2026-06-26 04:00 UTCOriginal source2 min readUpdated: 2026-06-26 08:15 UTC

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

This paper presents the first morphology-specific closed-loop task-space control framework for logarithmic-spiral continuum arms. Using a segmented tendon-driven model and online Jacobian error compensation (Broyden update and Kalman filter), it achieves accurate robust control, outperforming piecewise-constant-curvature methods in simulations, and enables manipulations like grasping and obstacle-assisted motions.

SourcearXiv RoboticsAuthor: Partha Datta (Laboratory for Soft Machines and Electronics, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, USA, Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA), Yi Jin (Laboratory for Soft Machines and Electronics, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, USA), Wei Lin (Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA), C. Chase Cao (Laboratory for Soft Machines and Electronics, Department of Mechanical and Aerospace Engineering, Case Western Reserve University, Cleveland, OH, USA, Department of Electrical, Computer and Systems Engineering, Case Western Reserve University, Cleveland, OH, USA, Advanced Platform Technology)

[2606.26188] Morphology-Specific Closed-Loop Control of Logarithmic-Spiral Continuum Arms via Online Jacobian Error Compensation

[Submitted on 24 Jun 2026]

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

View a PDF of the paper titled Morphology-Specific Closed-Loop Control of Logarithmic-Spiral Continuum Arms via Online Jacobian Error Compensation, by Partha Datta (1 and 22 other authors

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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.

Subjects:

Robotics (cs.RO); Applied Physics (physics.app-ph)

Cite as: arXiv:2606.26188 [cs.RO]

(or arXiv:2606.26188v1 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2606.26188

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Chase Cao [view email] [v1] Wed, 24 Jun 2026 13:54:23 UTC (7,447 KB)

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