Flexibility-Aware Robotic Manipulation: Deformation Estimation, Kinematics, and Control via Distributed Inertial Measurement

Amir Hossein Barjini; Sadeq Yaqubi; Pauli Mustalahti; Jouni Mattila

cs.ROOct 30, 2026

Flexibility-Aware Robotic Manipulation: Deformation Estimation, Kinematics, and Control via Distributed Inertial Measurement

Authors: Amir Hossein Barjini, Sadeq Yaqubi, Pauli Mustalahti, Jouni Mattila

Organizations: Authors are with the Department of Engineering and Natural Sciences, Tampere University, Finland.

Abstract

Flexible robot links challenge the rigid-body assumption, making joint measurements alone insufficient for accurate manipulation. This paper introduces a flexibility-aware manipulation framework that connects structural dynamics directly to sensing, kinematics, and control. Instead of prescribing a dense inertial measurement unit (IMU) network, the dominant vibration modes of each flexible link are first identified from response-convergence and excitation-bandwidth criteria. Under a full-rank modal observability condition, $m$ retained modes require only $m$ independent slope measurements and one reference IMU, defining the minimum observable IMU configuration. The resulting measurements are used to reconstruct the continuous link deformation, which is then incorporated into flexibility-aware forward kinematics and a deformation-informed partial differential equation-based controller. Experiments on hydraulic single- and double-link manipulators evaluate the framework. On the long-reach double-link platform, the proposed kinematics achieves end-effector root mean square errors of $0.0107$ ~m, $0.0194$ ~m, and $0.0102$ ~rad while using fewer sensors than the piecewise-rigid method. Closed-loop reaching experiments further demonstrate real-time integration of IMU-estimated joint states and reconstructed deformation into the proposed controller. The results show that dominant modal information can determine sensing requirements and enable real-time flexibility-aware robotic manipulation.

Figures & tables

Fig. 1: Overview of the proposed flexibility-aware manipulation framework, integrating mode selection, IMU-based deformation reconstruction, flexibility-aware kinematics, and control.

Fig. 2: Adjacent-link frames and IMU configuration used for joint-state estimation.

Fig. 3: Mode-informed deformation reconstruction using the minimum observable IMU configuration for a flexible link.

Fig. 4: Frame assignment for flexibility-aware forward kinematics of a planar serial flexible manipulator.

Fig. 5: DLFM configuration and deformation variables used for the deformation-informed PDE-based controller.

Fig. 6: Number of dominant modes identified by the convergence-of-observables criterion: (a) effects of flexural rigidity $E_{i}I_{i}$ and mass per unit length $\rho_{i}A_{i}$ ; (b) effects of link length $L_{i}$ and equivalent tip mass $M_{p_{i}}$ .

Fig. 7: Variation of the first four natural frequencies with flexural rigidity $E_{i}I_{i}$ and mass per unit length $\rho_{i}A_{i}$ under the first scenario.

Fig. 8: Variation of the first four natural frequencies with link length $L_{i}$ and equivalent tip mass $M_{p_{i}}$ under the second scenario.

Fig. 9: Experimental SLFM platform for deformation-estimation validation using distributed IMUs and laser-tracker ground truth.

Fig. 10: Experimental results of deformation estimation and corresponding estimation errors for the SLFM under 20 [kg] and 40 [kg] payloads.

Method	$M_{p}=20$ kg [m]	$M_{p}=40$ kg [m]
Piecewise Rigid	0.046593	0.045521
1 Mode	0.036284	0.026317
2 Modes	0.014001	0.025744
3 Modes	0.014123	0.024817

TABLE I: Experimental tip-deformation RMSE for different deformation reconstruction methods.

Fig. 11: Experimental DLFM platform for validation of the proposed flexibility-aware forward kinematics.

Fig. 12: Experimental comparison of IMU-estimated and encoder-measured joint angles

\theta_{1}

and

\theta_{2}

of the DLFM.

Fig. 13: Experimental DLFM end-effector pose estimation and corresponding absolute errors for the rigid, piecewise-rigid, and proposed flexibility-aware models.

Method	$y_{EE}$ RMSE	$z_{EE}$ RMSE	$\theta_{EE}$ RMSE
	[m]	[m]	[rad]
Rigid	0.144911	0.407625	0.092640
Piecewise rigid	0.035099	0.037915	0.045337
Proposed	0.010725	0.019378	0.010170

TABLE II: RMSE of end-effector pose estimation.

Fig. 14: Overview of the proposed flexibility-aware control.

Fig. 15: Experimental joint-space tracking performance of the deformation-informed PDE controller during the representative reaching task.

Joint	Tracking RMSE [deg]	Torque RMS [N m]
Joint 1	0.363	3179.57
Joint 2	0.477	310.40

TABLE III: Experimental joint tracking and control-effort performance.

Fig. 16: Experimental control effort of the proposed deformation-informed PDE controller during the reaching task.

Fig. 17: IMU-reconstructed flexible-link tip deformations during the representative closed-loop reaching task.

Robotic Manipulation

Robotic manipulation studies how robots perceive, plan, and control physical interactions to grasp, move, assemble, and use objects.

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Estimation and Control of Tensegrity Manipulator Kinematics based on Strut Inclination Angles

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Robotic Control Tensegrity Robotics Robotics Continuum Robot Control Robot State Estimation Continuum Robot Shape Estimation

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Unlike conventional rigid-link robots defined by discrete joints, continuum robots pose a fundamental challenge for expressing their complex continuous bending configurations for closed-loop control. Several modelling approaches have been proposed for conventional continuum robots, but tensegrity-based continuum robots remain largely open. Moreover, many of these approaches assume a continuous elastic backbone and are therefore not directly applicable to tensegrity manipulators, whose bodies are networks of rigid struts and tensioned cables. This work presents a reduced-order model for shape and posture control of a tensegrity-based continuum manipulator. The manipulator is modelled as a serially connected parallel-link mechanism. The proposed method is formulated as an optimization problem that uses geometric constraints of the tensegrity structure together with information from the Inertial Measurement Unit (IMU) sensors embedded in the strut elements. To the best of our knowledge, this work presents the first experimental demonstration of a real-time IMU-based shape estimation method on a full-scale tensegrity manipulator and demonstrates posture control using a simple Proportional-Integral (PI) controller. The results show that the proposed method can estimate the shape of both single-module tensegrity structures and multi-module tensegrity manipulators from arbitrary static configurations and achieve desired postures.

Abstract

Robotic Manipulation

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