Nonstationary Random Dynamics of a Mobile Robotic Manipulator

Abstract

The paper presents results from a study of the structural motion of a flexible mobile manipulator, and specifically, it discusses the time-dependent statistics and the deterministic response of this motion. The manipulator is mounted atop a vehicle which is supported by a suspension system. The vehicle accelerates uniformly on a rough surface generating a nonstationary random excitation and a deterministic excitation. The system response is separated into deterministic and stochastic components. The covariance Liapunov’s equation for the manipulator stochastic joint responses is developed. Further, expressions for the covariance matrices of the manipulator tip motion are developed and the transformation necessary to relate them to various Cartesian coordinate frames is derived. Expressions for the principal variances of the tip motion are developed by means of the singular value decomposition. The effects of damping, vehicle acceleration, surface roughness coeffifients, and manipulator configuration on the tip responses are explored.