## 1 Introduction
The second category refers to those technologies that continuously predict and compensate the positioning error throughout the application of suitable sensors and models of the MT structure, implemented into the machine center software. This work presents a novel active approach that focuses on this second category. The approach consists of developing a new class of \"smart adaptronic structures\" based on the integration of passive materials, Carbon Fiber Reinforced Polymers (CFRP), with sensing materials (smart sensors) able to measure the deformed conditions of the structure in real-time and to calculate the transposition at the end-effector through an appropriate thermo-mechanical model. The proposed solution is based on the use of a multiplexed optical fiber sensor with a sufficient number of Bragg gratings for measuring strains (in specific reticular grid points) embedded in the structure. The high sensitivity of the sensors (\(\sim\)0.2 \(\upmu\)c) suggests their potential use for MTs with very stiff structures. These smart sensors (FBG) are suitable to measure both strains and temperature with very high accuracy and resolution [22]. Then, the measurements (linear elongations) obtained by these sensors are post-processed to predict the distortion/deformation of the structure (at tool tip location) in the 3D space domain using special algorithms based on the Multiple-Regression Method [23]. The FBG sensors are embedded in the structure, this choice allows for improved accuracy in detecting any deformation due to thermo-mechanical disturbances. A multi-regression model is developed and presented to compensate the MT errors at the tool tip point (TTP). This model has been validated through a set of simulations and tests and improved by including a number of independent variables. In particular, this study aims to present a novel lightweight structure based on hybrid materials to damp mechanical vibrations, and an effective real-time system able to compensate thermo-mechanical errors by direct feedback. State of art presents a number of works that deal with the application of FBG sensors in order to detect thermal errors. [PERSON] et al. [24] illustrate a study for measuring the real-time temperature field of a heavy-duty machine tool based on fiber Bragg grating sensing technology. In this work, the FBG sensors are installed in different locations of the MT (e.g., frame, spindle, spindle housing, gearbox, and motors) in order to measure thermal effects. The study demonstrates that the surface temperatures and spindle thermal errors have a similar change trend following the ambient temperature. In the same way, [PERSON] et al. [25] presented a study to detect MT thermal deformations using FBG sensors. The study highlights that FBG sensors may be used for the measurement of conventional machine tool deformations, showing the high potential of FBG sensors. Both studies focus on the thermal error measurement using the FBG feedback, nevertheless an accurate MT compensation model is not developed. Instead, [PERSON] et al. [26] propose a complex reticular structure based on FBGs associated with a computation algorithm that allows for the reconstruction of the displacement field. A recent interesting work has been developed by [PERSON] et al. [27]. This study shows a new modelling methodology for compensation of the thermal errors. In particular, the proposed model is based on Grey system models, artificial neural networks (ANNs), and a Particle Swarm Optimization (PSO). To improve the accuracy of the predicted model, four laser displacement sensors and feedback information supplied by FBGs were used.