Complete Accessibility of Oscillations in Robotic Systems by Orthogonal Projections

The current practice of controller development for flexible robotic systems generally focuses on one-link robotic arms and is valid for small oscillations. This work addresses the control of n-link, serial, spatial robotic systems modeled with m₁ joint and m₂ link flexibilities such that n≥m₁+m₂. System compliance is modeled by local springs and nonactuated prismatic and revolute type pseudo joints. The coupled, nonlinear, error-driven system equations are derived for the complete model without linearization or neglecting certain terms. For this system, the complete accessibility of vibrations is studied by orthogonal projections. It is shown that under some configurations of a robotic system, the induced oscillations may not be accessible to the controller. Given accessibility, the controller developed in this work assures the global asymptotic stability of the system. Example numerical simulations are presented based on the model of a six-degree-of-freedom Cincinnati Milacron T3-776 industrial robot. One example models the system compliance in four joints, while another case study simulates four lateral link oscillations. These examples show that this controller, even under inaccurate payload description, eliminates the oscillations while tracking desired trajectories.