This paper proposes a new hybrid (i.e., physicsbased and data-driven) modeling approach for multirotor UAVs. The model favors the physics component to promote simplicity, physical consistency, and suitability for control and estimation tasks. It relies on a physics-based dynamic formulation derived from Blade Element Theory and Momentum Theory, while restricting learning to the induced velocity of each rotor. We study the impact of rotor flow interactions by comparing models with and without interaction terms. We also propose a velocitybased learning procedure and compare it with a force-based alternative. The proposed approach is evaluated on a realworld dataset. Results show that significant improvements in velocity prediction are obtained when rotor flow interactions are included. In addition, velocity-based training yields more accurate velocity prediction than force-based learning.

Zebrafish embryos have been of particular interest in developmental biology research in recent years. Among the properties of zebrafish eggs that need to be characterized, stiffness is a key feature. It is a good indicator of the developmental stage of the egg and embryo. A highly localized stiffness measurement and/or the related Young's modulus requires a force sensor with a tip radius as small as that of an atomic force microscope (AFM). However, the length of an AFM probe tip is often less than a hundred micrometers, whereas zebrafish eggs are about 0.7 mm in diameter. This makes it impossible to penetrate deep into the egg to mechanically characterise the outer membrane, the inner medium and the embryo. This paper presents the proof of concept of the efficiency of quartz tuning forks with tungsten probes of several millimeters long and tip radius of a few tens of nanometers to mechanically characterize zebrafish eggs. The work includes robotics, modelling and control developments as well as experiments on zebrafish eggs. It demonstrates that tungsten probes with tuning fork technology offer sufficient resolution to mechanically differentiate zebrafish eggs at different stages of development, as well as sufficient rigidity and strength to penetrate a zebrafish egg, which was not previously known or evaluated in the state of the art.

In this study, we present a semi-automated microrobotic platform based on a tuning fork for the characterization of the stiffness of soft polydimethylsiloxane (PDMS) samples involving very low-amplitude and highly localized interaction forces. Stiffness characterization is based on the measurement of the shift Delta(f) in the resonance frequency of the tuning fork. A control strategy is proposed and implemented to ensure safe landing and indentation of the tuning fork probe on the sample. A model describing Delta(f) as a function of PDMS stiffness and indentation depth is proposed. The results demonstrate the relevance of tungsten-tipped tuning forks controlled in permanent contact mode to distinguish PDMS samples of different rigidities through frequency shift and indentation depth measurements. Copyright (c) 2025 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification of physically consistent models, which are essential for model-based control synthesis. Lagrangian or Hamiltonian neural networks provide useful structural guarantees but the learning of such models often leads to inconsistent models, especially on real physical systems where training data are limited, partial and noisy. Motivated by this observation and the objective to exploit these models for model-based nonlinear control, a learning algorithm relying on an original loss function is proposed to improve the physical consistency of Lagrangian systems. A comparative analysis of different learning-based modeling approaches with the proposed solution shows significant improvements in terms of physical consistency of the learned models, on both simulated and experimental systems. The model's consistency is then exploited to demonstrate, on an experimental benchmark, the practical relevance of the proposed methodology for feedback linearization and energy-based control techniques.

Sorting of zebrafish embryos remains a challenging task in biomedical research. There is a need for accurate and efficient methods to distinguish between embryos at Stage 1, the zygote period immediately after fertilization, characterized by the single-cell stage, as well as those at advanced developmental stages (above single-cell stage) and non-viable (Dead) embryos. Manual sorting is labor-intensive, error-prone, and time-consuming. Traditional automated techniques, such as fluorescence-activated cell sorting (FACS) and robotic systems, are often invasive or prohibitively expensive, limiting their accessibility and scalability for routine zebrafish embryo sorting. This paper presents a novel approach that integrates deep learning with microfluidic technology to address these limitations. Our system utilizes a YOLOv8-based deep learning model for real-time embryo classification, whereas a microfluidic chip which is equipped with peristaltic pumps, ensures precise sorting with minimal manual intervention. Computational Fluid Dynamics (CFD) simulations are performed to optimise the flow parameters, and experimental validation demonstrate the system’s high accuracy and sorting efficiency. The YOLOv8 model demonstrate a detection accuracy of 97.6 % and a processing speed of 10.5 ms. The sorting experiments demonstrate the system’s efficacy, with the Stage 1 class achieving a detection accuracy of 90.63 % and a sorting efficiency of 88.13 %. The Advanced class exhibited enhanced performance, with a detection accuracy of 93.36 % and a sorting efficiency of 91.80 %. The Dead class demonstrate the highest performance, with a detection accuracy of 99.03 % and a sorting efficiency of 96.60 %. The system demonstrate an average sorting rate of 2.92 s per embryo. This approach provides a reliable, cost-effective alternative to traditional methods, significantly improving the speed and precision of embryo sorting.

