Technical Summary: Intention Assimilation Control for Accurate Tracking with Variable Impedance in Teleoperation

1. Problem Statement

Teleoperation systems typically rely on a spring-like force to pull a follower robot toward a leader's position. This traditional approach presents a fundamental trade-off:

• Low Stiffness: Ensures safety when interacting with delicate objects or humans but results in poor tracking accuracy, especially during dynamic movements.
• High Stiffness: Ensures accurate tracking but poses safety risks in shared environments and can cause instability or "whiplash" effects when the operator rapidly changes impedance.

Existing state-of-the-art solutions, such as Tele-Impedance Control (TIC), attempt to resolve this by estimating the operator's arm impedance (via EMG or grasp force) and matching the follower's impedance to it. However, TIC still transmits the leader's current position as the target. Consequently, if the follower's impedance is low (compliant), it cannot track the leader's trajectory accurately unless the operator maintains high physical stiffness (co-contraction), which is fatiguing and unsustainable. Conversely, if the follower is stiff, it risks damaging the environment.

The core problem addressed is how to enable a follower robot to accurately track a leader's movement while allowing the operator to freely modulate the follower's impedance from low to high, without compromising tracking performance or safety.

2. Methodology: Intention Assimilation Control (IAC)

The authors propose Intention Assimilation Control (IAC), a strategy that decouples tracking accuracy from the follower's instantaneous impedance.

Core Concept

Unlike traditional methods that transmit the leader's current position ($x_l$) to the follower, IAC estimates the leader's target position ($\tau_l$) based on the force applied by the operator and transmits this estimated target to the follower. The follower then tracks this virtual target ($\tau^*$) rather than the leader's instantaneous state.

Control Architecture

1. Target Estimation: The follower estimates the operator's intended trajectory ($\tau^*$) by observing the force applied to the leader robot. This is modeled using an internal model where the target trajectory is a function of time (e.g., fixed position or linear velocity).
2. State Observation: A Kalman filter is employed to estimate the extended state vector, which includes the robot's position, velocity, the target trajectory parameters, and the leader's control input. The observer minimizes the error between the estimated state and the measured state (position, velocity, and force).
3. Control Law: The follower's controller is designed as:
   $$u = -L_1(x - \tau^*) - L_2(\dot{x} - \dot{\tau}^*)$$
   Where $L_1$ and $L_2$ are the follower's stiffness and damping gains. Because the target $\tau^*$ is an estimate of the intended trajectory rather than the current position, the gains $L_1$ and $L_2$ do not need to be high to achieve convergence. They can be set low for safety or modulated dynamically.
4. Impedance Modulation: The operator controls the follower's impedance magnitude via their power grasp force, which linearly correlates with arm endpoint stiffness. This allows for real-time adjustment of the follower's compliance.
5. Stability: To prevent instability when rapidly increasing stiffness (a known issue in impedance control), the rate of stiffness increase is constrained using a condition derived from Kronander and Billard (2016), ensuring the system remains stable even during rapid transitions.

System Dynamics

The paper models the leader and follower robots using standard rigid-body dynamics. The follower's controller compensates for its own dynamics to match the leader's dynamics, effectively creating a "matched" system where the follower mimics the leader's behavior if the control inputs are identical.

3. Key Contributions

• Novel Control Strategy: Introduction of IAC, which shifts the control paradigm from tracking the leader's current position to tracking an estimated target position derived from operator intention.
• Decoupling Accuracy and Impedance: Demonstrating that high tracking accuracy can be maintained even when the follower's impedance is low, overcoming the limitations of TIC.
• Experimental Validation: A comprehensive comparison between IAC and TIC across four distinct experimental scenarios:
  1. Free Tracking: Multi-axis movement with variable impedance.
  2. Soft Interaction: Interaction with a balloon to test safety and compliance.
  3. Peg-in-Hole: A precision task requiring high compliance for alignment but accurate tracking for insertion.
  4. Bilateral Polishing: Force-feedback task where the operator modulates impedance via grasp force.

4. Experimental Results

The study utilized two 7-DOF Franka Emika manipulators with a 100 ms communication delay for unilateral tasks and 0 ms for bilateral tasks.

• Free Tracking:

  • TIC: Tracking error increased sharply when impedance dropped below 400 N/m. At low stiffness (80 N/m), errors exceeded 20 cm. High stiffness caused "whiplash" (rapid acceleration/deceleration) when the operator increased impedance.
  • IAC: Maintained tracking error below 10 cm (hovering around 5 cm) across the entire impedance range (80–1320 N/m). No whiplash was observed.
  • Quantitative: IAC reduced tracking error by a factor of 2.21 compared to TIC across the tested range.

• Balloon Interaction:

  • TIC: Even with a high gain (300 N/m), the follower failed to track accurately in free space and ruptured the balloon upon contact due to poor compliance control.
  • IAC: With a low gain (60 N/m), the follower tracked the leader accurately in free space and interacted gently with the balloon, preventing rupture.

• Peg-in-Hole:

  • Participants: 8 naive users.
  • Success Rate: IAC achieved an 88% success rate within 20 seconds, compared to 50% for TIC ($p=0.02$).
  • Completion Time: Successful trials with IAC took significantly less time (10.0s vs. 17.0s for TIC, $p<0.001$).
  • Mechanism: The improvement was primarily driven by the insertion phase. IAC allowed the follower's orientation to respond correctly to the leader's rotational adjustments, enabling users to "jiggle" the peg out of jams. TIC failed to transmit these rotational corrections effectively when the follower was compliant.

• Bilateral Polishing:

  • IAC successfully maintained low tracking error on the x-y plane even when the operator modulated impedance via grasp force.
  • Force feedback was accurately reflected to the leader in both modalities, confirming stable bilateral operation.

5. Significance and Claims

The paper claims that IAC provides an unprecedented level of control over the follower's position and impedance during both unilateral and bilateral teleoperation.

• Safety and Accuracy: IAC resolves the traditional trade-off, allowing for safe, low-stiffness interactions without sacrificing tracking precision.
• User Freedom: Operators can modulate impedance based on task requirements (e.g., low stiffness for polishing, high for drilling) without needing to physically co-contract muscles to maintain accuracy.
• Robustness: The method is robust to communication delays (tested at 100 ms) and does not require complex passivity algorithms for stability in the tested configurations.
• Practicality: By using power grasp force to estimate impedance, the system avoids the noise and calibration difficulties associated with EMG-based methods, making it more practical for real-world deployment.

The authors conclude that IAC enables robots to accurately replicate human movement while granting the user the freedom to adapt impedance to the environment, a capability that TIC cannot achieve without compromising either safety or performance.