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 EiIi and mass per unit length ρiAi ; (b) effects of link length Li and equivalent tip mass Mpi .
Fig. 7: Variation of the first four natural frequencies with flexural rigidity EiIi and mass per unit length ρiAi under the first scenario.
Fig. 8: Variation of the first four natural frequencies with link length Li and equivalent tip mass Mpi 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
Mp=20 kg [m]
Mp=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 θ1 and θ2 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
yEE RMSE
zEE RMSE
θEE 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.
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.
Physical flexibility plays a significant role not only in human motions but also in robot motions. For example, a humanoid robot with passive and flexible elements, which can be regarded as a rigid--soft hybrid-link system, has the advantages of storing energy and mitigating impact in a dynamic motion. However, the motion design and control of a hybrid-link system are challenging to achieve and have only been discussed in the literature. In this study, we propose the framework of inverse kinematics and compliance optimization-based control for a hybrid-link humanoid system that represents the continuous deformation of a flexible structure using the piece-wise constant strain (PCS) model. The proposed method was validated using forward dynamics simulations for standing, jumping, and walking motions. Then, we built an experimental setup using a biped humanoid robot with leaf-spring type prosthesis leg, in which the prosthesis deformation was measured by a motion capture system. Using this setup, we experimentally validated the proposed method for standing balance control in both double- and single-support cases.
Zewen He, Taiki Ishigaki, Ko Yamamoto
Department of Mechano-informatics, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, 113-8656, Tokyo, Japan
Contact-rich robotic manipulation requires an accurate model of the kinematic relationship between a robot's joints and the task features it senses. This relationship is rarely known exactly: it changes with each tool the robot picks up and shifts, sometimes almost instantaneously, as contact modes change --- especially for multi-fingered hands that make and break contact at points that are not exactly prescribed, as in full-hand grasping. This paper develops an adaptive scheme that estimates that relationship online, using only joint-angle sensing and a wrist-mounted force/torque sensor, with no exteroceptive measurement of the tool tip. We derive a provably stable kinematic update law that identifies the kinematics of an unknown tool from force/torque feedback alone, and prove stability of both the rigid case and the case with a compliance controller as an inner loop. We show that identification is confined to the directions the motion excites --- so that, for example, a tool's length is unobservable under a rigid insertion push, while a compliant loop's passive yielding partially excites it; and that with a second-order admittance the compliant certificate holds unconditionally in continuous time. We also pose the combined control and estimation problem as a Quadratic Program (QP): the formulation yields the prediction term of the update law exactly but, instructively, cannot reproduce the tracking adaptation term. We validate the scheme in simulation on a peg-in-hole insertion. This work is the first step in a research program aimed at factoring manipulation learning into a task policy which can be learned in isolation of the robot, for instance by reinforcement learning, and an adaptive kinematic component that adapts online to the particular robot, hand, or tool in use.
Carl Glen Henshaw
US Naval Research Laboratory · U.S. Naval Research Laboratory