Transcriptomics and metabolomics, two biological research fields that need large numbers of zebrafish embryos, require the removal of unfertilised or nonviable zebrafish embryos. Biologists routinely conduct the tedious, error-prone, and time-consuming manual sorting of embryos. We suggest a novel approach that combines deep learning and microfluidics for automated sorting to overcome this difficulty. To determine the developmental stage and viability of zebrafish eggs, we trained an optimized YOLOv5 model with 95.8% accuracy and a processing speed of 10.6 ms per frame, classifying them as dead, unfertilised, or alive. The eggs are contained in traps on a microfluidic chip using micro-pumps. After that, the deep learning system can identify and automatically sort the eggs according to their viability by positioning this chip on an XYZ motorized stage. The sorting experiment was conducted in two modes: without feedback and with feedback while using the dead egg position. The first one had a sorting success rate of 90% as opposed to 97.9% for the feedback mode with 3 seconds required for each dead egg. This automated approach provides a precise and efficient way to handle a large number of zebrafish embryos while also greatly reducing the workload associated with manual sorting. The success rates attained demonstrate the usefulness and effectiveness of our suggested methodology, opening new avenues for biological research involving accurate embryo selection.

Path following control of micrometer-sized tools is the key to improve automation capabilities at the small scales. This paper addresses the issue of path following control for piezoelectric inertia actuated nano-robotic systems operating inside electron microscopes. The aim is to control the trajectory of an end effector driven by a stick and slip principle using both electron microscope images and velocity measurements from optical encoders. The path following control is divided into two layers. The high level layer considers a Frenet frame kinematic model to compute velocity references along two orthogonal axes. The low level layer is based on an average closed loop velocity control of the nano-robotic system along the two orthogonal axes. The path following performances are evaluated and analyzed experimentally using an inertia nano-robotic system operating inside a Scanning Electron Microscope and holding an Atomic Force Microscope (AFM) cantilever. Experimental results show the effectiveness of the AFM cantilever for various paths following with a mean tracking error less than 2 mu m in the worst case. These tracking capabilities are of importance toward automated manipulation and assembly sequences inside electron microscopes.

This letter presents a method to determine and control the center of rotation of a parallel micro-robotic platform used as a sample holder for an Atomic Force Microscope (AFM). The AFM is operating inside a Scanning Electron Microscope (SEM) for correlative AFM in SEM imaging. The objective is to spatially co-localize the Pivot Point (PP) and the AFM tip at any region of interest of a sample within the reachable workspace of the AFM. To do so, SEM images are used to land the AFM tip on a desired Point Of Interest (POI). Topographic data obtained with the AFM are used to calculate the Tool Center Point (TCP) of the robot and to identify the coordinates of the POI in the AFM sample holder reference frame. The position of the PP is then controlled relying on the TCP and SEM vision to finally been able to perform, in a controlled way, in-plane rotations of the sample holder around the AFM tip with a micrometer precision. This work shows for the first time how SEM and AFM data can be used in tandem to calibrate the rotational degrees of freedom of an AFM system.

