1D and 2D trajectory optimization in weaving segments under a unified risk field framework: cooperative merging control strategy towards mixed traffic environment

Ramp merging in the mixed traffic environment of weaving segments requires connected and autonomous vehicle (CAV) technologies to achieve precise trajectory control. However, pre-merge one-dimensional trajectory optimization (1DTO), which coordinates longitudinal speeds among multi-vehicles to create merging gaps (global optimization), and lane-changing two-dimensional trajectory optimization (2DTO), which plans precise lateral maneuvers for the merging vehicle (individual optimization), are typically addressed separately. This separation causes each stage to employ independent risk assessment criteria and trajectory optimization objectives, thereby leading to suboptimal merging performance in terms of safety, efficiency, and stability. To overcome these limitations, we propose a unified merging sequence (MS), 1DTO, and 2DTO framework for multi-lane mixed traffic in weaving segments based on a risk field paradigm. First, we introduce a subjective-objective driving risk assessment method: CAVs utilize an objective risk field, while human-driven vehicles (HDVs) employ a subjective field coupling driver cognition. We then developed car-following models (SORFCF-CAV and SORFCF-HDV) to resolve the accuracy deficiencies of the IDM. Furthermore, we design a joint optimization framework integrating MS, 1DTO, and 2DTO. Strategies include: (i) SORFCF-CAV with virtual car-following for 1DTO; (ii) extending 1DTO for cooperative 2DTO via fifth-order polynomials; and (iii) a spatial-temporal risk occupancy map for safety-oriented 2DTO in non-cooperative cases. Extensive experiments demonstrate that the proposed strategy: (i) significantly outperforms multiple baselines in enhancing safety, merging efficiency, and traffic stability across various scenarios; (ii) exhibits a steady upward performance trend as the CAV penetration rate increases; and (iii) maintains excellent real-time computational efficiency even in extremely complex environments.