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Force Sensing Overview

Why Force Sensing Is Needed

Physical interaction between a robot and its environment is inseparable from force perception. Vision tells the robot "where things are," while force sensing tells the robot "how much force to apply." A robot without force sensing is like working with thick gloves -- it can see but cannot feel.

Force sensing plays the following core roles in robotic systems:

Role Description Typical Scenario
Manipulation Feedback Sense grasping force, contact force Grasping fragile objects
Locomotion Perception Detect ground reaction force, support state Legged robot walking
Collision Detection Identify unexpected contact Collaborative robot safety
Human-Robot Interaction Sense guidance forces applied by humans Hand-guided teaching
Assembly Tasks Force/torque-guided precision alignment Peg-in-hole assembly

Force, Torque, and Pressure

Force

Force is a vector quantity with magnitude and direction, measured in Newtons (N).

\[\vec{F} = m \vec{a}\]

In robotics, three orthogonal components are typically considered:

\[\vec{F} = \begin{bmatrix} F_x \\ F_y \\ F_z \end{bmatrix}\]

Torque

Torque describes rotational effects, measured in Newton-meters (N·m):

\[\vec{\tau} = \vec{r} \times \vec{F}\]
\[\vec{\tau} = \begin{bmatrix} M_x \\ M_y \\ M_z \end{bmatrix}\]

Pressure

Pressure is force per unit area, measured in Pascals (Pa):

\[P = \frac{F}{A}\]

Tactile sensors typically measure pressure distribution rather than single-point force.

Relationship Among the Three

Force (N)
├── Concentrated force → Measured by force/torque sensors (e.g., 6-axis F/T sensor)
├── Distributed force → Measured by pressure sensors (e.g., tactile arrays)
└── Torque = Force × Moment arm → Measured by torque sensors or computed indirectly

Application Domains

1. Manipulation

Grasping and manipulation are the most classic applications of force sensing:

  • Grip force control: Apply just enough force -- neither dropping nor crushing
  • Slip detection: Detect whether an object is slipping through tangential force changes
  • Contact state recognition: Distinguish "empty grip," "contact," and "stable grasp"
\[F_{grip} \geq \frac{mg}{\mu} + F_{margin}\]

where \(\mu\) is the friction coefficient and \(F_{margin}\) is the safety margin.

2. Locomotion

Legged robots need to perceive foot-ground interactions:

  • Ground Reaction Force (GRF): Determine load distribution across each leg
  • Terrain detection: Identify terrain types through contact force patterns
  • Gait switching: Switch gait phases based on contact/liftoff states

3. Collision Detection

Collaborative robot safety standards (ISO/TS 15066) require:

  • Strict limits on maximum allowable contact force/pressure for each body part
  • Typical thresholds: hand \(F \leq 140\) N, head \(F \leq 65\) N
  • Collision detection latency requirement < 10 ms

4. Human-Robot Interaction (HRI)

Force sensing enables robots to "feel" human intent:

  • Admittance control: Human pushes the robot, and it compliantly moves
  • Impedance control: Robot behaves like a spring-damper system
  • Collaborative carrying: Two people (or human-robot) jointly lift heavy objects

Sensing Principles

1. Strain Gauge

The most mature and widely used force sensing principle:

Working Principle: Metal or semiconductor strain gauges change resistance when deformed under force

\[\frac{\Delta R}{R} = G_F \cdot \varepsilon\]

where:

  • \(G_F\) is the gauge factor (metal ~2, semiconductor ~100-200)
  • \(\varepsilon\) is the strain

Wheatstone bridge converts small resistance changes into measurable voltage:

\[V_{out} = V_{ex} \cdot \frac{\Delta R}{4R}\]

Advantages: High accuracy, good linearity, mature and reliable

Disadvantages: Temperature sensitive, requires careful calibration

2. Piezoelectric

Working Principle: Certain crystal materials (quartz, PZT) generate charge under force

\[Q = d \cdot F\]

where \(d\) is the piezoelectric constant.

