Morphology-Specific Closed-Loop Control of Logarithmic-Spiral Continuum Arms via Online Jacobian Error Compensation

2026-06-24

AI Summary

Existing approaches struggle to achieve effective inverse kinematics and closed-loop task-space control for logarithmic-spiral continuum arms. This work proposes, for the first time, a segmented tendon-driven model that explicitly incorporates the geometric properties of logarithmic spirals, enabling analytical derivation of the task-space Jacobian. To address modeling inaccuracies arising from nonlinear deformations and contact, the method integrates Broyden’s secant update with Kalman filtering for online Jacobian error compensation within a closed-loop control framework. Evaluated in MuJoCo simulations, the approach significantly outperforms constant-curvature baselines, demonstrating high precision, strong robustness, and excellent scalability across trajectory tracking, pose regulation, and multi-degree-of-freedom manipulation tasks.

Abstract

Logarithmic spirals are ubiquitous in biological appendages and provide an attractive morphology for continuum manipulators capable of reaching, wrapping, and grasping. Recently reported logarithmic-spiral robots demonstrated scalable fabrication and versatile grasping but lacked inverse kinematics and closed-loop control. This work presents the first morphology-specific closed-loop task-space control framework for logarithmic-spiral continuum arms. A segmented tendon-driven model with a centerline backbone and equilateral tendon routing is developed in MuJoCo to capture tapered compliance and contact dynamics. An analytical task-space Jacobian is derived directly from the logarithmic-spiral kinematics and combined with online Jacobian error compensation using a Broyden secant update and Kalman-filter estimation. The resulting controller continuously corrects modeling errors arising from nonlinear deformation, contact, and geometric mismatch. The framework is validated through planar and spatial simulations, including trajectory tracking, attitude regulation, disturbance rejection, three-dimensional position tracking, and simultaneous position-orientation control. Compared with a piecewise-constant-curvature (PCC) baseline, the proposed method consistently reduces tracking errors, suppresses attitude drift, and maintains a bounded Jacobian estimation error. The controller is further applied to morphology-enabled manipulation tasks, including obstacle-assisted reach-wrap-release motions, adaptive whole-arm grasping, and cooperative multi-arm object handling. Results demonstrate that combining logarithmic-spiral morphology with online Jacobian compensation enables accurate, robust, and scalable control of highly underactuated continuum manipulators. The proposed framework establishes a physics-grounded baseline for future hardware implementation and learning-augmented soft robotic control.

Problem

• logarithmic-spiral continuum arms
• closed-loop control
• inverse kinematics
• Jacobian error
• underactuated manipulators

Innovation

• logarithmic-spiral continuum manipulator
• online Jacobian error compensation
• morphology-specific control
• closed-loop task-space control
• tendon-driven soft robotics