In [18], the dynamic modeling of a robotic manipulator is described using the Euler-Lagrange formulation. The robot has four degrees of freedom, and the location of the base is oriented to the ground/floor (horizontal mounting upwards). In addition to analyzing the properties of this model, they suggest using a PID controller to control the position of the manipulator. In [19], a combination of the Lagrange equation and the Morison formula is used to derive a dynamic model of a manipulator with 3 DOF, which can be used in a hydrostatic environment, while during modeling, they had to take into, for example, other forces acting on the joints when working with the manipulator underwater. The next publication [20] used the Euler-Lagrange method to derive dynamic equations for the prototypes of a four-legged robot--Mini-Bot--where they tracked the position and angular velocity of each leg in the Cartesian coordinate system. They used the Matlab-Mupad software tool as a tool for deriving dynamic equations. The Newton-Euler formulation was used in the publication [21] to derive object equations, while a recursive Gibbs-Appell formulation was used to obtain the dynamic equations of a flexible, cooperative manipulator. The manipulator consists of two arms, which have two flexible links. Two limitations had to be taken into account in the simulations, namely dynamic and kinematic limitations resulting from the placement of the object on a non-holonomic mobile platform. In the article [22], the research of the derivation of a dynamic model using a Newton-Euler formulation for a rigid manipulator is described, which consists of two links. Some papers also present new methods in their publications that can be used for the dynamic modeling of manipulators. For example, [23] proposes a new method for derivate a dynamic model of a manipulator with 6 DOF. The hysteresis effect of friction in the joints is described using a centrosymmetric static friction model. The dynamic parameters of the six joints were identified using a hybrid whale optimization algorithm and a genetic algorithm. One of the most recent publications [24], contains another new approach to deriving equations of motion, called Pseudo-Symbolic Dynamic Modeling. It is a numerical algorithm whose task is to create functions that form the basis for the inverse dynamics of the manipulator. The result is simplified dynamic models, while this algorithm has been implemented in Matlab and can be applied to manipulators up to 7 degrees of freedom of movement. To achieve better results of the modeling, models can be optimized using numerical iteration methods, for example, algorithms as, e.g., the Levenberg-Marquardt method or the Trust Region Algorithm. In [25], the Levenberg-Marquardt method for the unconstrained optimization problem is studied, whereas the method of convergence technique (using line search) is proposed. In one of the publication's chapters [26], the Levenberg-Marquardt method is used to determine the minimum volume of the longitudinal cooling fin. The Trust Region Algorithm is also used to solve nonlinear problems. At present, its popularity is higher than with the previously mentioned method. Many researchers describe algorithms that are derived from the Trust Region Algorithm. The aim is to increase its reliability and convergence properties. For example, in [27], two trust-region algorithms are proposed that examine trust outside the specified area. In [28] is described the application of the algorithm to the online estimation of tire/road friction parameters in real-time. In addition, a new LuGre model-based nonlinear least-squares parameter estimation algorithm is presented in this work. The aim of the research described in the article is to use an optimization method to estimate parameters of the model (improve the results of validation) and the comparison of the model with the parameters that come from CAD and its improvement by estimating the parameters based on gravitational measurements.