Admittance Control

The core principle of admittance control is the force-to-motion mapping. It treats the robot as a programmable mechanical admittance, where measured external forces (F_ext) are input to a virtual dynamic system (specified by desired inertia M_d, damping B_d, and stiffness K_d matrices) to output a commanded motion (position, velocity, or acceleration). The control law is typically formulated as:

M_d * (ẍ_d - ẍ_r) + B_d * (ẋ_d - ẋ_r) + K_d * (x_d - x_r) = F_ext

where x_r is a reference trajectory and x_d is the resulting desired motion sent to the inner position/velocity controller. This creates a predictable, spring-damper-like response to contact.

Admittance control is implemented as an outer-loop around a fast, high-gain inner-loop position or velocity controller. This two-layer structure is critical:

• Outer Loop (Admittance Law): Calculates a desired motion trajectory based on sensed force. It runs at a moderate frequency (e.g., 1 kHz).
• Inner Loop (Position Controller): A standard rigid position controller (e.g., PID) that tracks the trajectory from the outer loop. It runs at a very high frequency (e.g., 8 kHz) to ensure the robot behaves like the desired mass-spring-damper system.

This architecture assumes the inner loop's tracking performance is near-perfect, allowing the designer to focus on tuning the outer-loop admittance parameters (M_d, B_d, K_d) for the desired interactive behavior.

A key advantage of admittance control is its inherent stability when interacting with stiff environments (like a rigid wall). Since the controller outputs a motion command, the actual contact force is determined by the environment's stiffness and the robot's commanded position. This forms a stable feedback loop:

1. Contact force increases.
2. Admittance law commands motion away from the contact.
3. Force decreases.

This contrasts with impedance control, which commands force and can become unstable with stiff environments due to time delays and discrete sampling. Admittance control is therefore often preferred for industrial assembly tasks (e.g., peg-in-hole) and collaborative robotics where contact with rigid structures is common.

The performance of an admittance controller is fundamentally dependent on accurate, low-noise, low-latency force/torque (F/T) sensing. The measured force F_ext is the primary input to the control law. Key sensor requirements include:

• High Bandwidth: Must capture transient contact forces.
• Low Noise: Noise is interpreted as a false force command, causing jittery motion.
• Precise Calibration: To decouple gravitational forces from contact forces.
• Mounting Location: Typically at the robot's wrist, between the last joint and the end-effector, to measure pure interaction forces.

Without high-quality sensing, the admittance behavior becomes unpredictable. Sensor data is often filtered (e.g., with a low-pass filter) to reduce noise, but this introduces phase lag, requiring careful tuning.

Admittance control is often discussed alongside its dual, impedance control. Their fundamental difference lies in the causality of the controlled port (robot end-effector):

• Admittance Control: Force In, Motion Out. It accepts a force and outputs a motion command. It requires an inner-loop position controller.
• Impedance Control: Motion In, Force Out. It accepts a motion deviation and outputs a force/torque command. It typically requires an inner-loop torque controller.

Practical Implications:

• Admittance control is more compatible with standard industrial robots that have high-gain position controllers.
• Impedance control can render lower, more precise impedances and is often used in direct-drive or torque-controlled robots.
• Admittance control is generally more stable in stiff environments; impedance control can be more stable in soft environments.

Admittance control enables robots to perform compliant manipulation tasks that require safe and adaptive physical interaction. Common applications include:

• Compliant Assembly: Performing insertions (e.g., peg-in-hole, screw driving) by allowing the robot to deviate from a planned path based on contact forces.
• Human-Robot Collaboration (HRC): Allowing a collaborative robot (cobot) to yield to human push or guide, enabling hand-guiding teaching and safe co-existence.
• Surface Following: Maintaining consistent contact force while polishing, deburring, or applying sealant along a contoured surface.
• Hand-Guiding: The operator physically moves the robot, with the admittance controller interpreting the human-applied force as a motion command, facilitating quick programming.

In these tasks, the admittance parameters (K_d, B_d) are tuned to be soft (low stiffness) for safety and adaptability, or stiff in specific directions for precision.

Impedance control is the conceptual dual of admittance control. Instead of measuring force to command motion, it commands a force based on measured or commanded motion deviation. It directly regulates the dynamic relationship (stiffness, damping, inertia) between the robot's end-effector position and the contact force. This creates a desired mechanical impedance, making the robot behave like a spring-damper system when contacting the environment. Admittance control is often implemented on position-controlled hardware, while impedance control is typically implemented on torque-controlled hardware.

Force/torque (F/T) sensing is the critical enabling technology for admittance control. An F/T sensor, typically mounted at the robot's wrist, measures the six-axis wrench (three forces and three torques) applied to the end-effector. This real-time measurement is the primary input to the admittance controller. Key sensor characteristics for admittance control include:

• High bandwidth to capture dynamic contact forces.
• Low noise to prevent jittery commanded motions.
• Accurate calibration to decouple gravitational forces from external contact forces.

Compliant assembly is a major application domain for admittance control. Tasks like peg-in-hole insertion, screw driving, or connector mating require the robot to accommodate misalignments by yielding to contact forces. Admittance control enables this by making the robot soft in specific directions. For example, during insertion, the controller can be configured with high stiffness in the insertion axis but low rotational stiffness to allow the peg to align with the hole chamfer based on sensed torques.

MPC is an advanced model-based control strategy that can incorporate admittance-like behavior within an optimization framework. While a basic admittance controller reacts to current forces, an MPC controller uses a dynamic model to predict future states and optimize a sequence of control inputs. It can explicitly handle constraints (e.g., joint limits, force limits) while optimizing for smooth, collision-aware motion. MPC can be extended to force-controlled manipulation by including contact models and force objectives in its cost function, providing a more predictive and optimal form of compliance.

Whole-Body Control is a hierarchical control framework for complex robots (e.g., humanoids, mobile manipulators) that coordinates all degrees of freedom to execute multiple tasks. Admittance control at the end-effector is often implemented as one of several task-level controllers within a WBC architecture. The WBC solver manages potential conflicts by assigning task priorities. For instance, maintaining balance (a high-priority task) for a legged robot might constrain how the arm can comply with external forces during a manipulation task (a lower-priority admittance task).

Collaborative robots are a primary commercial embodiment of admittance control principles. To operate safely alongside humans, cobots often use inherent or controlled compliance. Many cobots implement admittance control using built-in joint torque sensors to detect unexpected contact (e.g., a collision with a human) and respond with compliant motion. This force-limited compliance is a key feature enabling physical human-robot interaction (pHRI) and is a major reason cobots can be deployed without traditional safety cages.