Safe Payload Transfer with Ship-Mounted Cranes: A Robust Model Predictive Control Approach

TL;DR

This paper tackles safe payload transfer on ship-mounted cranes subject to sea-induced disturbances by integrating a robust model predictive control (MPC) framework with time-varying safety sets and a robust zero-order control barrier function (R-ZOCBF). The approach defines dynamic, collision-avoidance bounding boxes and a smooth target safety function, and augments MPC with online adaptive tuning of the R-ZOCBF margin to balance safety and performance. The authors demonstrate the method on a 5-DOF crane with a Stewart platform simulating ocean motion, providing both simulations and hardware experiments that validate safety constraints and payload insertion accuracy under perturbations. The results imply a practical, real-time capable solution for safe robotic insertion tasks in dynamic environments and offer a foundation for extending to peg-in-hole, docking, and other contact-rich operations.

Abstract

Ensuring safe real-time control of ship-mounted cranes in unstructured transportation environments requires handling multiple safety constraints while maintaining effective payload transfer performance. Unlike traditional crane systems, ship-mounted cranes are consistently subjected to significant external disturbances affecting underactuated crane dynamics due to the ship's dynamic motion response to harsh sea conditions, which can lead to robustness issues. To tackle these challenges, we propose a robust and safe model predictive control (MPC) framework and demonstrate it on a 5-DOF crane system, where a Stewart platform simulates the external disturbances that ocean surface motions would have on the supporting ship. The crane payload transfer operation must avoid obstacles and accurately place the payload within a designated target area. We use a robust zero-order control barrier function (R-ZOCBF)-based safety constraint in the nonlinear MPC to ensure safe payload positioning, while time-varying bounding boxes are utilized for collision avoidance. We introduce a new optimization-based online robustness parameter adaptation scheme to reduce the conservativeness of R-ZOCBFs. Experimental trials on a crane prototype demonstrate the overall performance of our safe control approach under significant perturbing motions of the crane base. While our focus is on crane-facilitated transfer, the methods more generally apply to safe robotically-assisted parts mating and parts insertion.

Figures (6)

• Figure 1: 5-DOF ship-mounted crane with a task geometry and reference frames. Around the payload, time-varying collision-free bounding boxes are depicted (Top). The smooth safety function for the target, ${h_{\mathbf{ t }}}$, is visualized by its boundary, shown with a small display-only shift along ${x_{\mathcal{G}}}$ and ${-z_{\mathcal{G}}}$ to avoid occlusion (bottom-left). A cross-section of the zero-level set ${h_{\mathbf{ t }}(t, \mathbf{ x }(t)) \!=\! 0}$ (the boundary of the safe set $\mathcal{C}_{\mathbf{ t }}(t)$, $\partial \mathcal{C}_{\mathbf{ t }}(t)$) (bottom-right).
• Figure 2: Sequence of the platform-mounted crane performing payload insertion. Snapshots at $t\in\{0, 2, 4, 6, 10\}\ \mathrm{s}$ show approach, alignment and insertion of the payload while the base undergoes sinusoidal motion. A green-to-blue colored overlay shows the safety function constraint near the target. The MPC-calculated trajectories of the boom and payload are visualized using green segments for the boom and yellow segments for the payload.
• Figure 3: Comparison of nominal and robust safety configurations across simulation runs. Each subfigure contains the vertical payload tracking $(\mathbf{r}_{\mathbf{p},z}, \mathbf{p}_{\mathbf{p},z} \ \text{vs.\ time})$ on the left and the corresponding safety function $h_{\mathbf{ t }}(t,\mathbf{x}(t))$ on the right. Safety is violated when $h_{\mathbf{ t }}(t, \mathbf{ x }(t))<0$. Our robust MPC with R-ZOCBF constraint maintains safety, while the MPC with the nominal safety function violates safety.
• Figure 4: Experimental setup of the reference crane system and the Stewart platform.
• Figure 5: Hardware demonstration. The proposed robust MPC-based safe control framework ensures safe payload transfer to a target under external disturbances simulated by the Stewart platform and model uncertainties.

Theorems & Definitions (3)

• Definition 1: Robust Zero-Order Control Barrier Function
• Theorem 1
• proof