Extended Dynamic Model for the UR16e 6-Degree-of-Freedom Robotic Manipulator

This study develops and validates an Extended Analytical Dynamic Model (EADM) of the UR16e 6-Degree-of-Freedom (DoF) industrial robot, incorporating actuator dynamics and a friction model to address the lack of dynamic information provided by the manufacturer. A two-stage validation methodology is proposed using a Multibody Physical Model (MPM) developed in MATLAB^® R2024b/Simscape Multibody^TM as a reference. In the first stage, the Analytical Dynamic Model (ADM) without actuators or friction is evaluated by comparing its inverse dynamics torque with the torque required by the MPM under identical joint references. In the second stage, the EADM and the MPM are tested under a Proportional-Derivative Computed Torque Control (PD-CTC) scheme using Cartesian trajectories, comparing joint torques and positions. The methodology incorporates torque-level validation, a demanding criterion since torque is determined by the dynamic formulation, whereas position may be influenced by closed-loop control. The results show small torque errors in the first stage (e_τ) in the range of 10⁻¹⁷ to 10⁻¹³ Nm) and bounded position and torque errors in the second stage (e_q ≤ 4 × 10⁻⁴ rad; e_τ ≤ 0.4 Nm in q₁ − q₂ and e_τ ≤ 0.5 Nm in q₄ − q₆ ). The methodology provides a systematic validation framework and demonstrates that the EADM accurately matches the MPM’s dynamic behavior.extended analytical dynamic model; multibody physical model; Simscape Multibody; actuators; nonlinear system; PD computed torque control