A map-guided closed-form framework with Riccati-based tracking for low-speed mixed-traffic obstacle avoidance

Low-speed urban encounters with vehicles, bicycles, and pedestrians impose coupled safety and tracking-accuracy requirements on autonomous vehicles. This paper presents a map-guided obstacle-avoidance framework for low-density and weak-interaction mixed-traffic scenarios. The framework integrates an HD-map lane-feasibility decision layer, a closed-form reference-path generator, and a Riccati-recursion-based linear time-varying tracking controller. The decision layer selects a feasible adjacent driving lane from the CARLA waypoint graph, while the path layer synthesises an obstacle-aware reference through sigmoid blending, a fade-in factor that removes spawn-time cross-track artefacts, and a lateral-shift clamp that prevents unrealistic detours. The tracking layer solves the finite-horizon quadratic tracking problem analytically and applies actuator saturation to the resulting commands; it is therefore not claimed to provide the feasibility guarantees of a constrained quadratic-programming MPC. Evaluation is conducted in CARLA 0.9.16 on Town10HD_Opt at target speeds no higher than 8 m / s , using five vehicle, bicycle, and pedestrian profiles, four primary baselines, two ablation variants, an adaptive-MPC proxy, a Frenet-quintic planner baseline, and sensitivity/intensity stress tests. Across 60 main trials, the proposed framework achieves a success rate of 1.0 with zero collisions, a mean cross-track error of 0 . 021 m , and a maximum cross-track error of 0 . 178 m . The results support the framework as a reproducible low-speed benchmark and clarify its operational boundaries rather than claiming general validity for high-speed, dense, or strongly interactive traffic.