OPENTECHNICAL PUBLICATION OT-2026-000000017 Force Controlled Robotic Insertion with Bounded Spiral Search Published: 2026-09-15T19:01:18.032156Z Permanent URL: https://opentechnical.org/p/OT-2026-000000017 Categories: Robotics & Automation > Robot Control > Force Control ------------------------------------------------------------------------ ABSTRACT This disclosure describes a method for precisely inserting a mating component into a corresponding receptacle using a robotic manipulator. The system employs a force-controlled spiral search pattern to locate the receptacle's opening. The search is bounded by an accumulated lateral force threshold, which prevents galling or damage to the components. Upon exceeding this threshold without successful insertion, the system distinguishes between a jammed state and a seated state. If a jam is detected, the system executes a retry sequence involving a modified approach angle to facilitate engagement, improving insertion reliability for components with tight tolerances or non-ideal alignment. 1. Technical Field [0001] The present disclosure relates generally to automated assembly and, more specifically, to robotic systems and methods for force-controlled insertion operations where precise alignment of components is required. The field encompasses the control of robotic manipulators to perform delicate mating tasks, particularly when there is uncertainty in the exact position or orientation of the target receptacle. 2. Technical Context [0002] Automated assembly processes frequently involve inserting a component into a corresponding receptacle. These operations can be challenging due to manufacturing tolerances, fixturing inaccuracies, and robot positioning errors, which can lead to misalignments between the component and the receptacle. If a component is forced into a misaligned receptacle, galling, deformation, or damage to either part can occur, potentially leading to part rejection or assembly failure. Traditional blind search methods, such as simple spiral searches, may not adequately protect components from such damage if the search boundary is not carefully managed or if a jam condition is not differentiated from a successful seating. The objective is to achieve reliable, damage-free insertion even with initial positional uncertainty, by actively monitoring interaction forces and adapting the insertion strategy. 3. System Overview [0003] The described system (FIG. 1) facilitates automated insertion of a component (20) into a receptacle (22) using a robotic manipulator (10) equipped with an end effector (12) and a force/torque sensor (14). A controller (16) processes feedback from the force/torque sensor (14) to guide the manipulator (10) via a trajectory generator (18). The core of the system is a force-controlled insertion strategy that combines a bounded spiral search pattern with adaptive retry mechanisms. The search pattern is designed to locate the receptacle opening by systematically exploring a localized area. During this search, the system continuously monitors interaction forces, especially lateral forces, to detect contact and to prevent excessive loading that could damage components. A predetermined accumulated lateral force threshold defines the practical boundary of the search. If insertion is not achieved within this boundary, the system analyzes force signatures to differentiate between a jammed condition and a successful seating, and if a jam is detected, it initiates a retry sequence involving a modification of the approach angle. 4. Components [0004] The primary components of the system are detailed below: [0005] - Robot Manipulator (10): This is a multi-axis robotic arm capable of precise position and force control. It provides the necessary degrees of freedom to position and orient the component (20) during the insertion process. The manipulator (10) receives trajectory commands from the trajectory generator (18). - End Effector (12): Attached to the wrist of the robot manipulator (10), the end effector (12) is designed to grasp and securely hold the component (20) that is to be inserted. It may be a gripper, a vacuum cup, or another specialized tool appropriate for the component's geometry and material. - Force/Torque Sensor (14): This sensor is typically mounted between the end effector (12) and the robot wrist, or directly within the end effector (12). It measures forces and torques acting along and about three orthogonal axes (Fx, Fy, Fz, Tx, Ty, Tz). The sensor (14) has a specified resolution, for example, 0.1 N for forces and 0.01 Nm for torques. These measurements are fed back to the controller (16) at a high sampling rate, such as 1000 Hz. - Controller (16): This is the central processing unit of the system. It executes the insertion algorithm, processes sensor data, and generates control signals for the trajectory generator (18). The controller (16) contains logic for interpreting force feedback, managing the search pattern, detecting insertion events, and implementing retry strategies. It typically operates with a control loop frequency of 100 Hz or higher. - Trajectory Generator (18): This module translates high-level commands from the controller (16) into specific joint or Cartesian position commands for the robot manipulator (10). It manages motion profiles, acceleration, and deceleration, ensuring smooth and controlled movements. - Component (20): This is the part being inserted, such as a shaft, pin, or electronic connector. It possesses specific dimensions and material properties that dictate insertion forces and tolerances. - Receptacle (22): This is the target for the component (20), such as a bore, a hole, or a socket. It also has specific dimensions, material properties, and may have chamfers or lead-ins to facilitate insertion. 