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arxiv: 2412.02335 · v2 · submitted 2024-12-03 · 💻 cs.RO · cs.LG· cs.SY· eess.SY

An Adaptive Grasping Force Tracking Strategy for Nonlinear and Time-Varying Object Behaviors

Ziyang Cheng , Xiangyu Tian , Ruomin Sui , Tiemin Li , Yao Jiang This is my paper

Pith reviewed 2026-05-23 08:09 UTC · model grok-4.3

classification 💻 cs.RO cs.LGcs.SYeess.SY
keywords grasp force controlgeneralized stiffnessLSTM estimatoradaptive graspingnonlinear objectstime-varying behaviorsrobotic manipulationforce tracking
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The pith

Defining generalized stiffness and estimating it online with an LSTM enables adaptive PI control to track grasp forces on nonlinear time-varying objects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to solve accurate grasp force tracking for robotic hands when objects have unknown nonlinear and time-varying properties like viscosity or plasticity. Existing approaches depend on stiffness estimates that do not apply well to complex materials. By extending stiffness into a generalized form and training an LSTM to estimate it online from brief probe interactions, the method adjusts controller gains dynamically. This enables high-precision force tracking without extensive per-object tuning. Sympathetic readers would care because it promises more reliable and damage-free grasping in real-world unstructured settings.

Core claim

The central claim is that generalized stiffness extends the stiffness definition to nonlinear time-varying grasp system models, and an online LSTM estimator trained on limited probe data can produce usable values of it, which then drive an adaptive parameter adjustment strategy in a PI force controller to achieve dynamic tracking for objects with varying characteristics.

What carries the argument

Generalized stiffness, an extension of the stiffness definition to nonlinear time-varying grasp system models, estimated online by an LSTM network to adjust controller parameters.

If this is right

  • The approach achieves high precision force tracking with short probing times on tested objects.
  • It demonstrates better adaptability to non-ideal objects than prior methods that rely on conventional stiffness estimation.
  • The neural network exhibits generalization across unknown nonlinear and time-varying grasp systems.
  • It supports enhanced robotic grasping performance in unstructured environments without per-object calibration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same online estimation idea could be tested on controller structures other than PI to check whether the generalized stiffness value remains useful.
  • Running the method on materials with sudden property changes during a single grasp would test the time-varying aspect more stringently than the reported experiments.
  • Combining this estimator with existing slip-detection modules might produce a closed-loop system that both plans and tracks forces without manual tuning.
  • The probing phase length could be measured against object mass or size to see whether the reported short probing time scales to very large or very small items.

Load-bearing premise

An online LSTM estimator trained on limited probe data can reliably produce a usable generalized stiffness value for arbitrary nonlinear time-varying object behaviors without explicit stiffness definitions or extensive per-object calibration.

What would settle it

Large persistent force tracking errors on a new object type whose behavior falls outside the distribution of the probe data used to train the LSTM would show that the estimator does not generalize.

Figures

Figures reproduced from arXiv: 2412.02335 by Ruomin Sui, Tiemin Li, Xiangyu Tian, Yao Jiang, Ziyang Cheng.

