A Statistical Dynamical Algorithm for Gaussian Multi-agent Systems under Hamel’s Formalism

This paper focuses on a formulation of stochastic dynamics of Gaussian process on the general affine group. The proposed dynamical system could be a candidate model for large-scale UAV swarms. In particular, deterministic differential equations on the Lie algebra for the Gaussian process are derived based on Hamel’s formalism. By adopting the variational integrator technique, possible inaccuracies that are caused by the commonly used numerical integration schemes are eliminated. The resulting geometric integrator is implemented compared with a reference algorithm to validate its conciseness and efficiency in preserving total energy of the conservative Gaussian system.