Admittance Control

The core principle of admittance control is the force-to-motion mapping. An external force or torque measured at the end-effector is fed into a virtual admittance model (often a mass-spring-damper system). This model outputs a desired velocity or positional displacement. The robot's inner position controller then tracks this generated motion command. This creates the perception of a compliant, responsive robot.

• Key Equation: The relationship is often defined as ( F_{ext} = M_d \ddot{x} + B_d \dot{x} + K_d x ), where ( F_{ext} ) is the measured force, and ( M_d, B_d, K_d ) are the desired virtual inertia, damping, and stiffness matrices.

Admittance control is classified as indirect force control. It does not directly command joint torques to achieve a target force. Instead, it uses force measurements to modify a motion reference. This makes it highly compatible with standard industrial robots, which are typically designed as high-gear-ratio, stiff position-controlled devices. The approach effectively wraps a compliant outer loop around a stiff inner position loop.

Admittance control is the dual of impedance control. While both aim to regulate the dynamic relationship between force and motion, their implementations differ fundamentally based on hardware.

• Admittance Control: Measures force, commands motion. Best for stiff, position-controlled robots (common in industry).
• Impedance Control: Measures motion (position/velocity), commands torque. Requires direct-drive or torque-controlled actuators.

The choice hinges on whether the robot's natural hardware behavior is better modeled as an admittance (accepts force, yields motion) or an impedance (accepts motion, yields force).

Accurate implementation depends entirely on high-bandwidth, low-noise force/torque (F/T) sensing. A six-axis F/T sensor mounted at the robot's wrist is standard. The quality of the sensed force data directly limits performance. Issues like sensor noise, calibration drift, and dynamic forces from the robot's own acceleration (gravity compensation is critical) must be carefully managed. Without clean force measurements, the computed motion reference will be erroneous.

A major challenge is maintaining stability during contact with rigid environments. When the robot's commanded motion meets an unyielding surface, the interaction force can spike. The inner position loop's high gain can fight against this, leading to oscillations or instability. Mitigation strategies include:

• Careful tuning of the virtual admittance parameters (especially damping).
• Implementing a lower-bound on the virtual mass.
• Using passivity-based control frameworks to guarantee stability.

Admittance control is the go-to method for collaborative robotics (cobots) and tasks requiring physical human-robot interaction (pHRI).

• Hand Guiding: An operator physically pushes the robot; it moves compliantly.
• Assembly: Inserting a peg into a hole, where contact forces guide the alignment.
• Polishing/Grinding: Maintaining a consistent contact force against a curved surface.
• Medical Robotics: Enabling compliant interaction for rehabilitation or surgical assistance. Its ability to make inherently stiff robots behave softly is its key engineering value.

Admittance control allows a robot to maintain a desired contact force while traversing an unknown or complex surface contour. Key applications include:

• Deburring metal parts.
• Polishing and sanding curved surfaces (e.g., automotive bodies).
• Applying sealant along a seam. The controller adjusts the end-effector's normal position based on force error, ensuring consistent material removal or application pressure regardless of surface variations, unlike pure trajectory tracking which would lose contact or crash.

Admittance control is often implemented on the master side of a teleoperation system. When the human operator moves the master device (e.g., a haptic interface), its low inertia and backdrivability (enabled by admittance control) provide a natural feel. The commanded motion is sent to a slave robot (often using impedance control) to execute the task in a remote environment. Force feedback from the slave can be reflected to the master, allowing the operator to feel contact forces, creating a transparent and intuitive link between human and remote robot.

While both strategies manage interaction dynamics, they are architectural duals. Understanding the distinction is critical for application selection:

• Admittance Control: Force in, motion out. Measures force/torque, computes a motion command. Best for interacting with stiff environments (like a rigid assembly) where accurate force regulation is needed. Requires an accurate inner-loop position controller.
• Impedance Control: Motion in, force out. Commands a motion, but modulates it to achieve a desired force-motion relationship. Best for interacting with soft or dynamic environments (like a human) where compliant behavior is paramount. More naturally stable in unstructured contact. Many advanced systems use a hybrid approach, switching or blending strategies based on task phase.

Impedance control is a robot control strategy that regulates the dynamic relationship between force and motion at the end-effector, making the robot behave as a programmable mass-spring-damper system. It is the conceptual dual to admittance control.

• Key Difference: Impedance control takes a commanded motion as input and outputs the force/torque to achieve it, reacting to external forces by deviating from the trajectory. Admittance control takes measured force as input and outputs a modified motion.
• Use Case: Often preferred for lightweight, direct-drive arms where high-fidelity force control is paramount, as it directly commands joint torques.

A force/torque (F/T) sensor is a transducer that measures the six-dimensional wrench (three forces and three torques) applied at the point where it is mounted, typically between a robot's wrist and its end-effector.

• Critical for Admittance: This sensor provides the essential external force feedback that the admittance controller uses to compute the desired compensatory motion.
• Types: Common technologies include strain gauges and optical sensors. Key specifications include range, resolution, and bandwidth, which directly limit the performance of the admittance control loop.

A series elastic actuator is a robotic actuator that incorporates a compliant element (like a spring) in series with the motor. This design enables accurate force control and intrinsic shock absorption.

• Synergy with Admittance: While admittance control is often implemented with rigid actuators and an external F/T sensor, an SEA provides a built-in, high-fidelity force measurement via spring deflection. This can simplify the implementation of compliant, force-responsive behaviors.
• Benefits: Provides low-impedance output, protects gears from impacts, and allows for energy storage.

Gravity compensation is a feedforward control technique that calculates and commands the joint torques needed to counteract the weight of a robot's own links, allowing it to move as if in zero gravity.

• Prerequisite for Admittance: Effective admittance control requires isolating external contact forces from the robot's own dynamics. Accurate gravity compensation is essential so that the F/T sensor readings reflect only interaction forces with the environment, not the arm's weight.
• Implementation: Relies on a dynamic model of the robot's mass properties and current configuration.

Hybrid force/position control is a framework that explicitly separates control directions into force-controlled and position-controlled subspaces within the same task.

• Comparison to Admittance: While admittance control modulates motion in response to force across all directions, hybrid control pre-defines which Cartesian degrees of freedom (DOF) are under strict position control and which are under strict force control. For example, maintaining a constant force while sliding along a surface.
• Application: Ideal for tasks like insertion, polishing, or assembly where specific constraints are known a priori.

Model predictive control is an advanced control method where a dynamic model of the system is used to predict future behavior and optimize a sequence of control inputs over a receding horizon.

• Integration with Admittance: MPC can be used as the high-level planner that generates the reference trajectory for an admittance-controlled robot. The admittance controller then executes this trajectory while compliantly handling unmodeled contact events and disturbances in real-time.
• Benefit: This combination allows for long-horizon, optimal task planning with robust, short-horizon contact reactivity.