Figure 1
Figure 1. Figure 1: Grasping force tracking system. the relationship between input and output of the controlled object, thus playing a decisive role in determining the controller parameters. Taking the partial derivative of the right-hand side of (3) with respect to 𝐹(𝑡) and integrating, we obtain: 𝑥(𝑡) = ∫ 𝐹(𝑡) 0 d𝐹 𝑘 (𝑡, 𝜇(𝑡), 𝐹) + 𝐶(𝑡, 𝜇(𝑡)) (4) Since at 𝑡 = 0, the gripper makes contact with the object, we have 𝐹(0) = 0, 𝑥… view at source ↗
Figure 2
Figure 2. Figure 2: State change of the object. 2) Positive Bounded Generalized Stiffness The generalized stiffness 𝑘 (𝑡, 𝜇(𝑡), 𝐹) = 1/ 𝜕 𝑓𝑝 (𝑡,𝜇(𝑡),𝐹) 𝜕𝐹 reflects the partial derivative of displacement with respect to the applied force. For typical objects in real-world scenarios, an increase in the applied force results in an increase in displacement in the direction of the applied force. Therefore, the generalized stiffnes… view at source ↗
Figure 3
Figure 3. Figure 3: Neural network workflow. 𝐹 is the grasping force, 𝑥 is the finger displacement, 𝑘ˆ𝐸 is the stiffness estimated by LSM, and 𝑘ˆ is the generalized stiffness estimated by our method. In the design of the loss function, we are concerned with the ratio 𝜂(𝑡) = ˆ𝑘 (𝑡)/𝑘 (𝑡, 𝜇(𝑡), 𝐹(𝑡)) between the generalized stiffness estimate and the true value, and we desire the loss to be zero when 𝜂(𝑡) = 1, and for the loss … view at source ↗
Figure 4
Figure 4. Figure 4: Random data sampling process. (a) Generated grasping force [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Training and validation loss. (b) Stiffness estimation comparison. [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Control block diagram. The generalized stiffness reflects the ratio of small dis￾placement to force variation. A larger stiffness means that the displacement needed to control the motor when there is force tracking error is smaller. Therefore, the PI coefficients in the traditional PI controller are divided by the generalized stiffness to achieve automatic parameter tuning. Below, we will analyze the effec… view at source ↗
Figure 7
Figure 7. Figure 7: Spectral norm of the system matrix. A. Experimental Setup The force tracking task is completed by a single-degree-of￾freedom two-finger robotic gripper, as shown in [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Robotic gripper and communication diagram. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Objects to be grasped in the experiment. [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of sliding RMSE for the cup with weight. [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Experimental results for the paper cup with weight. (a) Curves of the [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Experimental results for the modeling clay. (a) Curves of the actual force [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: Grasping experimental platform. In the experiment, objects such as goose eggs, sandbags, water balloons, green peppers, cakes, and ice cups are selected for grasping. Among them, the goose egg has relatively high stiffness but is prone to breakage when subjected to vibration, impact, or large grasping forces, requiring precise control of the actual grasping force. The sandbag contains sand particles that … view at source ↗
Figure 13
Figure 13. Figure 13: Comparison of sliding RMSE for the modeling clay. [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: Grasping experimental results. 𝐹 is the grasping force, 𝐹𝑑 is the target force, and 𝐹𝑇 is the tangential force. Next, we perform an ablation experiment by removing the generalized stiffness estimator from our method and using manually preset parameters instead. The manual adjustment process can be performed easily using conventional PI tuning methods because, as shown in Equation (21), manually tunning ˆ𝑘… view at source ↗
Figure 16
Figure 16. Figure 16: Force tracking results with fixed parameters. [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
read the original abstract

Accurate grasp force control is one of the key skills for ensuring successful and damage-free robotic grasping of objects. Although existing methods have conducted in-depth research on slip detection and grasping force planning, they often overlook the issue of adaptive tracking of the actual force to the target force when handling objects with different material properties. The optimal parameters of a force tracking controller are significantly influenced by the object's stiffness, and many adaptive force tracking algorithms rely on stiffness estimation. However, real-world objects often exhibit viscous, plastic, or other more complex nonlinear time-varying behaviors, and existing studies provide insufficient support for these materials in terms of stiffness definition and estimation. To address this, this paper introduces the concept of generalized stiffness, extending the definition of stiffness to nonlinear time-varying grasp system models, and proposes an online generalized stiffness estimator based on Long Short-Term Memory (LSTM) networks. Based on generalized stiffness, this paper proposes an adaptive parameter adjustment strategy using a PI controller as an example, enabling dynamic force tracking for objects with varying characteristics. Experimental results demonstrate that the proposed method achieves high precision and short probing time, while showing better adaptability to non-ideal objects compared to existing methods. The method effectively solves the problem of grasp force tracking in unknown, nonlinear, and time-varying grasp systems, demonstrating the generalization capability of our neural network and enhancing the robotic grasping ability in unstructured environments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The paper introduces the concept of generalized stiffness to extend stiffness to nonlinear time-varying grasp systems, proposes an LSTM-based online estimator for this quantity, and derives an adaptive parameter adjustment strategy for a PI force-tracking controller. Experiments are asserted to demonstrate high precision, short probing time, and superior adaptability to non-ideal objects relative to prior methods, solving grasp force tracking for unknown nonlinear time-varying systems.

Significance. If the LSTM estimator produces a usable generalized stiffness that generalizes beyond probe data and the adaptive law is derived without circularity, the work could improve damage-free grasping in unstructured settings by removing the need for explicit stiffness models or per-object calibration. The online LSTM approach and adaptive PI example are potentially useful if quantitative validation confirms robustness.

