Real-Time Projected Adaptive Control for Closed-Chain Co-Manipulative Continuum Robots

2026-04-05

AI Summary

This work addresses the challenge of controlling continuum robots during cooperative manipulation of compliant objects, where strong coupling, dynamic interactions, internal forces, and unknown time-varying parameters render conventional nominal-model-based controllers ineffective. The authors propose a projection-based adaptive control framework that employs a finite-dimensional dynamic model derived from geometrically exact variable strain (GVS) theory. Pfaffian velocity constraints and orthogonal projection are integrated to enforce closed-loop kinematic constraints while preserving linear parameterization, ensuring both constraint consistency and real-time computability. A Lyapunov-based adaptive law guarantees asymptotic convergence of task-space tracking errors. To the best of the authors’ knowledge, this is the first application of projection adaptive control to such systems. Simulations and tendon-driven robot experiments demonstrate the approach’s stability, high tracking accuracy, and real-time performance in both regulation and trajectory-following tasks.

Abstract

In co-manipulative continuum robots (CCRs), multiple continuum arms cooperate by grasping a common flexible object, forming a closed-chain deformable mechanical system. The closed-chain coupling induces strong dynamic interactions and internal reaction forces. Moreover, in practical tasks, the flexible object's physical parameters are often unknown and vary between operations, rendering nominal model-based controllers inadequate. This paper presents a projected adaptive control framework for CCRs formulated at the dynamic level. The coupled dynamics are expressed using the Geometric Variable Strain (GVS) representation, yielding a finite-dimensional model that accurately represents the system, preserves the linear-in-parameters structure required for adaptive control, and is suitable for real-time implementation. Closed-chain interactions are enforced through Pfaffian velocity constraints, and an orthogonal projection is used to express the dynamics in the constraint-consistent motion subspace. Based on the projected dynamics, an adaptive control law is developed to compensate online for uncertain dynamic parameters of both the continuum robots and the manipulated flexible object. Lyapunov analysis establishes closed-loop stability and convergence of the task-space tracking errors to zero. Simulation and experiments on a tendon-driven CCR platform validate the proposed framework in task-space regulation and trajectory tracking.

Problem

• co-manipulative continuum robots
• closed-chain dynamics
• parameter uncertainty
• flexible object manipulation
• adaptive control

Innovation

• projected adaptive control
• continuum robots
• closed-chain dynamics
• Geometric Variable Strain (GVS)
• Pfaffian constraints