Compact heavy-duty skid-steer robots are increasingly used for city logistics and intralogistics tasks where high payload capacity and stability are required. However, their limited maneuverability and non-negligible turning radius challenge conventional waypoint-tracking controllers that assume unconstrained motion. This paper proposes a curvature-constrained trajectory planning and control framework that guarantees geometrically feasible motion for such platforms. The controller integrates an explicit curvature limit into a finite-state machine, ensuring smooth heading transitions without in-place rotation. The overall architecture integrates GNSS-RTK and IMU localization, modular ROS 2 nodes for trajectory execution, and a supervisory interface developed in Foxglove Studio for intuitive mission planning. Field trials on a custom four-wheel-drive skid-steer platform demonstrate centimeter-scale waypoint accuracy on straight and curved trajectories, with stable curvature compliance across all tested scenarios. The proposed method achieves the smoothness required by most applications while maintaining the computational simplicity of geometric followers. Computational simplicity is reflected in the absence of online optimization or trajectory reparameterization; the controller executes a constant-time geometric update per cycle, independent of waypoint count. The results confirm that curvature-aware control enables reliable navigation of compact heavy-duty robots in semi-structured outdoor environments and provides a practical foundation for future extensions.