Considering microbotics, microforce sensing, their working environment, and their control architecture together, microrobotic force-sensing systems provide the potential to outperform traditional stand-alone approaches. Microrobotics is a unique way for humans to control interactions between a robot and micrometer-size samples by enabling the control of speeds, dynamics, approach angles, and localization of the contact in a highly versatile manner. Many highly integrated microforce sensors attempt to measure forces occurring during these interactions, which are highly difficult to predict because the forces strongly depend on many environmental and system parameters. This article discusses state-of-the-art microrobotic systems for microforce sensing, considering all of these factors. It starts by presenting the basic principles of microrobotic microforce sensing, robotics, and control. It then discusses the importance of microforce sensor calibration and active microforce-sensing techniques. Finally, it provides an overview of microrobotic microforce-sensing systems and applications, including both tethered and untethered microrobotic approaches.

This paper presents a functionality that has been developed for the home-made AFM-in-SEM robotic system at the ISIR laboratory. The method allows extending the range of an Atomic Force Microscope (AFM) and dealing with drift issues by fusing multiple individually AFM topography patches. The merging of the patches into a single image is done through a Generalized Procrustes Analysis Iterative Closest Point (GPA-ICP) algorithm. To validate the effectiveness of the approach, an AFM image of a TGX1 calibration grid and a 3.4- billion-year-old organic-walled microfossil are reconstructed by automatically merging 50 AFM elementary topography patches of dimension 0.9 μm × 1.2 μm based on feature matching. The overlap between two adjacent patches is 50 % and 33 % in the X and Y axes respectively. The result is a coherent 3.2 μm × 3.0 μm drift-free long range AFM topography without significant artifacts. The method is tested using an AFM-in- SEM system based on a 3-DOF cartesian robot equipped with inertial piezoelectric actuators. This method can be used to extend the range of any type of AFM with a dual XY stage setup. Thus, it opens the door for high-resolution long-range AFM by adding a long-range coarse resolution stage to a preexisting AFM system all without needing to actuate both stages simultaneously.

Many of biological studies like transcripromics or metabolomics requires a large number of zebrafish embryos. Dead or unfertilized embryos that will not be useful for studies should be eliminated. Biologists frequently perform this manually, which is laborious, error-prone, and time consuming. We therefore proposed a method for sorting these undesired cells using deep learning and microfluidics. A YOLOv5 model was trained with a 95% accuracy and a processing speed of 10.6 ms per frame to assess the stage of development as well as whether a zebrafish egg is dead, unfertilized, or alive. Eggs are housed in traps on a microfluidic chip using micro-pumps. Once all the zebrafish eggs are housed in the traps, the microfluidic chip is placed in an XYZ motorized stage which, by moving, allows the detection of the eggs by the deep learning system and automatically sorting them based on dead or unfertilized embryo detected. The sorting experiment was conducted in two modes: without feedback and with feedback while using the dead egg position. The first one had a sorting success rate of 90% as opposed to 100% for the feedback mode with 3 seconds required for each dead egg.

An emerging actuation technique in piezo driven nanopositioners is differential actuation, where each axis has two opposing actuators that operate differentially and provide bilateral motion. It has simultaneous benefits of improving linearity and range of displacement. However, few methods for displacement sensing employing in-situ transducers have been considered for this kind of nanopositioners. We address a novel application of PZT piezoelectric chips for direct displacement sensing in differentially driven nanopositioners. First, an electromechanical force analysis is performed in order to increase the PZT sensor sensitivity through the structural design of the nanopositioner. Secondly, the sensing performances of the proposed in-situ PZT sensor are compared with those from an alternative built-in piezoresistive (PZR) strain gauge sensor under equal circumstances, in different sensing and actuation configurations. While the PZR sensor has a larger sensing bandwidth than the PZT one and performs better if the actuation frequency is smaller than 30 Hz, the PZT sensors provides better accuracy when the actuation is well within its sensing bandwidth. The accuracy of the differential sensors and the input-displacement linearity are improved when the mechanical preload force magnitudes on the opposing actuators are balanced. The differential PZT sensor can provide accurate measurements even in a non-differential mode after recalibration.

