Shape Control of a Planar Hyper-Redundant Robot via Hybrid Kinematics-Informed and Learning-based Approach

Hyper-redundant robots offer high dexterity, making them good at operating in confined and unstructured environments. To extend the reachable workspace, we built a multi-segment flexible rack actuated planar robot. However, the compliance of the flexible mechanism introduces instability, rendering it sensitive to external and internal uncertainties. To address these limitations, we propose a hybrid kinematics-informed and learning-based shape control method, named SpatioCoupledNet. The neural network adopts a hierarchical design that explicitly captures bidirectional spatial coupling between segments while modeling local disturbance along the robot body. A confidence-gating mechanism integrates prior kinematic knowledge, allowing the controller to adaptively balance model-based and learned components for improved convergence and fidelity. The framework is validated on a five-segment planar hyper-redundant robot under three representative shape configurations. Experimental results demonstrate that the proposed method consistently outperforms both analytical and purely neural controllers. In complex scenarios, it reduces steady-state error by up to 75.5% against the analytical model, and accelerates convergence by up to 20.5% compared to the data-driven baseline. Furthermore, gating analysis reveals a state-dependent authority fusion, shifting toward data-driven predictions in unstable states, while relying on physical priors in the remaining cases. Finally, we demonstrate robust performance in a dynamic task where the robot maintains a fixed end-effector position while avoiding moving obstacles, achieving a precise tip-positioning accuracy with a mean error of 10.47 mm.