Contact Sensing via Joint Torque Sensors and a Force/Torque Sensor for Legged Robots

AI summary

Overview

Research area: Robotics — proprioceptive contact sensing, physical human-robot interaction, and legged robot manipulation/locomotion hardware.

Technical level: Intermediate. The sensing algorithm relies on generalized momentum observers and robot equations of motion, but the motivating problem (a robot leg hitting something it cannot see) is intuitive, and the paper reports its results with concrete hardware numbers.

One-sentence scope: This paper builds a low-cost strain-gauge joint torque sensor, combines it with a single hip-mounted force-torque sensor inside a generalized momentum-based observer, and validates in simulation and on a 2-DoF planar leg that contact can be detected, identified by link, and localized along the leg with force errors below 0.2 N and sub-centimeter position accuracy.

What This Paper Is About

Legged robots typically sense contact only at the foot, so an unexpected collision with the thigh or shank can go undetected and destabilize the robot. The authors ask whether contact anywhere along a robot leg — not just the foot — can be detected, attributed to the correct link, and localized in real time using direct joint torque measurements rather than inferred motor current. Their goal is to achieve this while avoiding complex drivetrain friction models and while using as few additional sensors as possible.

Key Contributions

1. A low-cost custom strain-gauge-based joint torque sensor (fabricated from 6061 aluminum with a full Wheatstone bridge of 1 kΩ gauges at 5 V excitation) that demonstrates high-accuracy torque sensing and measures torque directly at the joint output, bypassing drivetrain friction entirely.
2. A generalized momentum-based observer algorithm that fuses distributed joint torque sensor data with a single base (hip-mounted) force-torque sensor to detect collisions and localize them along robot links.
3. A link-identification rule that determines which link is contacted by finding the highest-indexed residual component exceeding a threshold, plus a closed-form solution for contact location along that link using static moment balance.
4. Hardware experimental validation on a fixed-base 2-link leg showing sub-centimeter contact localization and force errors below 0.2 N, alongside simulation validation on both a fixed-base and a floating-base 2-DoF leg.

Main Findings

• Torque sensor accuracy: Through a calibration procedure, the custom joint torque sensor achieved an average 96.4% accuracy relative to ground truth torque measurements, with an RMSE of 0.0317 Nm and R² = 0.9998, compared to motor-current estimation at RMSE 0.1638 Nm and R² = 0.9609. The sensor's mean absolute error (MAE) was 0.0286 Nm, and its maximum torque capacity before yielding was 8.5 Nm as determined through finite element analysis.

• Calibration linearity: Sensor responses were linear over the operational load range of 0.0196 Nm to 1.962 Nm, with fits y = 0.0115x + 5.0069 (R² = 0.9991) and y = −0.0108x − 2.3260 (R² = 0.9999), confirming minimal hysteresis and good repeatability.

• Fixed-base simulation: In two scenarios (a 5 N force on Link 1 at α = 0.5 and a 7 N force on Link 2 at α = 0.8, both oriented at −π/3 rad), the observer detected the collision after t = 0.5 s, localized the contact to within a few millimeters on a leg measuring roughly 200 mm per link, and produced force errors below 0.15 N.

• Configuration robustness sweep: Across a 10 × 10 grid of joint angle configurations over [0, π] × [0, π] with contacts placed at four positions along each link (α ∈ {0.25, 0.5, 0.75, 1.0}), location error remained below 13.5 mm (approximately 7% of link length) and force error below 0.15 N (about 2% of applied force). An elevated-error line in the heatmap is attributed to configurations where the applied force becomes nearly collinear with local link geometry, making the contact point ambiguous.

• Floating-base simulation: On a planar floating-base leg standing with a joint PD controller, average force estimation error remained below 0.17 N, but with higher variance than the fixed-base case — attributed to transient dynamics as the system stabilizes after contact.

• Hardware results: On a fixed-base 2-DoF planar manipulator, static loading tests gave sub-centimeter location accuracy, with Link 2 outperforming Link 1. Link 1 (thigh), loaded at 0.1 kg and 0.5 kg, showed RMS location errors of 8.89 mm and 7.91 mm with RMS force errors of 0.129 N and 0.174 N. Link 2 (shank), loaded at 0.05 kg and 0.1 kg, showed RMS location errors of 4.09 mm and 4.87 mm with RMS force errors of 0.045 N and 0.106 N. These correspond to approximately 4–4.5% and 2–2.5% of the respective link lengths.

• Sensing rationale: A planar point contact has 3 degrees of freedom (Fx, Fz, and contact position), but a 2-DoF serial chain provides only 2 joint torque measurements, creating an underdetermined system; the base-mounted FT sensor supplies the additional measurements needed for complete localization while remaining effective for contacts on any link.

Methodology in Plain English

The approach rests on a simple physical idea: a robot's momentum changes in a predictable way based on its own dynamics and the torques its motors are producing. Using a generalized momentum formulation, the authors avoid having to numerically differentiate noisy velocity data or invert large inertia matrices, which is what makes direct use of the equations of motion difficult for collision detection in practice.

The team defines a "residual" — a running comparison between the robot's actual momentum and an internal observer's prediction of it. When nothing external touches the robot, the residual stays near zero. When something does, the residual rises. A collision is declared once the residual magnitude exceeds a threshold.

