Compliant Assembly

A control strategy that regulates the dynamic relationship between the robot's position and the contact force. Instead of strictly tracking a position, the controller makes the end-effector behave like a spring-damper system. Key parameters are:

• Stiffness: How much force resists positional deviation (low stiffness = more compliant).
• Damping: How quickly oscillations from contact settle.
• Inertia: The apparent mass of the end-effector. By tuning these parameters, engineers create a "soft" virtual behavior that allows the peg to deflect and slide into the hole when contact forces are detected, mimicking the skilled "feel" of a human assembler.

The dual approach to impedance control. In admittance control, the measured external force from the sensor is the input, and a resulting motion is the output. The controller implements a desired admittance (inverse of impedance), specifying how much to move per unit of force applied. This architecture is often implemented in an outer loop:

1. Force sensor reads contact.
2. Admittance law computes a velocity or position correction.
3. This correction is sent to the robot's inner position/velocity controller. This method is particularly effective when using high-gear-ratio, position-controlled industrial robots, as it adds a compliant layer on top of their typically stiff mechanics.

A purely mechanical solution using specialized hardware. A Remote Center of Compliance (RCC) device is a passive, spring-loaded mechanism installed between the robot wrist and the end-effector. When a misaligned peg contacts the hole, the RCC allows small, compliant translations and rotations about a virtual center, absorbing insertion forces without requiring sensor feedback or complex control. This is a robust, low-latency solution for high-speed, repetitive assembly tasks with known, consistent part geometries. It exemplifies the principle of mechanical intelligence.

Algorithms that actively use compliance to find the correct mating pose when initial positioning is uncertain. Instead of relying on perfect vision, the robot executes a compliant search pattern:

• Spiral Search: The end-effector moves in an outward spiral while maintaining light contact force, exploring the local area until the hole is found.
• Chamfer Tracking: When a peg contacts the chamfered (beveled) edge of a hole, the robot uses force feedback to slide the peg down the chamfer and into the hole—a classic example of force-guided mating. These strategies combine sensing, control, and geometric understanding to solve assembly where pure precision is impossible or too costly.

A framework that explicitly defines which degrees of freedom are force-controlled and which are position-controlled based on the task geometry. For a classic peg-in-hole insertion:

• Position Control is applied in the axial (insertion) direction and around the axial rotation (to avoid twisting).
• Force Control (or impedance/admittance) is applied in the two lateral directions, allowing the peg to yield to contact forces from the hole's edges. This selective control is defined in a task frame aligned with the assembly direction. It provides a structured methodology for decomposing complex assembly tasks into simpler, orthogonal control objectives, ensuring both precise insertion and safe, compliant interaction.

A primary industrial application is the insertion of pistons into engine blocks or connecting rods onto crankshafts. The chamfer on the piston and cylinder bore guides initial alignment, while a force-controlled robot or remote center of compliance (RCC) device accommodates lateral misalignment and overcomes binding friction. This allows for high-speed, reliable assembly without damaging expensive, precision-machined components.

• Key Technology: Often uses admittance control, where a force sensor commands motion corrections.
• Benefit: Enables automation of tasks previously requiring skilled human fitters due to subtle 'feel'.

Used for inserting connectors, USB ports, or other through-hole components onto printed circuit boards. The compliance compensates for:

• PCB flex and warping during the manufacturing process.
• Small tolerances between pin headers and plated holes.
• Thermal expansion differences between the component and the board. A passively compliant tool or an active force feedback system ensures pins slide into holes without bending, preventing costly board scrap. This is a classic peg-in-hole problem at a miniature scale.

Critical for drilling and riveting operations on aircraft fuselages and wings. A compliant end-effector maintains optimal contact force between the drill bit/rivet gun and the curved, composite workpiece. This ensures:

• Consistent hole quality and countersink depth for structural integrity.
• Prevention of delamination in composite materials.
• Compensation for large-scale part deflections. The system often combines force control with visual servoing to follow seam lines, making the robot 'soft' in the contact direction while remaining rigid in others.

