RANDOM FIELD ESTIMATION APPROACH TO ROBOT DYNAMICS

Random field models provide an alternative to the deterministic models of classical mechanics used to describe multibody robot arm dynamics. These alternative models can be used to establish a relationship between the methodologies of estimation theory and robot dynamics. A new class of algorithms that use computations typical in estimation theory can be developed for such fundamental robotics problems as inverse dynamics, inverse kinematics, forward dynamics, etc. The central result is an equivalence between inertia and covariance. This allows much of what is known about covariance factorization and inversion to be used for inertia matrix inversion. In particular, it is known that the difference equations of Kaiman filtering and smoothing factor and invert recursively the covariance of the output of a linear state-space system driven by a white-noise process. Here it is shown that similar recursive techniques factor and invert the inertia matrix of a multibody robot system. The random field models are based on the assumption that all of the inertial (D’Alembert) forces in the system are represented by a spatially distributed white-noise model. They are easier to describe than the models based on classical mechanics, which typically require extensive derivation and manipulation of equations of motion for complex mechanical systems. In contrast, with the spatially random models, more primitive (i.e., simpler and less dependent on mathematical derivations), locally specified computations result in a global collective system behavior (as represented by the inertia matrix) equivalent to that obtained with the deterministic models. The primary goal in investigating robot dynamics from the point of view of random field estimation is to provide a concise analytical foundation for solving robot control and motion planning problems. © 1990 IEEE