Markov Parameters Generation for Data-based Modeling of Tensegrity Robots Considering Finite Word-Length Effects

Abstract

This paper studies the impact of finite word-length effects on the Markov parameters of tensegrity robots during digital simulations. First, the round-off noise models are introduced, where round-off noise is applied to the system’s inputs, outputs, and states. The deterministic and stochastic definitions of the Markov parameters are then presented. It is proven that stochastic Markov parameters remain invariant under finite word-length effects in linear time-invariant (LTI) systems, regardless of the round-off noise in inputs, outputs, or states. The nonlinear tensegrity dynamics and a linearization approach are introduced, with a tensegrity morphing airfoil studied as an illustrative example. The results indicate that using twisted input and output signals, the Markov parameters can converge correctly through white noise experiments. This supports the theoretical findings. The proposed approach allows accurate Markov parameter generation via simulation tests, which can be further used as model reduction or linearization of tensegrity robots to eliminate the distortions caused by round-off errors.