Applied in sterile environments for tasks like inserting syringes into housings, placing stoppers in vials, or assembling auto-injectors. Compliance is essential because:

• Components are often delicate plastic or glass, easily damaged by rigid misalignment.
• Cleanroom constraints limit the use of bulky, corrective fixtures.
• High reliability is non-negotiable. Robots use low-force sensing and gentle impedance control to perform insertions that mimic human dexterity without contamination risk.

Used for inserting dowels, screwing into pre-tapped holes, or aligning cabinet doors. In these consumer goods applications, parts often have higher geometric variability and looser tolerances than machined metal. A compliant strategy allows a single robot program to handle this natural variation without constant re-teaching. For example, a force-torque sensor can detect cross-threading during screw insertion and execute a corrective spiral search pattern, preventing stripped threads.

This is a foundational passive mechanical device that enables compliant assembly without sensors or software. It is a purely mechanical wrist placed between the robot and the tool.

• How it works: It is designed to be very stiff in rotation and translation at the tool tip, but intentionally compliant in lateral directions, with a compliance center located at the tip. When a lateral force is applied during an insertion, the RCC allows the tool to translate and rotate slightly about that center, perfectly aligning the peg with the hole.
• Use Case: Ideal for high-speed, repetitive insertions of rigid parts (like electronic connectors) where an active sensing loop would be too slow. It is a elegant solution to the classic chamfered peg-in-hole problem.

Impedance control is a model-based control strategy that regulates the dynamic relationship between a robot's position and the contact forces it exerts. Instead of tracking position perfectly, it makes the end-effector behave like a programmable spring-damper system.

• The controller establishes a target impedance, defined by virtual stiffness, damping, and inertia parameters.
• When contact occurs, the end-effector deviates from its commanded position in a physically predictable way, absorbing and responding to forces.
• This is often implemented in joint space and is highly effective for tasks requiring gentle, stable contact like polishing or assembly with tight tolerances.

Admittance control is a complementary strategy to impedance control. Here, measured external forces are used to generate a commanded motion. The controller specifies how the robot should move in response to contact.

• A force/torque sensor measures contact.
• The controller uses a desired admittance (inverse of impedance) to translate that force measurement into a velocity or position correction.
• This correction is added to the original trajectory command. This approach is often easier to implement on traditional industrial robots with high-gain position controllers, as it treats force sensing as an outer control loop.

A Remote Center of Compliance (RCC) is a passive mechanical device mounted between the robot and its tool that provides selective compliance to aid in assembly. It is a purely hardware-based solution.

• The RCC is designed to be very stiff in certain directions (e.g., rotation) while compliant in others (e.g., lateral translation).
• Its geometry creates a virtual pivot point (the remote center) in space. When a peg contacts a hole's chamfer, the RCC allows it to tilt and translate slightly, self-aligning for insertion.
• This is a classic, low-cost solution for high-speed, repetitive peg-in-hole tasks where active force sensing and control may be too slow or complex.

Hybrid force/position control is a framework that explicitly decouples control directions into those governed by force and those governed by position. It is the conceptual foundation for many compliant assembly algorithms.

• The task space is decomposed into force-controlled subspaces and position-controlled subspaces based on the geometry of the contact.
• For example, during a peg-in-hole insertion: force is controlled in the axial (insertion) direction, while position is controlled in the two lateral directions to keep the peg centered.
• This requires accurate task frame specification and switching logic between contact states (e.g., search, chamfer crossing, insertion).

Search strategies are the reactive motion primitives used when a robot cannot achieve a assembly goal through pure position control due to uncertainty or friction. They are triggered by force sensing.

• Spiral Search: Upon initial contact, the end-effector executes an outward or inward spiral pattern to locate a feature like a hole's center.
• Linear/Planar Search: The robot moves along a programmed plane, using force thresholds to detect edges or surfaces.
• Force-Guided Alignment: The robot uses measured moment (torque) feedback to actively rotate the part until the moments are minimized, indicating proper angular alignment for insertion.
• These strategies transform a rigid position-controlled task into a sensor-guided, closed-loop process.