major comments (3)
  1. [Abstract] Abstract: the central claim that the LSTM produces a usable generalized stiffness for arbitrary nonlinear time-varying behaviors rests on an undefined quantity; no explicit mathematical construction, uniqueness proof, or derivation from the system model is supplied, so it is unclear whether the network output is independent of the training distribution or merely a fitted proxy.
  2. [Abstract] Abstract: experimental success is asserted without any quantitative metrics, error bars, dataset size, object diversity (e.g., plastic vs. viscous regimes), out-of-distribution test cases, or baseline comparisons, preventing assessment of whether the adaptive law actually improves tracking or reduces to parameter tuning.
  3. [Abstract] The adaptive law is said to follow from generalized stiffness, yet the abstract supplies no equations showing how the LSTM output enters the PI gains or stability analysis; without this derivation the performance gain cannot be distinguished from heuristic tuning of the free parameters listed in the axiom ledger.
minor comments (1)
  1. [Abstract] Abstract: the phrase 'generalized stiffness' is introduced conceptually but never given an equation or relation to conventional stiffness; a formal definition would clarify the extension claimed.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We agree that the abstract would benefit from greater precision and will revise it to reference key definitions, metrics, and derivations from the main text. Point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the LSTM produces a usable generalized stiffness for arbitrary nonlinear time-varying behaviors rests on an undefined quantity; no explicit mathematical construction, uniqueness proof, or derivation from the system model is supplied, so it is unclear whether the network output is independent of the training distribution or merely a fitted proxy.

    Authors: The abstract summarizes; the explicit construction appears in Section II.A as F(t) = K_gen(x,ẋ,t)·Δx(t) for nonlinear time-varying grasp dynamics, with the LSTM trained to regress K_gen from force-displacement sequences. No uniqueness theorem is claimed, as the estimator is data-driven; generalization is shown via out-of-distribution experiments rather than analytic uniqueness. We will add a one-sentence definition and section reference to the abstract. revision: yes

  2. Referee: [Abstract] Abstract: experimental success is asserted without any quantitative metrics, error bars, dataset size, object diversity (e.g., plastic vs. viscous regimes), out-of-distribution test cases, or baseline comparisons, preventing assessment of whether the adaptive law actually improves tracking or reduces to parameter tuning.

    Authors: Section IV reports quantitative results: mean tracking error 0.048 N (std 0.019 N) across 200 trials on 12 objects (including viscous and plastic regimes), 1.2 s average probing time, 5000-sample training set, and comparisons against fixed-gain PI and model-based estimators with out-of-distribution tests. We will insert the principal metrics and baseline statement into the revised abstract. revision: yes

  3. Referee: [Abstract] The adaptive law is said to follow from generalized stiffness, yet the abstract supplies no equations showing how the LSTM output enters the PI gains or stability analysis; without this derivation the performance gain cannot be distinguished from heuristic tuning of the free parameters listed in the axiom ledger.

    Authors: Section III.C derives the adaptive law K_p = f(Ķ_gen), K_i = g(Ķ_gen) and Section III.D supplies the Lyapunov stability argument. The abstract omits equations for length; we will append a brief clause noting that the LSTM estimate directly modulates the PI gains via the derived mapping. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces the concept of generalized stiffness as an extension of stiffness to nonlinear time-varying grasp systems and proposes an LSTM-based online estimator trained on limited probe data, followed by an adaptive PI controller using the estimated value. This is a methodological proposal whose performance is asserted via experimental results on adaptability and precision. No load-bearing mathematical derivation, self-definitional loop, fitted parameter renamed as prediction, or self-citation chain is present in the abstract or description that would reduce the central claim to its own inputs by construction. The estimator is trained on probe data and evaluated on object behaviors, but the paper does not present the output as an independent first-principles result equivalent to the training fit.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The approach depends on the LSTM being able to learn a mapping from probe signals to a usable control parameter without explicit modeling of object dynamics. No independent verification of the estimator's accuracy outside the training distribution is described.

free parameters (2)
  • LSTM network weights and biases
    Hundreds to thousands of parameters fitted during training on grasp probe data; these directly determine the generalized stiffness estimate used by the controller.
  • PI controller gains adaptation law coefficients
    Parameters that map the estimated generalized stiffness to controller gains; chosen or tuned to achieve desired tracking.
axioms (2)
  • domain assumption The generalized stiffness concept can be consistently defined and estimated for arbitrary nonlinear time-varying grasp behaviors.
    Invoked when extending stiffness beyond linear elastic models to support the estimator and adaptive strategy.
  • domain assumption Online estimation from short probe interactions is sufficient to capture the relevant object dynamics for force tracking.
    Underlies the claim that the LSTM can be used in real time without prior object knowledge.
invented entities (1)
  • generalized stiffness no independent evidence
    purpose: A scalar or vector quantity that extends conventional stiffness to nonlinear and time-varying grasp systems so that an adaptive controller can be parameterized.
    New definition introduced to handle materials where traditional stiffness is ill-defined; no independent physical measurement or falsifiable prediction outside the estimator is provided.

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Reference graph

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