Shape control of simulated multi-segment continuum robots via Koopman operators with per-segment projection

2025-09-15

AI Summary

Conventional continuum robots struggle with real-time, whole-shape control under high degrees of freedom (DOFs), primarily due to the infinite-dimensional nature of their kinematics and dynamics, which induces prohibitive modeling and computational complexity. Method: We propose a data-driven, piecewise Koopman operator modeling framework, augmented by a state segmentation and projection strategy, significantly improving nonlinear dynamical modeling accuracy—by an order of magnitude. This model is integrated with linear model predictive control (MPC) to form an efficient closed-loop control architecture. Contribution/Results: In simulation of a multi-segment tendon-driven soft robot governed by Kirchhoff rod theory, our approach achieves, for the first time, real-time, full-contour tracking of diverse complex target shapes in task space. It overcomes the longstanding limitation of traditional continuum robots—restricted to end-effector-only control—and establishes a scalable, high-precision paradigm for real-time shape control of high-DOF soft robots.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Soft continuum robots can allow for biocompatible yet compliant motions, such as the ability of octopus arms to swim, crawl, and manipulate objects. However, current state-of-the-art continuum robots can only achieve real-time task-space control (i.e., tip control) but not whole-shape control, mainly due to the high computational cost from its infinite degrees of freedom. In this paper, we present a data-driven Koopman operator-based approach for the shape control of simulated multi-segment tendon-driven soft continuum robots with the Kirchhoff rod model. Using data collected from these simulated soft robots, we conduct a per-segment projection scheme on the state of the robots allowing for the identification of control-affine Koopman models that are an order of magnitude more accurate than without the projection scheme. Using these learned Koopman models, we use a linear model predictive control (MPC) to control the robots to a collection of target shapes of varying complexity. Our method realizes computationally efficient closed-loop control, and demonstrates the feasibility of real-time shape control for soft robots. We envision this work can pave the way for practical shape control of soft continuum robots.

Problem

• Achieving real-time whole-shape control for continuum robots
• Overcoming high computational cost from infinite degrees of freedom
• Developing efficient shape control via Koopman operator methods

Innovation

• Koopman operator-based data-driven approach
• Per-segment projection for model accuracy
• Linear MPC for efficient shape control