Infinite-Dimensional Closed-Loop Inverse Kinematics for Soft Robots via Neural Operators

2026-02-20

AI Summary

This work addresses the inverse kinematics challenge in underactuated soft robots arising from their infinite degrees of freedom by proposing an end-to-end closed-loop control framework. The approach leverages a differentiable neural operator trained on simulation data to learn the actuation-to-shape mapping and incorporates an infinite-dimensional chain rule to construct a differential kinematic model, enabling Jacobian-based, whole-body shape-aware inverse kinematics control. For the first time, closed-loop inverse kinematics is extended into an infinite-dimensional setting, seamlessly integrating continuous deformation with task-space information. The method is theoretically validated under the constant-curvature assumption and successfully demonstrated on a three-fiber soft robotic arm, achieving high-precision, differentiable morphological compliance control.

Technology Category

• Intelligent Robots: Manipulation
• Machine Learning: Imitation Learning & Inverse Reinforcement Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

While kinematic inversion is a purely geometric problem for fully actuated rigid robots, it becomes extremely challenging for underactuated soft robots with infinitely many degrees of freedom. Closed-loop inverse kinematics (CLIK) schemes address this by introducing end-to-end mappings from actuation to task space for the controller to operate on, but typically assume finite dimensions of the underlying virtual configuration space. In this work, we extend CLIK to the infinite-dimensional domain to reason about the entire soft robot shape while solving tasks. We do this by composing an actuation-to-shape map with a shape-to-task map, deriving the differential end-to-end kinematics via an infinite-dimensional chain rule, and thereby obtaining a Jacobian-based CLIK algorithm. Since the actuation-to-shape mapping is rarely available in closed form, we propose to learn it from simulation data using neural operator networks, which are differentiable. We first present an analytical study on a constant-curvature segment, and then apply the neural version of the algorithm to a three-fiber soft robotic arm whose underlying model relies on morphoelasticity and active filament theory. This opens new possibilities for differentiable control of soft robots by exploiting full-body shape information in a continuous, infinite-dimensional framework.

Problem

• inverse kinematics
• soft robots
• infinite-dimensional
• closed-loop control
• underactuated systems

Innovation

• infinite-dimensional inverse kinematics
• neural operators
• closed-loop inverse kinematics
• soft robotics
• differentiable control