5. Operation [0006] The insertion process initiates with the robot manipulator (10) positioning the component (20) above the estimated location of the receptacle (22) with a predefined initial offset (FIG. 2). The approach typically involves a vertical downward movement to a standoff distance above the receptacle (22), where contact is anticipated. [0007] - Initial Contact and Axial Search: The component (20) moves downward along the insertion axis. The force/torque sensor (14) monitors axial force (Fz). Upon detecting a sudden increase in Fz, indicating contact with the surface around the receptacle (22), the downward motion halts. The system then retracts slightly to relieve initial contact pressure, establishing a reference point. - Spiral Search Initiation: From this reference point, the system initiates a two-dimensional spiral search pattern in the plane perpendicular to the insertion axis (FIG. 2). The trajectory generator (18) commands the end effector (12) to move in an outward spiral path (34) with a defined pitch and angular velocity. Concurrently, the component (20) maintains a constant, small downward compliance force (e.g., 2-5 N) to allow for slight vertical movement if the hole is found. - Lateral Force Monitoring and Accumulation: During the spiral search, the controller (16) continuously monitors lateral forces (Fx, Fy) measured by the force/torque sensor (14). When the component (20) encounters the edge of the receptacle (22), there will be a sudden increase in these lateral forces. The controller (16) accumulates the magnitude of the lateral forces over time or distance. For example, it might sum the absolute values of Fx and Fy over specific path segments. - Bounded Search Termination: The spiral search continues until one of two conditions is met: - Successful Engagement: A sudden drop in axial force (Fz) combined with a decrease in lateral forces indicates that the component (20) has entered the receptacle (22). At this point, the system transitions to the seating phase. - Accumulated Lateral Force Threshold: The accumulated lateral force exceeds a predefined maximum threshold. This threshold is calculated to prevent galling or damage, for example, 10-20 N accumulated over a 5 mm path segment. Exceeding this threshold without successful engagement indicates that the search has been exhaustive within safe limits (search limit boundary 36) without finding the opening, or that the component is jammed. - Jamming vs. Seating Discrimination: If the accumulated lateral force threshold is met or exceeded without a clear engagement, the system performs a diagnostic step. It attempts a slight downward motion (e.g., 0.5 mm) while monitoring force. - If the axial force (Fz) rapidly increases to a high value (e.g., >50 N) and lateral forces remain elevated, it indicates a jammed condition where the component (20) is wedged against the receptacle (22). - If the axial force (Fz) can be maintained at a low, consistent value (e.g., 5-10 N) and lateral forces reduce, it suggests the component (20) is seated or near seating, but perhaps at a slight angle or with minor friction. - Retry with Modified Approach Angle: If a jammed condition is detected, the system executes a retry sequence. The component (20) is fully retracted from the receptacle (22) to a safe clearance distance. The controller (16) then modifies the approach angle of the component (20) relative to the receptacle (22). This modification might involve a small tilt (e.g., 0.5 to 1.5 degrees) about one or both lateral axes. The entire process, from initial contact, spiral search, and force monitoring, is then repeated with the new approach angle. A limited number of retries (e.g., 1 to 3) with different angles may be configured. If all retries fail, the system may signal a fault or attempt a different recovery strategy. - Seating: Once engagement is achieved, the component (20) is driven downward with a controlled axial force (e.g., 10-20 N) to fully seat it within the receptacle (22). Force and position are monitored to confirm the final seated position. 6. Example Embodiments [0008] Embodiment 1 This embodiment focuses on the insertion of a cylindrical pin into a circular bore. The initial approach positions the pin's axis nominally coaxial with the bore's axis. The spiral search (FIG. 2) is executed with a constant radial pitch, for instance, 0.5 mm per revolution, and a search radius (36) of 5 mm. The accumulated lateral force threshold is set at 15 N over any 3 mm segment of the spiral path. If this threshold is exceeded, indicating excessive friction or misalignment, the system retracts the pin by 2 mm. It then attempts a retry by tilting the pin by 1 degree about the X-axis relative to the bore's estimated normal, and re-executes the spiral search. A second retry would involve a 1-degree tilt about the Y-axis. [0009] Embodiment 2 This embodiment addresses the insertion of a rectangular electronic connector into a corresponding socket. Due to the asymmetric nature of the components, the spiral search pattern is modified to prioritize movement along the primary axes of the connector, for example, an expanding square-wave pattern rather than a continuous spiral. The search starts from a corner of the estimated socket location. The downward compliance force is set to 3 N. The lateral force accumulation is tracked separately for the X and Y axes, with individual thresholds of 8 N for Fx and 12 N for Fy, reflecting the differing resistance along the connector's