Because a robot is a serial chain, a contact on link c only loads joints 1 through c; joints further down the chain never feel that force. This gives the authors a way to identify which link was hit: find the highest-indexed residual component that exceeds the threshold.

Joint torque sensors alone cannot fully determine contact, since a 2-DoF chain gives only two torque readings for a planar contact with three unknowns. So the authors also mount a commercial six-axis force-torque sensor (PixONE by Bota Systems) at the hip and use only its planar components (Fx, Fz, My). They treat the base as three "virtual joints" (two prismatic, one revolute) and subtract the measured base wrench from the dynamics-derived generalized force to isolate the unexpected external force. Enforcing static moment balance about the base point then yields a closed-form scalar α ∈ [0, 1] describing where along the link the contact lies.

The hardware side involved designing and fabricating the torque sensor, then characterizing it. The team used a full Wheatstone bridge of 1 kΩ strain gauges with 5 V excitation and differential output, reading through a 24-bit ADC (ADS127L21EVM-PDK) connected via an Arduino Due over SPI at 2 MHz baud, yielding a 3–4 kSps sampling rate. A quasi-direct-drive mjbots qdd100 (6:1 gearbox) drove the hip and an mj5208 direct drive motor drove the knee. Encoder positions and velocities came from the mjbots controllers, the hip FT sensor data arrived over a separate channel, and all streams were synchronized and forwarded to MATLAB in real time where the observer ran continuously. Validation used simulations in MATLAB with ode45 and hardware static loading tests with known masses placed at specific fractions of each link length.

Why This Matters

Impact on research. The paper argues that estimating joint torque from motor current is acceptable for quasi-direct-drive motors due to their low gear ratio, but actuators with moderately high gear ratios suffer from nonlinear friction, backlash, hysteresis, and torque ripple that contaminate torque estimates. Measuring torque directly at the joint output sidesteps these effects and removes the need for a friction model. It also shows a practical path to multi-link contact sensing without the extensive, fragile sensing arrays that tactile skins require — hardware that the authors note is poorly suited to the high-impact conditions common in legged robots, which also tend to have slower update rates in tactile approaches.

Real-world applications:

• Legged robots navigating cluttered indoor or disaster-response environments where they must detect and clear obstacles with their limbs, not just their feet.
• Field and industrial inspection robots operating in vegetation, rubble, or tight spaces where undetected limb contact could cause falls.
• Humanoid or quadruped platforms operating near people or equipment, where contact awareness supports safer physical interaction.
• Warehouse and logistics robots that must sense incidental contact with shelving or cargo during movement.

Industry relevance. The sensor is explicitly low-cost and built from 6061 aluminum with commodity strain gauges, which lowers the barrier to adding torque sensing across every joint of a commercial leg rather than relying on motor-current estimates. The paper's framing also gives hardware teams a design rationale for how many sensors a leg needs: distributed torque sensors cover distal links, and a single base force-torque sensor covers proximal links, with the intermediate links acting as a suspension system that protects the fragile FT sensor from direct impact.

Future Directions

• The authors note that a key open challenge is making actuators equipped with torque sensors widely adopted on legged robots — specifically, the ability to endure high impact while still satisfying stringent design specifications. The presented sensor has a maximum torque capacity of 8.5 Nm before yielding, determined via FEA, so impact durability beyond that remains an open question.
• Hardware validation was performed only on a fixed-base 2-DoF planar manipulator; the floating-base results come from simulation alone. Extending hardware validation to a floating-base legged robot, and eventually to a higher-DoF leg or full robot, is a natural next step.
• The floating-base simulation showed higher force-error variance than the fixed-base case, which the authors attribute to transient dynamics as the system stabilizes after contact. Reducing this sensitivity would matter for deployment during dynamic locomotion.
• The parametric sweep revealed that configurations where the applied force is nearly collinear with local link geometry produce ambiguous contact-point solutions and elevated localization error. Handling or flagging these degenerate geometries is an unresolved practical issue. The paper does not state explicit planned future work beyond noting the potential for safe, responsive operation of dynamic legged robots in cluttered environments.

Target Audience

Robotics researchers and graduate students working on legged locomotion, contact sensing, proprioceptive state estimation, and robot hardware design. It is also relevant to engineers building actuated joints who want a concrete comparison between direct torque sensing and motor-current-based torque estimation, and to practitioners deciding how to distribute force and torque sensing across a robot limb. Readers should be comfortable with robot dynamics notation and momentum-based observer concepts to get full value from the derivations, though the experimental results and hardware design are accessible without them.

Authors’ abstract

This paper presents a method for detecting and localizing contact along robot legs using distributed joint torque sensors and a single hip-mounted force-torque (FT) sensor using a generalized momentum-based observer framework. We designed a low-cost strain-gauge-based joint torque sensor that can be installed on every joint to provide direct torque measurements, eliminating the need for complex friction models and providing more accurate torque readings than estimation based on motor current. Simulation studies on a floating-based 2-DoF robot leg verified that the proposed framework accurately recovers contact force and location along the thigh and shin links. Through a calibration procedure, our torque sensor achieved an average 96.4% accuracy relative to ground truth measurements. Building upon the torque sensor, we performed hardware experiments on a 2-DoF manipulator, which showed sub-centimeter contact localization accuracy and force errors below 0.2 N.