Organizations: Singapore MIT Alliance for Research and Technology (SMART) centre, Singapore · Department of Mechanical Engineering, National University of Singapore, Singapore · Jiangsu Key laboratory for design and Manufacturing of Precision Medicine equipment, School of Mechanical engineering, Southeast University, China · CSAIL, Massachusetts Institute of Technology, Cambridge, USA · Advanced Robotic Centre, National University of Singapore, Singapore
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 & tables
Fig. 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 ( β ) that smoothly balances control authority between the idealized physical model ( Jphy ) and the data-driven neural prediction ( Jnet ). The resulting fused Jacobian ( Jfused ) ensures high-fidelity closed-loop control, even under complex structural deformations.
Fig. 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 qi,L and qi,R explicitly determine the bending angle θi and the central arc length Li , where ci denotes the structural width.
Fig. 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 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 β(i) adaptively balances analytical nominal physics and data-driven predictions.
Fig. 4: Schematic of the physics-constrained multi-objective loss function. The total loss Ltotal is composed of: (1) a local coordinate loss Llocal penalizing deviations in segment-wise incremental poses; and (2) a global shape loss Lglobal enforced through a Differentiable Forward Kinematics (FK) layer. Both objectives utilize a Huber penalty to ensure robustness against perception outliers.
Fig. 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 ( emean ) 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 ( ∥Δ3q∥ ) per step.
Config.
controller
emean
T95%
Chatter.
Cost
(mm) ↓
(steps) ↓
(mm) ↓
(mm) ↓
Easy
PHY
2.13
23
0.095
408.9
PURE_NN
1.18
47
0.179
378.5
HYBRID
0.74
47
0.154
371.6
Medium
PHY
7.53
106
0.062
2078.0
PURE_NN
6.32
127
0.646
1749.0
TABLE I: Quantitative Tracking Performance Across Configurations. Bold values indicate the best (lowest) performance.
Fig. 6: Evolution of Robot Configuration and Confidence Gating. (a) Snapshots of spatial configurations at key intervals ( T={0,120,240,310,400} ) during a continuous trajectory. (b) Real-time evolution of the dimension-wise confidence gate β for all five segments ( N=1 to N=5 ) over 400 control steps. The heatmaps illustrate the dynamic shift of control authority between the analytical PCC prior ( β→1 , blue) and the data-driven neural prediction ( β→0 , red).
Fig. 7: Real-time Null-Space Obstacle Avoidance. (a) Sequential snapshots of the physical demonstration. As a moving obstacle intrudes from the left into the robot’s original workspace, the mechanism dynamically reconfigures its backbone to avoid collision while strictly maintaining the target end-effector pose. (b) The spatial trajectories of all five nodes during the avoidance task. The color gradient (transitioning from light to dark) represents the temporal progression of the movement. (c) The tracking error of the tip position over the control steps.
Hyper-redundant robots are well suited for confined-space manipulation due to their high dexterity, but safe operation in cluttered environments remains challenging. In addition, their slender structures often lead to uneven load distributions and nonuniform tracking errors along the body. To address these issues, this work proposes a weighted control barrier functions (W-CBFs) framework that enforces safety constraints while reducing tracking errors caused by uneven loading. The proposed controller was first evaluated on a circular path-following task under different obstacle configurations. With fixed weights, compared to the non-weighted method, the maximum reduction in root-mean-square (RMS) tracking error was 59.6% in simulation and 87.7% in physical experiments. An adaptive weighting strategy was then investigated based on the discrepancy between simulated and experimental performance under different mapping functions. The RMS errors were further reduced by 21.9% and 8.5%, respectively, although the error increases when obstacles were located close to the robot body. Finally, the robot was evaluated in a cleaning task requiring coverage of a rectangular area and compared with manual teleoperation. Although the controller was not explicitly optimized for area coverage, the autonomous strategy achieved comparable or better coverage performance while avoiding collisions with the surrounding frame, whereas collisions occurred during manual operation.
Zijian Cai, Kiwan Wong, Wenci Xin +3
Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore · CSAIL, Massachusetts Institute of Technology, Cambridge, USA · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore +1
Continuum robots possess high flexibility and redundancy, making them well suited for safe interaction in complex environments, yet their continuous deformation and nonlinear dynamics pose fundamental challenges to perception, modeling, and control. Existing vision-based control approaches often rely on end-to-end learning, achieving shape regulation without explicit awareness of robot geometry or its interaction with the environment. Here, we introduce a shape-interpretable visual self-modeling framework for continuum robots that enables geometry-aware control. Robot shapes are encoded from multi-view planar images using a Bezier-curve representation, transforming visual observations into a compact and physically meaningful shape space that uniquely characterizes the robot's three-dimensional configuration. Based on this representation, neural ordinary differential equations are employed to self-model both shape and end-effector dynamics directly from data, enabling hybrid shape-position control without analytical models or dense body markers. The explicit geometric structure of the learned shape space allows the robot to reason about its body and surroundings, supporting environment-aware behaviors such as obstacle avoidance and self-motion while maintaining end-effector objectives. Experiments on a cable-driven continuum robot demonstrate accurate shape-position regulation and tracking, with shape errors within 1.56% of image resolution and end-effector errors within 2% of robot length, as well as robust performance in constrained environments. By elevating visual shape representations from two-dimensional observations to an interpretable three-dimensional self-model, this work establishes a principled alternative to vision-based end-to-end control and advances autonomous, geometry-aware manipulation for continuum robots.
Peng Yu, Xin Wang, Ning Tan
School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China.
Motion mimicking, i.e., encouraging the control policy to mimic human motion, facilitates the learning of complex tasks via reinforcement learning (RL) for humanoid robots. Although standard RL frameworks demonstrate impressive locomotion agility, they often bypass explicit reasoning about robot dynamics during deployment, which is a design choice that can lead to physically infeasible commands when the robot encounters out-of-distribution environments. By integrating model-based principles, hybrid approaches can improve performance; however, existing methods typically rely on predefined contact timing, limiting their versatility. This paper introduces HybridMimic, a framework in which a learned policy dynamically modulates a centroidal-model-based controller by predicting continuous contact states and desired centroidal velocities. This architecture exploits the physical grounding of centroidal dynamics to generate feedforward torques that remain feasible even under domain shift. Using physics-informed rewards, the policy is trained to efficiently utilize the centroidal controller's optimization by outputting precise control targets and reference torques. Through hardware experiments on the Booster T1 humanoid, HybridMimic reduces the average base position tracking error by 13% compared to a state-of-the-art RL baseline, demonstrating the robustness of dynamics-aware deployment.
Ludwig Chee-Ying Tay, I-Chia Chang, Yan Gu
Department of Computer Science, Purdue University, West Lafayette, IN 47907, USA. · School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA.