The research introduces a methodology for identifying the primary parameters necessary for the trajectory construction of a mobile robot, utilizing chaotic, dynamic systems. This enhances the ergodicity and adaptability of movement in a dynamic context. The suggested mathematical model integrates the production of chaotic sequences to establish reference points and algorithms for their localized tracking, considering safety limitations, including the regulation of barrier functions. The numerical simulations demonstrated the method's efficacy in circumventing local minima and achieving uniform workspace coverage while preserving movement stability. This facilitates the formulation of paths that consider unforeseen impediments and enhances the resilience of control algorithms against external disturbances. Simultaneously, it has been demonstrated that chaotic models are advantageous for developing nonlinear adaptive trajectories in intricate contexts where traditional methods exhibit constrained efficacy. Consequently, the suggested methodology ensures precise positioning and secure interaction with other agents within the Industry 5.0 context.

adaptive control, barrier function control, chaotic dynamical systems, Lorentz system, mobile robot, trajectory planning