Analytical dynamic modeling of Delta robot with experimental verification

Abstract

In this paper, an explicit dynamic model of Delta robot is obtained analytically. The main contribution of this work is that, unlike existing prior work, the final dynamics model is given directly in the form of [Formula: see text], with explicit expressions for M, C and G. This is of great importance, since many advanced control techniques like Optimal Control need dynamic model in an explicit form, i.e. time derivative of state vector given explicitly in terms of the states and control vectors. To this goal, first, velocity and acceleration analysis is done by differentiating robot's geometrical loops directly. Then, Jacobian matrices are calculated to have kinematic relations in a more compact form. After that, principle of virtual work is implemented to derive the dynamic equations. In this part, Jacobian matrices are substituted into dynamic model. This is unlike other referenced works on Delta robot dynamics that need to continue the derivation in symbolic software or derive the model implicitly. Using Jacobians, dramatically simplifies the final explicit dynamic model. Therefore, the final dynamic equations are calculated in a straightforward manner without any use of symbolic calculation software. After all, the presented model is verified with an experimental setup. The model shows good accuracy in terms of torque prediction.