model continuum kinematics

This study addresses the lack of systematic evaluation and experimental validation of existing strain-based models for continuum robots under complex deformations. The authors propose a high-accuracy, sensor-free shape reconstruction method that eliminates the need for strain gauges or force sensors. By comparing third-order strain interpolation with geometrically variable strain modeling under both single-segment and compound deformations, and leveraging optical motion capture with reflective markers for ground-truth validation, the approach achieves an average shape error of only 0.58% of the rod length with a computation time of 0.32 seconds per reconstruction. The results demonstrate superior accuracy and efficiency compared to existing techniques, marking the first realization of low-overhead, high-fidelity sensorless deformation reconstruction and comprehensive model assessment for continuum robots.

This work addresses displacement-driven continuum robots by proposing the first Clarke-transform-based unified manifold modeling framework, scalable to arbitrary numbers of joints. Methodologically, it introduces Clarke coordinates into manifold modeling, establishing an analytical mapping between joint displacement constraints and manifold geometric structures—such as parallel curves—and designs three tightly integrated modules—sampling, trajectory generation, and control—entirely based on branch-free, compact, and code-efficient differential-geometric algorithms, while remaining compatible with non-Clarke coordinate interfaces. The key contribution is the first theoretical unification and practical implementation of the Clarke transform for manifold-based planning of continuum robots. Simulation results demonstrate millisecond-level module response times, smooth trajectories, real-time control execution, and branch-free computation—collectively enhancing computational efficiency and system integrability.

Kinematic modeling of displacement-driven continuum robots is challenging due to arbitrary joint placement and variable joint counts, hindering generalizable modeling and cross-configuration knowledge transfer. Method: This paper proposes a modified Clarke transform tailored for asymmetric joint layouts, integrated into an encoder–decoder neural network architecture. Unlike conventional approaches constrained to symmetric configurations, the method enables joint-value mapping and forward/inverse kinematics for arbitrary joint numbers and positions. Contribution/Results: The framework achieves high-precision trajectory tracking and closed-loop control under asymmetric configurations in simulation, while maintaining full compatibility with existing three-joint symmetric systems. Notably, this work pioneers the application of the Clarke transform to soft robotic kinematic representation—establishing a novel paradigm for universal modeling, cross-configuration knowledge sharing, and modular control of displacement-driven continuum robots.

To address the challenge of real-time, robust shape estimation for continuum robots operating in complex environments, this paper proposes a dynamic estimation framework based on a stochastic observer. The shape state is modeled via polynomial curvature mode coefficients, and recursive estimation is performed by fusing sparse pose sensor measurements. A noise-weighted observability matrix is innovatively introduced, and an IMM-EKF-driven adaptive switching mechanism among multi-order curvature models is designed to achieve online co-optimization of dynamical complexity and estimation accuracy. The method integrates Polynomial Curvature Kinematics (PCK), Extended Kalman Filtering (EKF), and the Interacting Multiple Model (IMM) algorithm. Both simulation and physical experiments demonstrate significant improvements in estimation accuracy and robustness, with strong adaptability to sensor noise and configuration changes. The approach effectively enables real-time motion planning and control under physical interaction.

Addressing the structural design challenge of multi-segment continuum robots caused by curvature coupling, this paper proposes a joint topology and sizing optimization method with workspace reachability as a hard constraint. The approach innovatively integrates numerical reachability analysis, torque-aware inverse kinematics modeling, and the Estimation of Distribution Algorithm (EDA), enabling minimization of joint torques under forward/inverse kinematic consistency constraints. Compared to conventional genetic algorithms, EDA improves the composite performance—measuring both robot length and actuation energy consumption—by 4–15% across three representative tasks, significantly enhancing solution quality and convergence efficiency. To the best of our knowledge, this work is the first to synergistically combine reachability analysis, torque-aware kinematics, and EDA for continuum robot structural optimization. It establishes a novel paradigm for autonomous configuration design that simultaneously achieves high workspace reachability and low energy consumption.

This work addresses the challenges of insufficient modeling accuracy in continuum robot dynamics and the susceptibility of state estimation to model uncertainties and external disturbances. To overcome these issues, the authors propose a fully discrete modeling framework that integrates the geometrically exact beam formulation based on the minimum strain representation with a Lie group variational integrator. Furthermore, an extended Kalman filter–based disturbance observer is designed to simultaneously estimate the system states, model errors, and external disturbances. By preserving the intrinsic geometric structure of the system, the proposed approach significantly enhances both modeling accuracy and robustness. Experimental validation on a physical platform demonstrates that the developed model and observer achieve high precision, computational efficiency, and reliable disturbance estimation under real-world conditions.

This work addresses the trade-off between infinite-dimensional modeling, compact state representation, and uncertainty quantification in reconstructing the shape of continuum robots from sparse, noisy sensor data. The authors propose a low-dimensional state estimation approach based on factor graphs, leveraging geometrically varying strain (GVS) to parameterize the strain field. For the first time, closed-form kinematic constraints derived via the Magnus expansion are incorporated as factors into the graphical model, establishing a geometric prior—grounded in Cosserat rod theory—between strain and pose. This enables compact, probabilistic, and modular state inference. In simulations on a 0.4-meter tendon-driven continuum robot, the method achieves average positional errors below 2 mm across three sensing configurations; when using only position measurements, it reduces orientation error by a factor of six compared to a Gaussian process regression baseline.

本文针对连续体机器人动态运动中的状态估计问题，采用近似Cosserat杆动力学的方法，通过模拟和实验验证了其在肌腱驱动机器人上的有效性。

This work addresses the challenge of accurately predicting the steady-state shape of tendon-driven continuum robots, which arises from their continuous deformation, intricate tendon routing, compliance, friction, and manufacturing variations. The authors propose a self-modeling approach based on action-conditioned point cloud flow matching. By developing a lightweight 3D-printed robotic platform coupled with a multi-camera RGB-D capture system, and leveraging random quasi-static configuration sampling with conditional generative modeling, they introduce action-conditioned flow matching to the continuum robotics domain for the first time. This enables high-fidelity mapping from motor states to full 3D geometric configurations. The method demonstrates strong generalization within the same design family, extends effectively to loaded scenarios, and significantly outperforms existing approaches across real and simulated robots with 2, 3, and 5 modules, achieving substantial improvements in both Chamfer Distance (CD) and Earth Mover’s Distance (EMD) metrics.

本文提出一种自包含模块化连续体机器人平台，通过可互换的连续关节和基于磁传感器与学习框架的本体感知技术解决现有系统任务特定性和依赖外部传感的问题。