Reduced-order state-space reformulation for task-space predictive control of an under-actuated hydraulic boom

Hydraulic booms used in material handling are typically commanded in cylindrical task-space coordinates, while dynamic models used for control are commonly formulated in joint coordinates. This mismatch leads to unnecessarily high-dimensional system representations when predictive control is applied to underactuated suspended loads. This paper addresses this modeling inconsistency by introducing a reduced-order state-space reformulation of grapple sway dynamics directly in cylindrical task-space velocity coordinates. The proposed input-consistent state transformation eliminates the dependence of the dynamics on input accelerations by embedding actuator-sway coupling within modified velocity states, yielding a nonlinear model driven solely by cylindrical velocity commands. Based on this representation, a nonlinear model predictive control (NMPC) framework is developed for simultaneous goal reaching, sway suppression, and obstacle avoidance. The NMPC cost function is designed to capture the practical trade-off between rapid boom motion and suppression of suspended load oscillations. In addition, approximate hydraulic actuator dynamics identified from a high-fidelity AMESim simulator model of a forwarder crane are incorporated to better reflect realistic boom behavior. Simulation studies in representative boom operation scenarios demonstrate that the proposed formulation enables effective sway regulation and accurate task-space motion control using a reduced set of states without requiring full joint-space models or payload sensing. The results indicate that the proposed cylindrical state-space reformulation simplifies predictive control design for underactuated hydraulic booms while preserving the essential dynamics of the suspended load.