Optimizing adaptive robust formation tracking control for traffic cone robots under environmental constraints: a Nash game theory-based approach

Abstract Road maintenance is fundamental to ensuring safe and comfortable transportation. As critical safety elements, traffic cone robots (TCRs) autonomously secure work zones and guide vehicle flow during road construction and maintenance. This study addresses the formation placement and recovery control of TCRs under environmental and system uncertainties. The TCRs are capable of coordinated formation maneuvers while simultaneously tracking placement and recovery targets within constrained environments. To address these constraints, a diffeomorphism is introduced to systematically mitigate their effects. The uncertainties of the TCRs are bounded, including both matching and mismatching components, with known boundary values belonging to a fuzzy set. Based on this, we propose an adaptive robust control methodology that ensures both uniform boundedness and uniform ultimate boundedness of the TCR system. Additionally, to enhance system performance, we introduce a multi-parameter optimization method based on Nash game theory. The Nash equilibrium, representing the optimal control parameters, is achieved by minimizing the associated cost functions. Comprehensive comparative and ablation analyses are conducted to explicitly distinguish the respective contributions of uncertainty decomposition and Nash-equilibrium-based parameter optimization to robustness and dynamic performance. The performance of the TCR system is illustrated through a series of numerical simulations. These findings provide essential theoretical and technical support for the placement and recovery operations of TCRs in construction road maintenance.