Among the many challenges of parallel kinematic manipulators, achieving high-speed and accurate control remains crucial. Estimating their dynamic properties is essential for designing precise and efficient control schemes. Conventional methods for dynamic model identification have been effective, though deep learning approaches have historically faced limitations due to data inefficiencies. However, recent advancements in physics-informed neural networks (PINNs) offer a way to improve both control and the extraction of interpretable physical properties from these robots. In this work, we propose and validate a PINN-based dynamic model for a Delta parallel robot, specifically the ABB IRB 360-6/1600. Our approach incorporates known physical properties, such as mass matrix sparsity, to improve accuracy and computational efficiency in dynamic model identification. To the best of our knowledge, this is the first study applying PINNs to model parallel robots. The method is validated experimentally, and its performance is compared to a validated identification technique for physically consistent identification, demonstrating the effectiveness of this approach for real-world applications in parallel robots.

Parallel kinematics machines (PKM) operate with maximal acceleration being designed for highly dynamic manipulation tasks. This leads to extreme loads of the joints, which is usually not accounted for in the motion planning. In this paper an extended inverse dynamics method is introduced, which allows computing the joint reaction forces along with the actuation torques, and provides a basis for time optimal motion planning and control minimizing wear of the components. To this end, PKM are modeled using absolute coordinates. The joint constraints are complemented with servo constraints so that the motion can be described by the actuator motion or by the end-effector motion. The presented method is particularly advantageous when certain model parameters are unknown and allows for model simplification, which would not be possible for the relative coordinate formulation. The sparsity of the obtained velocity constraint Jacobian matrix, due to the use of absolute coordinates, can be efficiently exploited to minimize computation time. The method is demonstrated and numerical results are reported for a time-optimal pick and place movement of a 4-DOF Delta robot.