Error Propagation Analysis of Kinematic Quantities for Robots and Mechanisms

Abstract

We introduce a comprehensive methodology for calculating the propagation of errors in kinematic quantities up to the jerk for robotic systems and mechanical linkages. Our study utilizes two distinct computational approaches: a deterministic method that relies on derivative calculations, and a stochastic method that utilizes Monte Carlo simulations. Kinematic quantities are computed using dual numbers while the variation in the parameters is computed using the complex step approximation method, as well as with the use of dual numbers to include the general case of a function of complex variables. Although the deterministic approach is generally more efficient, the stochastic method stands out for its simplicity and ease of implementation. The efficacy of our methodology is demonstrated through practical applications. We perform error propagation analyses up to the jerk for planar and spherical four-bar (4R) mechanisms and a revolute–cylindrical–revolute (RCR) robot manipulator, highlighting its versatility across different mechanical systems.