Random Matrix Based Input Shaping Control of Uncertain Parallel Manipulators

Input shaping control techniques have proven to be very effective in improving performance and lowering actuation requirements for Linear Time-Invariant (LTI) systems. However, deployments tend to be very sensitive to variation of the system natural frequencies and damping ratios. This limits the application of input shaping schemes in the nonlinear systems (e.g., robotic manipulators) or systems with uncertain parameters. The main focus of this paper is to address the parametric uncertainty in the system and the design of an input shaping control based upon the estimated parameters. The variations induced by system non-linearity are tackled by the method of the linearization. The uncertainty is characterized by treating the linearized system mass matrix as a random matrix. This provides the probability density function of the eigenvalues of the underdamped system that are then used to design the input shaping control for the uncertain system. We believe that such a characterization (and desensitization to production variability) is especially important for successful deployment of newer generations of 3D printed robotic systems. This is verified via a Monte Carlo simulation — the statistics of the percent residual vibration verifies the superiority of the input shaping control scheme based on the estimated parameter values (compared to the one based on the nominal parameters).