dimensions. If a jam is detected, the system retracts and applies a small rotational adjustment (e.g., 0.2 degrees) in addition to a tilt of 0.7 degrees about the X-axis, before retrying the search. [0010] Embodiment 3 This embodiment considers the insertion of a component with a conical lead-in into a receptacle with a corresponding chamfer. The initial downward force is set higher, for example, 8 N, to ensure positive contact with the chamfer. The spiral search initiates at a larger radius, 3 mm from the estimated center, to account for the lead-in, and the pitch is increased to 1.0 mm per revolution. The accumulated lateral force threshold is set to 20 N over 4 mm path length. The jam detection logic is refined to also consider sudden increases in torque (Tz) as an indicator of jamming, which might occur with conical features. Upon detection of a jam, the system retracts and executes a single retry with a reduced downward compliance force of 4 N, combined with a 0.8-degree tilt about an axis passing through the component's center, perpendicular to the current approach direction. 7. Alternative Configurations [0011] The force/torque sensor (14) could be integrated directly into the robot's wrist or forearm, rather than between the end effector (12) and the wrist, depending on the robot's design and payload requirements. Alternatively, some manipulators (10) may incorporate intrinsic force sensing capabilities at their joints, which could provide the necessary feedback, albeit with potentially lower resolution or indirect measurement. The end effector (12) could be designed with compliant elements, such as a remote center compliance (RCC) device, to passively absorb some initial misalignment and reduce lateral forces, thereby widening the effective capture range before the active force control intervenes. The trajectory generator (18) could also implement more complex search patterns, such as Lissajous curves or adaptive patterns that prioritize areas based on previous contact points, rather than a simple spiral. 8. Parameter Variations [0012] Parameter | Realistic Range | Effect of Increase | Effect of Decrease Spiral Search Pitch | 0.1 to 2.0 mm per revolution | Faster search, potential to miss small holes, less precise contact detection. | Slower search, higher resolution, more sensitive to minor surface features, increased search time. Search Radius | 3 to 20 mm | Covers larger initial positional uncertainty, increases search time, higher risk of accumulated force. | Faster search, limited ability to compensate for large misalignments, may miss hole if offset is large. Downward Compliance Force | 1 to 10 N | More robust contact, less prone to lifting off, higher potential for friction and galling if misaligned. | Less friction, reduced risk of galling, potential for component to lose contact during search. Lateral Force Threshold | 5 to 50 N (accumulated) | Allows for more force to be exerted before retry, potentially risking damage if set too high. | Triggers retry or fault more readily, potentially before sufficient search, reduced risk of damage. Approach Angle Tilt | 0.5 to 2.5 degrees | Greater change in orientation, may facilitate engagement but could lead to jamming if excessive. | Smaller change, may not be sufficient to resolve jamming, requires more retries for complex misalignments. Number of Retries | 1 to 5 attempts | Increases overall cycle time if retries are frequent, higher chance of eventual success for complex cases. | Faster failure detection, less robust to persistent misalignments, may indicate fault prematurely. Sampling Rate of Sensor | 100 to 1000 Hz | More responsive force control, better detection of transient contact events, higher computational load. | Slower response, potential to miss brief contact, reduced accuracy in force signature analysis. 9. Additional Implementations [0013] The disclosed system can be extended to include real-time visual feedback from a camera mounted on the end effector (12). This vision system could provide a coarse initial estimate of the receptacle's (22) position, reducing the required search radius (36) and search time. Furthermore, the force/torque sensor (14) data could be used not only for detection but also for active compliance control during the entire insertion process, allowing the robot to dynamically adjust its stiffness or damping to accommodate part variations. For applications with very high precision requirements, the system could incorporate a fine-adjustment stage, such as a piezoelectric actuator, mounted on the end effector (12) to provide sub-micrometer positioning corrections based on fine force feedback or vision data, particularly during the final seating phase. The logic for distinguishing jamming from seating could also be enhanced using machine learning algorithms trained on various force-time profiles associated with different insertion outcomes. 10. Figures FIG. 1 A block diagram illustrating the primary components and data flow within the force-controlled insertion system. FIG. 2 An overhead view showing the general path of the end effector during a spiral search for a receptacle, indicating the search parameters. FIGURES FIG. 1 A block diagram illustrating the primary components and data flow within the force-controlled insertion system. FIG. 2 An overhead view showing the general path of the end effector during a spiral search for a receptacle, indicating the search parameters. ------------------------------------------------------------------------ OpenTechnical publication OT-2026-000000017 Published 2026-09-15T19:01:18.032156Z https://opentechnical.org/p/OT-2026-000000017