Sensorless Force Estimation

• Also called: sensorless force sensing, external force estimation, model-based force estimation, proprioceptive force estimation, sensorless torque estimation
• Category: Sensing › Contact & force
• Tags: force-estimation, proprioception, dynamics, collision-detection, actuator-modeling, compliant-control

Estimating the forces and torques a robot exerts on, or receives from, its environment using motor currents, joint states and a dynamic model instead of a dedicated force sensor.

Definition

Sensorless force estimation is the practice of inferring contact forces or external torques on a robot without a dedicated force/torque sensor. It uses signals the robot already measures, such as motor currents and joint positions and velocities, together with a model of the robot's dynamics and actuators. The estimate is the part of the measured actuator effort that the model cannot explain through the robot's own motion, gravity and friction: whatever is left over is attributed to external interaction.

The basic chain starts with motor current. For an electric motor, torque is roughly proportional to current through the torque constant, and passing through the gear ratio gives an approximate joint torque. Subtracting the torque the rigid-body dynamics model predicts for the measured motion gives an estimate of external joint torques. If a single contact location is assumed, these can be mapped to a force at the end effector through the transpose of the manipulator Jacobian. Because accelerations from noisy encoder data are unreliable, common methods avoid them: disturbance observers filter the residual torque, and generalized momentum observers use the robot's momentum to estimate external torque without differentiating velocity.

The largest source of error is usually the actuator rather than the arm. Gearboxes add friction that depends on speed, load, temperature and direction, as well as backlash and torque ripple, and high gear ratios make external forces hard to separate from internal losses. This is why sensorless estimation works best on backdrivable designs such as direct-drive and quasi-direct-drive actuators, and why friction identification is a large part of any implementation. Learned models, such as neural networks that predict actuator torque or friction from motor signals, capture effects that are hard to write down.

Sensorless estimation is less precise than a calibrated force/torque sensor, but it is cheaper, adds no mass or wiring at the wrist, and can detect contact on any link rather than only at the sensor's mounting point. It is widely used for collision detection and for compliant behavior in legged robots.

Why it matters

Force information is needed for collision detection, compliant interaction and contact-rich manipulation, but force/torque sensors are expensive, fragile and measure at only one point. Sensorless estimation gives low-cost robots and legged platforms a usable sense of contact from hardware they already have.

Key applications

• Collision detection — stopping or retracting a robot arm when unexpected contact occurs
• Legged robots — detecting foot contact and estimating ground reaction forces from joint torques
• Low-cost manipulators — enabling compliant control and hand guiding without a wrist sensor
• Surgical and medical robots — estimating tool interaction forces where sensors are hard to fit
• Haptic teleoperation — giving an operator force feedback from estimated contact forces

In practice

A team typically starts by identifying the robot's dynamic and friction parameters from logged motions with no contact, fitting Coulomb and viscous friction for each joint and checking each motor's torque constant. They then run a momentum observer or disturbance observer in the real-time control loop and compare its output against a reference force/torque sensor or known weights to calibrate thresholds. For collision detection they set per-joint thresholds high enough to ignore model error during fast motion but low enough to stop the robot quickly on contact; for force control they accept lower bandwidth and accuracy than a sensor would give, and recheck friction parameters as the robot warms up.

Common misconceptions

• Motor current directly measures joint torque — friction, gear losses and the robot's own dynamics must be subtracted before external forces can be estimated
• Sensorless estimation is as accurate as a force/torque sensor — it is usually noisier and less accurate, especially with high-ratio gearboxes and at low speeds
• It works equally well on any robot — backdrivable, low-friction actuators give far better estimates than highly geared ones
• A joint torque estimate tells you where the contact is — mapping to a Cartesian force requires knowing or estimating the contact location

Who should know this

• Control engineers building compliant and collaborative robots
• Legged robot developers
• Teams designing low-cost manipulators
• Researchers working on actuator modeling and robot safety

Related technologies

• Momentum Observer
• Disturbance Observer
• Force/Torque Sensor
• Quasi Direct Drive
• System Identification
• Manipulator Jacobian

Related terms

• Force/Torque Sensor
• Torque Control
• Backdrivability
• Proprioception

Related projects

• Drake: MIT robotics toolbox for model-based dynamics, optimization, and control system design
• MoveIt 2: Motion planning framework for ROS 2 robot arms, with kinematics and collision checking
• DART: C++ physics engine for articulated rigid body dynamics and robotics simulation
• frax: JAX library for fast, differentiable robot kinematics, dynamics and inverse kinematics
• mjfit: Exact convex collision geometry for MuJoCo pegs, holes, threads and gears