Grasp Force Control in Robotic Manipulation

• Grasp force control is the regulated application of minimal force by robotic hands to prevent slip while avoiding object damage.
• It integrates sensor calibration, distributed tactile sensing, and data-driven models to accurately estimate contact forces within an error margin of 0.01–0.15 N.
• A discrete PI controller dynamically adjusts force setpoints to achieve rapid settling times (<1 s) and safe manipulation of delicate objects.

Grasp force control is the field concerned with regulating the force applied by robotic hands or grippers to objects during grasping in order to ensure both stability and safety. Effective grasp force control is essential for avoiding both slippage (by providing sufficient force) and object damage (by not exceeding a safe threshold), particularly when handling delicate, deformable, or unknown objects. State-of-the-art robotic applications require precision in force regulation, robustness to substantial variations in object properties, and often the adaptability to operate based on partial or ambiguous sensory feedback.

1. Core Principles and Challenges

The fundamental challenge in grasp force control is to apply the minimal force required to prevent object slip, while not exceeding the level that would damage or excessively deform the object. This often requires:

• Accurate estimation of contact forces, despite sensor noise, nonlinearity, or ambiguous signals (e.g., soft or distributed contacts).
• Real-time feedback and modulation of control signals to respond to uncertainties, disturbances, and unmodeled behaviors.
• Adaptation to variations in object properties, including mass, stiffness, shape, friction, and possible time- or history-dependent behaviors (e.g., viscoelasticity, plasticity).
• Dealing with soft, compliant end effectors (e.g., soft robotic hands), which add significant nonlinearity and dynamics.

While passive compliance in soft hands improves safety, it is insufficient alone for guaranteeing object integrity; active grasp force regulation is essential even with soft or adaptive hands (Le et al., 2019).

2. Sensor Integration and Force Estimation

The accuracy of force estimation is critical. Sensing modalities and corresponding estimation algorithms include:

• Resistive and Bend Sensors: Used alongside force-sensitive resistors (FSRs) to measure distributed contact force and finger curvature. However, FSRs are subject to artifacts arising from finger bending in free space, requiring data-driven calibration. The internal force artifact is modeled as a polynomial in the bend angle ($F_i(x) = \sum_{d=0}^D w_d x^d$); estimated contact force is thus $F_c = F_m - F_i(x)$, where $F_m$ is the raw measurement (Le et al., 2019).
• Calibration and Model Selection: Polynomial degree is chosen via Bayesian Information Criterion to prevent overfitting.
• Distributed Tactile Sensing: Placing sensors over the entire length of the finger allows for robust detection of contact location and magnitude, supporting reliable force estimation over irregular objects (Le et al., 2019).
• Validation: Error in contact force estimation can be held within 0.01–0.15 N, suitable for delicate manipulations (Le et al., 2019).

Contact force estimation forms the basis for feedback control; the absence of reliable force measurements is a major limitation for force-controlled grasping.

3. Control Architectures for Force Regulation

The dominant architecture for grasp force regulation is the feedback controller, typically realized as a Proportional-Integral (PI) loop. Key features include:

• Discrete PI Control: The output command (e.g., valve PWM duty cycle for pneumatic actuators) is

$u_n = K_p e_n + K_i T \sum_{k=1}^n e_k$

where $e_n = F^*_n - F_{meas}$ is the force error at time step $n$, and $K_p$, $K_i$, and $T$ are the proportional gain, integral gain, and sampling period, respectively (Le et al., 2019).

• No Derivative Action: Derivative terms are commonly omitted to prevent amplification of sensor noise (Le et al., 2019).
• Phase-Switching Logic: Control usually transitions from position or bend control to force control upon detection of contact (e.g., via tactile sensor events).
• Implementation in Soft Hands: For pneumatic actuators, PI controllers modulate the pressure to achieve smooth and precise actuation.
• Tuning and Performance: Gains are set experimentally to achieve fast settling (400–800 ms), low RMS force error (~0.1 N), and minimal overshoot (critical for fragile objects).
• Contact Detection and Switch Control: The force control loop activates only after contact, ensuring that objects are not unnecessarily compressed during approach (Le et al., 2019).

These PI-based controllers provide a balance between implementation simplicity and robustness to the nematic, nonlinear dynamics of soft actuators.

4. Experimental Validation and Performance Metrics

Force-controlled grasping is validated through systematic experimentation:

• Contact Force Tracking: Accuracy is demonstrated by pushing instrumented fingers on a calibrated scale and comparing estimated vs. measured forces. Reported errors of 0.01–0.15 N are well within practical requirements (Le et al., 2019).
• Set Point Regulation: Step responses (e.g., 0→3 N followed by 3 N→2 N) show RMS force errors of ~0.1 N, rapid (<1 s) settling, and no overshoot or induced object damage.
• Safety–Stability Trade-off: Experiments across a range of contact forces (0.5–4 N) with deformable and fragile objects establish a clear trade-off: at higher forces, objects are stably held but may deform (up to 100% deformation rate for light plastic at ≥2 N); at lower forces, objects are not deformed but may slip or be dropped (higher dropping rates at ≤1 N). The optimal control objective is to set force just above the slip threshold (Le et al., 2019).
• Applicability to Various Objects: Successful grasping of a plastic cup, a paper cup, and an eggshell—across multiple force setpoints and trials—demonstrates both adaptability and safety.
• Object Property Estimation: Combined bend and force readings during pressing trials allow discrimination between hard and compliant objects, suggesting potential for in-hand haptic property estimation (Le et al., 2019).

5. Contributions to the State of the Art

This approach advances the state of grasp force control in several respects:

Contribution	Technical Summary
Robust, Data-driven Force Sensing	Model-based calibration overcomes FSR nonlinearity, enabling accurate force feedback
Distributed Sensing Integration	Sensors along the finger offer improved reliability for irregular objects
Low-complexity, Effective Force Control	Simple discrete PI achieves high-accuracy regulation in noisy, nonlinear soft systems
First Experimentally Proved Safe Grasping with Soft Hands	Both drops and object deformation can be avoided via closed-loop force regulation
Framework for High-level Haptics and Advanced Control	Enables estimation of object properties and supports future model-predictive/learning control

The experimental results provide the first (according to the authors) evidence that soft hands, customarily relying on passive compliance alone, benefit substantially from active, feedback-driven force regulation for both safety and stability (Le et al., 2019).

6. Implications, Limitations, and Future Directions

Accurate and robust grasp force control, as realized in soft robotic hands with distributed sensors and data-driven calibration, is critical for deploying robots in environments with fragile, deformable, or unpredictable objects. The approach offers a pathway for:

• Enhanced haptic perception, including in-hand object property assessment.
• Integration with higher-level manipulation strategies, potentially via model-predictive or reinforcement learning frameworks that rely on trustworthy force feedback.
• Safe deployment with diverse and delicate objects, particularly in service robotics or medical assistive devices.

Limitations include:

• Sensitivity to sensor calibration; drift or mechanical wear may necessitate periodic recalibration.
• The simplicity of PI control may be challenged by faster dynamics or in the presence of significant unmodeled disturbances; further improvement may require model-based or learning-augmented architectures.

Overall, the combination of distributed data-driven force estimation and discrete PI control enables soft hands to reliably balance the competing demands of safety and stability, achieving practical and adaptive manipulation of fragile and deformable objects (Le et al., 2019).