This paper presents the first experimental implementation of a XY differential piezo-driven stage in closed loop for tracking reference signals at the kHz with nanometer resolution by an exclusive use of piezoelectric sensors. The sensors are arranged differentially and in series with piezoelectric actuators. The control scheme consists of an internal loop with an analog damping controller and an external digital loop with an Internal Model Control (IMC) tracking controller. The damping controller is designed to attenuate the lightly damped resonances of the system. The tracking controller is especially designed for tracking only single tone sinusoidal reference trajectories. This particularity allows the use of piezoelectric transducers in a narrow frequency band and thus does not require a low frequency correction or the use of additional sensors to compensate for the high pass response of the transducers. The experimental results show that the nano-positioning stage is able to track a sinusoidal trajectory of 1 kHz frequency and 1.25 µm amplitude with a maximum tracking error of 4 nm. These results have never been demonstrated previously with differential piezo-driven stages and open perspectives towards high speed Atomic Force Microscopy (AFM) at the nanoscale using differential actuation and piezoelectric sensing.

Traditional Atomic Force Microscopes (AFM) allow a short range displacement of the AFM probe, on the order of several tens of micrometers. When used inside an Electron Microscope (EM), the probe must be able to move on a millimeter scale with nanometer resolution. This is essential for the probe to reach any region of interest on a sample observed by an EM. In this paper, we address a challenging issue related to semi-automated long-range landing of an AFM probe on a sample. The probe is mounted on a piezoelectric inertial actuator. It is initially several millimeters away from the sample and must be safely landed to a distance on the order of hundred of nanometers (intermittent contact region). The control strategy is divided into three steps: (i) long-range velocity control using a stepping control, (ii) short and fine position control using a mixed stepping/scanning control, and (iii) position/force control using a scanning control. While traditional manual landing methods take a tremendous amount of time to complete the procedure, the proposed semi-automated method enables a safe long-range landing in less than 3 minutes. More generally, this is the first experimental demonstration in the literature of such a capability in AFM.

This article proposes a method for the correction of angular deviations caused during the fixing process of samples prepared for Atomic Force Microscopy (AFM). The correction is done using the angular control of a 6-DOF PPPS parallel platform were the sample is placed, while the AFM scan is performed by a 3-DOF serial cartesian robot with a tuning fork probe designed to perform FM-AFM. The method uses the generic x, y, and z data provided by the AFM after performing a scan on a free surface of the sample substrate. This is used to calculate the plane that closest approximates the points by solving a system of linear equations. This plane is then used to estimate the angular corrections that the 6-DOF parallel robot has to do in order to compensate the deviations. The proposed algorithm can be performed iteratively in order to refine the correction. The method also does not require any special preparation of the substrate. It only requires to have a free surface to scan. Experiments are performed using this algorithm to correct the orientation deviation of a substrate of V1 High-grade mica. The results show that the method is able to correct the angular deviation of the sample relatively to the AFM probe with an error of 0.2° after only two iterations of the algorithm.

The Atomic Force Microscope (AFM) is a reliable tool for 3D imaging and manipulation at the micrometer and nanometer scales. When used inside a Scanning Electron Microscope (SEM), AFM probes can be localized and controlled with a nanometer resolution by visual feedback. However, achieving trajectory control and obstacles avoidance is still a major concern for manipulation tasks. We propose a Model Predictive Control (MPC) to address these two issues while AFM probes are actuated by Piezoelectric Inertia type Actuators (PIA). The novelty of this letter is that the model of our MPC-based approach relies on a velocity map of PIAs. It enables path following and obstacle avoidance while preserving safety margins. Control inputs are optimized by Quadratic Programming, referring to their increment and distance constraints. A cost function is defined to navigate the AFM probe with a specified velocity. Simulations and experiments are carried out to demonstrate that the proposed algorithm is suitable to perform path following with obstacle avoidance using map-based velocity references. This is the first time that MPC is implemented in micro/nano-robotic systems for autonomous control inside SEM.

