*Article* **Estimation of Grey-Box Dynamic Model of 2-DOF Pneumatic Actuator Robotic Arm Using Gravity Tests**

**Monika Trojanová 1, Tomáš Cakurda ˇ 1, Alexander Hošovský <sup>1</sup> and Tibor Krenický 2,\***


**Abstract:** This article describes the dynamics of a manipulator with two degrees of freedom, while the dynamic model of the manipulator's arm is derived using Lagrangian formalism, which considers the difference between the kinetic and potential energy of the system. The compiled dynamic model was implemented in Matlab, taking into account the physical parameters of the manipulator and friction term. Physical parameters were exported from the 3D CAD model. A scheme (model) was compiled in the Simulink, which was used for the subsequent validation process. The outputs of the validations were compared with measured data of joint angles from the system (expected condition) obtained by using gravity tests. For obtaining better results were parameters of the model optimizing by using the Trust Region Algorithm for Nonlinear Least Squares optimization method. Therefore, the aim of the research described in the article is the comparison of the model with the parameters that come from CAD and its improvement by estimating the parameters based on gravitational measurements. The model with estimated parameters achieved an improvement in the results of the Normal Root Mean Square Error compared to the model with CAD parameters. For link 1 was an improvement from 28.49% to 67.93% depending on the initial joint angle, and for link 2, from 63.84% to 66.46%.

**Keywords:** planar robotic arm; pneumatic artificial muscle (PAM); gravity test; dynamic model; validation; optimization; trust region algorithm
