Computing forward statics from tendon-length in flexible-joint hyper-redundant manipulators

2025-09-15

AI Summary

Open-loop static control of large tendon-driven hyper-redundant manipulators under gravity remains challenging due to the difficulty in accurately measuring or estimating tendon tensions. Method: This paper proposes a forward statics iterative solver that directly uses tendon lengths as inputs. It unifies tendon length and tension modeling, constructs a statics model for multi-segment manipulators with elastic joints using screw theory, and integrates nonlinear optimization to map tendon lengths to static equilibrium configurations. Contribution/Results: The method eliminates the need for tendon force sensors or state estimation algorithms, significantly reducing hardware requirements and computational complexity. Experimental results demonstrate high open-loop pose accuracy and robustness against gravitational disturbances, effectively resolving the static modeling and control challenges inherent in such systems under gravity.

Technology Category

• Intelligent Robots: Manipulation
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Hyper-redundant tendon-driven manipulators of- fer greater flexibility and compliance over traditional manipu- lators. A common way of controlling such manipulators relies on adjusting tendon lengths, which is an accessible control parameter. This approach works well when the kinematic configuration is representative of the real operational con- ditions. However, when dealing with manipulators of larger size subject to gravity, it becomes necessary to solve a static force problem, using tendon force as the input and employing a mapping from the configuration space to retrieve tendon length. Alternatively, measurements of the manipulator posture can be used to iteratively adjust tendon lengths to achieve a desired posture. Hence, either tension measurement or state estimation of the manipulator are required, both of which are not always accurately available. Here, we propose a solution by reconciling cables tension and length as the input for the solution of the system forward statics. We develop a screw-based formulation for a tendon-driven, multi-segment, hyper-redundant manipulator with elastic joints and introduce a forward statics iterative solution method that equivalently makes use of either tendon length or tension as the input. This strategy is experimentally validated using a traditional tension input first, subsequently showing the efficacy of the method when exclusively tendon lengths are used. The results confirm the possibility to perform open-loop control in static conditions using a kinematic input only, thus bypassing some of the practical problems with tension measurement and state estimation of hyper-redundant systems.

Problem

• Solving forward statics using tendon length instead of force input
• Eliminating need for tension measurement or state estimation
• Enabling open-loop control via kinematic input only

Innovation

• Screw-based formulation for tendon-driven manipulators
• Iterative forward statics solution method
• Uses tendon length or tension as input