Abstract
This paper presents a subsystem-based adaptive control framework for serial flexible manipulators with an arbitrary number of links, in which the elastic deformation PDE of each link is carried through the entire control design without spatial discretization or modal truncation. All dynamic quantities -- rigid-body motion, elastic deformation, and inter-link constraint forces -- are expressed uniformly as body-fixed twists and wrenches within the se3 Lie-algebraic structure. A controllable form of the per-link dynamics is derived by substituting the strain-based deformation PDE into the dynamic equation, eliminating distributed elastic acceleration and yielding a model governed by the body-fixed twist acceleration and deformation field. Desired subsystem twist trajectories are generated via a deflection-compensating inverse kinematics procedure. A nominal per-link controller is proven to produce exponential twist error decay via a per-subsystem Lyapunov function. An adaptive modification replaces exact physical parameters with online estimates governed by a projection-based law, augmenting with a parameter estimation error term. Upon summing over all links, the interaction power terms telescope to zero by Newton's third law and the frame invariance of the natural power pairing on se3se(3), establishing exponential convergence of all twist errors and bounded elastic deformation under both nominal and adaptive controllers. The screw-theoretic structure renders interaction term cancellation exact, making the stability certificate modular and scalable to chains of arbitrary length. The framework is validated numerically on a two-link flexible manipulator in three-dimensional motion.
Explore similar work
Jul 15, 2026cs.RO
Model-based control of flexible joint robots with position-controlled actuators relies on accurate knowledge of the joint compliance. In practice, precise stiffness models are often unavailable as the properties of physical elastic elements vary with operating conditions and slowly change over time due to wear and aging. To improve model-based control of these systems, we propose an adaptive control approach in this work, which updates an estimate of the uncertain, nonlinear torque-deflection relation of each joint. As opposed to classical adaptive control approaches for non-elastic robots, we rely on an implicit control law and a control-input-dependent regressor matrix to account for the uncertain joint stiffness. We analyze robustness of the approach against errors induced by the motor position controller. Experimental results on a flexible joint with nonlinear stiffness characteristics demonstrate the effectiveness of the proposed approach.
Annika Kirner, Grazia Zambella, Igor Kovacevic +3
May 17, 2026cs.RO
Flexible robotic manipulators (FRMs) offer advantages in lightweight design and large workspace, but their structural flexibility induces vibrations, accelerates fatigue, degrades tracking performance, and limits operational speed. These challenges are further amplified in multi-link serial manipulators, where increased overall length leads to greater structural flexibility. This article presents a backstepping output-feedback framework for fast vibration suppression and tip tracking of an n-degree-of-freedom serial flexible manipulator robot (nDSFMR), with a DeepONet-based approximation for practical deployment. Each link-joint is modeled as a Timoshenko beam coupled with an ODE and transformed into a canonical hyperbolic PDE with boundary dynamics. A backstepping-based boundary controller at the joint is developed to equivalently inject distributed damping along the beam, enabling rapid vibration suppression and trajectory tracking, only using available boundary measurements. To enable real-time implementation and scalability, a DeepONet neural operator is introduced to approximate the backstepping kernels, significantly reducing computational cost and facilitating fast controller updates under varying operating conditions. Experiments on a two-link flexible manipulator demonstrate faster vibration suppression and convergence of the end-effector to the desired trajectory, compared with a linear quadratic regulator (LQR) with feedforward control.
Chengyi Wang, Yilong Huang, Ji Wang
Sep 22, 2026cs.RO
Most research on the manipulation of deformable objects focuses on lightweight systems with negligible mechanical response, effectively restricting attention to quasi-static regimes. This assumption excludes a broad class of practically relevant objects, such as hoses, pipes, and wiring harnesses, whose dynamics cannot be ignored during manipulation. In this work, we address this limitation by introducing a closed-loop control architecture that explicitly accounts for object dynamics and recasts manipulation as a shape-regulation problem. Control is achieved by modulating forces and torques applied at multiple fixed points along the object. This approach builds on three methodological contributions: a fully dynamic model of linear deformable objects based on discrete strain parameterizations; an extension of the notion of actuation coordinates to SE(3), yielding a structured and inherently underactuated control architecture; and nonlinear feedback strategies providing explicit conditions for steady-state convergence to desired configurations. Extensive simulations on representative manipulation tasks demonstrate the performance gains enabled by the proposed modelbased formulation. We finally validate the approach experimentally through a real-time closed-loop implementation with online shape estimation, confirming its practical feasibility and effectiveness
Daniel Feliu-Talegon, Cosimo Della Santina