## 9 Conclusions  
The research described in this article aimed to compare the model with the parameters that come from CAD and its improvement by estimating the parameters based on gravitational measurements. An improvements model could be subsequently applied to the control phase.  
The study described in this article can be summarized in four stages:  
* Obtain a representative set of joint angle data by performing gravity tests.
* Creation of a simulation model in the Matlab and Simulink, which presented the dynamics of a real system--a planar robotic arm with two degrees of freedom (taking into account the friction component).
* The validation of a dynamic model built based on Lagrange formalism. However, at this stage, the expected results based on the MAE and NRMSE indicators were not achieved.
* The estimation of parameters--as the initial results of validation were insufficient, the research was extended to the estimation of model parameters using the Trust Region Algorithm, which helped to significantly improve the values of MAE and NRSME.  
Based on the results of parameter validation and estimation, it can be stated that the values of system parameters, which serve as input data for the model, significantly affect the validation results, which was demonstrated after estimating these parameters significantly affected the results. Within the course of the estimated parameters, a certain connection between the parameters was seen, which gives rise to the assumption that the values of the parameters not only influence the results of the validation but also interact with each other. The more accurate the system parameters are obtained in the step, the more accurate the validation results will be. By reducing the oscillations (especially for link 2 and at higher initial rotation angles) which occur in the system due to the individual structural bonds, it would be possible to achieve a more accurate stabilization of the arm movement to zero, and thus to improve the validation results.  
In further research, the authors would like to extend this research to the following parts:  
* Accurate identification of system parameter values, including drive parameters.
* The inclusion of drive dynamics, which would create a more complex dynamic system model.
* The addition of a part of the drives to the simulation scheme in Simulink, the use of other tools, such as SimMechanics.  
Conceptualization, A.H. and M.T.; methodology, A.H.; model design, M.T. and T.C.; measuring data, A.H. and T.K.; validation in Matlab, T.C.; estimation in Matlab, T.C.; formal analysis, M.T.; investigation, M.T.; writing--original draft preparation, M.T.; writing--review and editing, M.T., A.H., T.K. and T.C.; visualization, M.T. and T.C.; project administration, T.K.; funding acquisition, A.H. All authors have read and agreed to the published version of the manuscript.  
The project was supported by the Project VEGA no. 1/0393/18--Research of Methods for Modeling and Compensation of Hysteresis in Pneumatic Artificial Muscles and PAM-actuated Mechanisms to Improve the Control Performance Using Computational Intelligence and by the Project of the Structural Funds of the EU, ITMS code: 2622020103.  
The authors declare no conflict of interest.