The spherical joint is an effective solution to design parallel micro-robotic systems with rotation capabilities in the three-dimensional space. This type of joint has however some non-linear characteristics, such as the clearance, which affect the positioning accuracy in micro-robotic tasks. The starting point of this study lies in experimental observations of rotation errors from a 3-PPPS 6-DOF parallel micro-robotic systems operating inside a scanning electron microscope. The objective of the paper is to assess the role of the spherical joints in the rotation errors and to evaluate whether the joints non-linearities can cause errors with the same order of magnitude as those observed experimentally. To this end, the first part of the study addresses the modeling of 3-PPPS 6-DOF parallel micro-robotic systems with spherical joints including the clearance. This model allows for analysing the effect of the clearance on position and rotation accuracies of the micro-robotic system. It is found by simulations that the same positioning behavior as in the experiments occurs when the clearance of the spherical joint is included in the model, supporting the hypothesis. Therefore, it is concluded that clearance in spherical joints has a significant effect on the precision of parallel type micro-robotic systems which opens new challenges in the control of poly-articulated micro-robotic systems with clearance compensation.

We address design, implementation, and characterization of semiconductor strain gauges as stage displacement sensors with small footprint for piezo-driven nanopositioners in differential actuation mode. The strain gauges are not collocated with the stage of the nanopositioner. They are attached to piezo stack actuators in both longitudinal and transverse directions. We address two differential configurations for the displacement sensing. The first configuration uses all strain gauges and provides three output signals. Two of them are proportional to the length variations of the piezo actuators, which are considered as conventional non-differential sensing method. The last output in the first configuration is the first proposed differential sensor. In the second configuration, we propose an alternative differential sensor using only the longitudinal strain gauges and a simpler readout circuit. The results indicate that in the differential actuation mode, a differential sensing strategy provides much better accuracy than the conventional non-differential schemes. Using a laser interferometer as an independent collocated sensor for stage displacement, we obtained constant calibration factors both proposed differential sensors and characterized their sensing accuracies.

This article deals with a novel hybrid control of an atomic force microscope (AFM) for the robust characterization of interaction tip/sample force regions. The hybrid structure is composed of several position and force controllers and a specific switch compensation structure. A single selected controller is online at a time, and a robust bumpless switch between different control laws is designed. The objectives are the robustness of each controller and switch compensator with respect to uncertain parameters of the AFM. The method uses discrete points in the range of uncertainties. For each operating point, the hybrid controller is designed by an eigenstructure assignment. The method is generalized by a multimodel approach considering only uncertainties defined by a worst-case analysis, thus reducing the conservatism. The order of the controller is related to the number of observers selected by the user. This offers the possibility to design a low-order controller depending on the control specifications. The experimental results demonstrate the effectiveness of the hybrid controller for a fully automated landing procedure of the AFM tip on a sample surface and for force distance curve cycle characterization. Thanks to the robustness of the control method, landing and cycles are reproducible despite actuator uncertainties, friction variation due to aging, and instrumental issues such as the real-time data acquisition.

The existence of hysteresis phenomenon in piezoelectric actuators of nanopositioners adversely affects their performance, e.g. image distortion in Atomic Force Microscopy. A usual approach to circumnavigate hysteresis nonlinearity is feedforward compensation where the performance depends extensively on the accuracy of the hysteresis model. To achieve accurate modeling of hysteresis in nanopositioners driven by piezoelectric stacks, we used a dual-stack differential driving configuration. Comparing hysteresis in single-stack piezoelectric actuators with dual-stack piezoelectric actuators in differential driving configuration, we observed a more symmetric behavior for the hysteresis in dual-stack differential driving actuators. Then, we modeled the differential driving configuration by utilizing coupled electromechanical equations with hysteresis models applied to them. In particular, Duhem and Prandtl-Ishlinskii (P–I) methods were used for hysteresis modeling. Based on the models and experimental data, we observed that the maximum value of the Duhem modeling error reduced from 9.63% for the nondifferential configuration to 1.85% for the differential configuration. For the P–I method, the maximum modeling error decreased from 7.46% to 2.77%. This observation shows that the dual-actuated differential driving configuration improves hysteresis modeling accuracy. Therefore, this configuration is a suitable choice for the applications where accuracy is of prime importance.