbitrary sensor may be studied using the method of numerical continuation, and apply this technique both to the quad-cell sensor and a photonic lantern sensor. Finally, we briefly consider the extension of nonlinear techniques to polychromatic sensors. 

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