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

TL;DR

This work proposes a hybrid kinematics-informed and learning-based shape control method, named SpatioCoupledNet, which consistently outperforms both analytical and purely neural controllers.

Abstract

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.

Figures (7)

• Figure 1: Overview of the proposed hybrid kinematics-informed and learning-based framework for shape control. (Top) Real-world physical uncertainties in a planar hyper-redundant robot. It illustrates how unmodeled physical effects (e.g., unexpected positioning shifts and non-ideal bending) and inter-segment force coupling complicate the actual motion. (Middle) The SpatioCoupledNet architecture. By explicitly mirroring the physical mechanism, it employs a bidirectional neural structure to capture how forces propagate and interact across different segments. (Bottom) The dynamic confidence gating mechanism. It acts as an adaptive dial ($\beta$) that smoothly balances control authority between the idealized physical model ($\mathbf{J}_{phy}$) and the data-driven neural prediction ($\mathbf{J}_{net}$). The resulting fused Jacobian ($\mathbf{J}_{fused}$) ensures high-fidelity closed-loop control, even under complex structural deformations.
• Figure 2: Kinematic parameterization of the proposed hyper-redundant robot. (a) Planar hyper-redundant robotic platform used during the study with five continuum segments. (b) Local geometric model of the $i$-th segment based on the PCC assumption. The differential rack extensions $q_{i,L}$ and $q_{i,R}$ explicitly determine the bending angle $\theta_i$ and the central arc length $L_i$, where $c_i$ denotes the structural width.
• Figure 3: Architectural hierarchy of SpatioCoupledNet for $N$-segment continuum robots. The framework explicitly mirrors the robot's physical kinematics through three stages: (a) Local Expert Stage where independent MLPs extract segment-specific features $\mathbf{h}^{(i)}$; (b) Global Communication Stage utilizing a Bi-GRU to model bidirectional spatial coupling arising from distal actuation and proximal reaction forces; and (c) Dual-Head Gated Fusion Stage where a dimension-wise confidence vector $\boldsymbol{\beta}^{(i)}$ adaptively balances analytical nominal physics and data-driven predictions.
• Figure 4: Schematic of the physics-constrained multi-objective loss function. The total loss $\mathcal{L}_{total}$ is composed of: (1) a local coordinate loss $\mathcal{L}_{local}$ penalizing deviations in segment-wise incremental poses; and (2) a global shape loss $\mathcal{L}_{global}$ enforced through a Differentiable Forward Kinematics (FK) layer. Both objectives utilize a Huber penalty to ensure robustness against perception outliers.
• Figure 5: Tracking performance across three configuration difficulties in the tracking experiment. The three rows correspond to the Easy (a--c), Medium (d--f), and Extreme (g--i) target configurations, respectively. Left column (a, d, g): The target spatial configurations of the robot. Middle column (b, e, h): The evolution of the mean node error ($e_{mean}$) over control steps, illustrating the convergence speed and steady-state accuracy. Right column (c, f, i): Control action chattering, quantified by the third-order difference of joint positions ($\|\Delta^3 \mathbf{q}\|$) per step.