Characteristics:

  • Excellent dynamic response (bandwidth up to tens of kHz)
  • Not suitable for static force measurement (charge leaks)
  • Ideal for impact force and vibration detection

3. Capacitive

Working Principle: Changes in plate spacing or overlap area cause capacitance changes

\[C = \varepsilon_0 \varepsilon_r \frac{A}{d}\]

Characteristics:

  • High sensitivity
  • Can be fabricated as arrays (tactile skin)
  • Susceptible to electromagnetic interference
  • Nonlinearity requires compensation

4. Optical

Working Principle: Detects force through changes in light intensity or optical path

  • Fiber Bragg Grating (FBG): Strain shifts the reflected wavelength \(\Delta\lambda_B = \lambda_B(1-p_e)\varepsilon\)
  • GelSight type: Elastomer deformation + camera captures surface geometry changes
  • Light barrier type: Force moves a light blocker, changing light flux

Characteristics:

  • Immune to electromagnetic interference
  • Can be embedded within structures
  • GelSight provides rich tactile imagery

Force Sensing Across Different Robots

graph TB
    subgraph "Industrial Manipulator"
        A1[Joint Torque Sensor] --> A2[Collision Detection]
        A3[Wrist 6-axis F/T Sensor] --> A4[Precision Assembly]
        A5[Gripper Force Sensor] --> A6[Grip Force Control]
    end

    subgraph "Legged Robot"
        B1[Foot Force Sensor] --> B2[GRF Measurement]
        B1 --> B3[Contact State Detection]
        B4[Joint Current Estimation] --> B5[Torque Estimation]
    end

    subgraph "Dexterous Hand"
        C1[Fingertip Tactile Sensor] --> C2[Texture Recognition]
        C1 --> C3[Slip Detection]
        C4[Phalanx Force Sensor] --> C5[Grip Force Distribution]
    end

    subgraph "Mobile Service Robot"
        D1[Bumper Strip/Force-sensitive Skin] --> D2[Obstacle Avoidance/Stop]
        D3[End-effector F/T Sensor] --> D4[Safe Interaction]
    end

Force Sensor Selection Reference

Parameter Typical Range Notes
Range 0.1 N ~ 10 kN Choose based on application
Resolution 0.01 N ~ 1 N Precision tasks need high resolution
Sampling Rate 100 Hz ~ 10 kHz Collision detection needs high rate
Dimensions 1-axis ~ 6-axis 6-axis F/T sensor is the most complete
Interface Analog/SPI/I2C/EtherCAT EtherCAT recommended for industrial use
Protection Rating IP20 ~ IP67 Outdoor use requires waterproofing
Overload Protection 2x ~ 10x full scale Prevents damage from collisions

Force Sensing vs. Proprioception

Not all force perception requires dedicated sensors. Many modern robots estimate external torques through motor current:

\[\hat{\tau}_{ext} = K_t \cdot i_{motor} - \hat{\tau}_{friction} - J^T \hat{\tau}_{gravity}\]

Dedicated Force Sensor vs. Current Estimation:

Aspect Dedicated Force Sensor Current Estimation
Accuracy High (0.1% FS) Medium (affected by friction model)
Cost High Low (no additional hardware)
Bandwidth High (>1 kHz) Medium (limited by control loop)
Installation Requires mechanical integration No additional installation
Robustness Sensor may be damaged Depends on model accuracy

Chapter Structure

This chapter delves into the following topics:

  1. 6-Axis Force/Torque Sensor -- The gold standard of industrial force sensing
  2. Tactile Sensors -- From GelSight to tactile skins
  3. Foot Force Sensors -- The "sense of touch" for legged robots
  4. Force Control Applications -- Impedance control, collision detection, and force-guided assembly

References

  • Siciliano, B. et al., Robotics: Modelling, Planning and Control, Ch. 9 Force Control
  • ATI Industrial Automation: ati-ia.com
  • GelSight project: gelsight.com
  • ISO/TS 15066: Robots and robotic devices -- Collaborative robots

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