Force, torque and tactile sensing

Position sensors tell a robot where it is; force sensors tell it what it is touching and how hard. They make the difference between a robot that can only follow a programmed path and one that can insert a peg into a tight hole, polish a curved surface, hand an object to a person or stop when it bumps into someone. This lesson explains the strain gauge and the bridge circuit at the heart of most force sensors, builds up to six-axis force-torque sensors and joint torque sensing, and surveys tactile skins. Force control itself, which uses these measurements to command motion, belongs to ROB-300.

Strain gauges

Almost every industrial force sensor measures strain: the tiny fractional change in length of a carefully shaped metal element as it deflects under load. A metal-foil strain gauge is a zigzag pattern of thin foil on a flexible backing, glued to the element. When the element stretches, the foil gets longer and thinner and its resistance rises; when it compresses, the resistance falls. The gauge factor GF relates the fractional resistance change to the strain \( \varepsilon \), and for metal foil gauges it is about 2.

The second equation, Hooke's law, links strain to stress \( \sigma \) through the material's Young's modulus E. The difficulty is scale: a well-designed sensing element is strained to perhaps 500 to 1,000 microstrain (µε, millionths) at full load, so a 350 Ω gauge with GF = 2 changes by only 0.35 to 0.7 Ω, about 0.1 to 0.2 %. Temperature changes the gauge's resistance by a similar amount, so strain gauges are always used in bridge circuits that cancel common effects. Semiconductor gauges have gauge factors of 100 or more but are more temperature-sensitive and nonlinear.

The Wheatstone bridge

A Wheatstone bridge arranges four resistances in a diamond, excited by a voltage \( V_{ex} \) across one diagonal, with the output measured across the other. When all four are equal, the output is zero. If one arm changes slightly, the output becomes a small voltage proportional to the change. Using two or four active gauges, placed where the element is in tension and compression, increases the output and makes the bridge self-compensating for temperature, because a uniform temperature rise changes all arms equally and cancels.

Load cell datasheets quote sensitivity in millivolts per volt (mV/V) at full scale: a 2 mV/V load cell excited at 10 V gives 20 mV at full load. That signal is amplified by an instrumentation amplifier or fed to a dedicated bridge converter with a 24-bit delta-sigma ADC, as ROB-200 described for analog front ends.

Six-axis force-torque sensors

A load cell measures force along one axis. A robot wrist needs all six components of the wrench: three forces \( (F_x, F_y, F_z) \) and three torques \( (T_x, T_y, T_z) \). Six-axis force-torque (F/T) sensors use a monolithic metal element, often shaped like a wheel with spokes or a cross with beams, carrying many strain gauges. Each load direction strains the beams in a different pattern. A calibration matrix C, found by the manufacturer by applying known loads, maps the vector of gauge signals s to the wrench:

Typical F/T sensors for collaborative arms measure up to a few hundred newtons and tens of newton-meters with resolutions around 0.1 N. Using them well involves three corrections. Bias: subtract the reading with no contact before each task, because the zero drifts with temperature. Gravity compensation: the tool's weight produces a force and a torque that change with orientation, and must be subtracted using the tool's mass and center of mass and the current wrist orientation from forward kinematics. Frame transformation: the measured wrench is expressed in the sensor frame and usually needs moving to the tool tip, which changes the torques as \( \mathbf{T}_{tip} = \mathbf{T}_s - \mathbf{r} \times \mathbf{F} \), where r points from the sensor origin to the tip.

Joint torque sensing and current-based estimation

An alternative to a wrist F/T sensor is to measure torque in every joint. Collaborative arms from several manufacturers place a strain-gauge torque sensor between the gearbox and the link in each joint, which lets the controller feel contact anywhere along the arm, not just at the wrist, and supports smooth hand-guiding. Others estimate torque without a dedicated sensor, from motor current through the torque constant (lesson 8): \( \tau \approx k_t\,i\,N\,\eta \) for a gear ratio N and efficiency \( \eta \). Current-based estimation is cheap but blurred by gearbox friction, which can be a large and variable fraction of the torque, especially in high-ratio gearboxes. A third option is the dual-encoder joint from lesson 2: a deliberately compliant element whose deflection, measured by encoders on both sides, gives torque through its known stiffness. Lesson 10 develops that idea as the series elastic actuator.

Tactile sensing

Human fingertips contain thousands of mechanoreceptors that sense pressure, vibration and slip. Robot tactile sensors try to provide some of the same information across a gripper finger or a robot's skin. The main technologies are: resistive arrays, such as force-sensing resistors (FSRs) and piezoresistive textiles, whose resistance falls under pressure (cheap and simple but with large hysteresis and drift, better at detecting contact than measuring force); capacitive arrays, in which pressure compresses a dielectric between electrodes (sensitive and widely used in robot skins and touchscreens); piezoelectric films, which respond to changes in force and are excellent for detecting vibration and slip but not steady pressure; magnetic sensors, which track a magnet embedded in a soft skin; and vision-based tactile sensors, in which a small camera inside the fingertip watches a soft gel deform against an object, giving high-resolution contact images and shear.

Tactile data is useful for detecting first contact (so the gripper can slow down), estimating contact location and object pose in the hand, detecting slip from high-frequency vibrations so that grip force can be increased, and recognizing materials by texture. The engineering challenges are wiring many sensing points, robustness of soft materials and turning large, noisy arrays into useful features. ROB-400, Manipulation and Grasping, uses these signals.

Practical issues

Force sensors live in the load path, so they must survive overloads, such as a collision or a dropped tool, that may be ten times their rated range. Good F/T sensors have mechanical overload stops and specify a separate overload rating. Strain-gauge signals are tiny, so cable routing, shielding and grounding matter, and digital-output sensors that convert near the gauges avoid many problems. Temperature gradients, for instance from a motor heating one side of the wrist, cause drift that simple bias removal cannot fix; re-zero often, and allow warm-up. Finally, any compliance added for sensing reduces the stiffness of the robot, which affects positioning accuracy and the bandwidth of the control loops.