Diffusion-Based Impedance Learning for Contact-Rich Manipulation Tasks
Abstract
Learning-based methods excel at robot motion generation but remain limited in contact-rich physical interaction. Impedance control provides stable and safe contact behavior but requires task-specific tuning of stiffness and damping parameters. We present Diffusion-Based Impedance Learning, a framework that bridges these paradigms by combining generative modeling with energy-consistent impedance control. A Transformer-based Diffusion Model, conditioned via cross-attention on measured external wrenches, reconstructs simulated Zero-Force Trajectories (sZFTs) that represent contact-consistent equilibrium behavior. A SLERP-based quaternion noise scheduler preserves geometric consistency for rotations on the unit sphere. The reconstructed sZFT is used by an energy-based estimator to adapt impedance online through directional stiffness and damping modulation. Trained on parkour and robot-assisted therapy demonstrations collected via Apple Vision Pro teleoperation, the model achieves sub-millimeter positional and sub-degree rotational accuracy using only tens of thousands of samples. Deployed in real-time torque control on a KUKA LBR iiwa, the approach enables smooth obstacle traversal and generalizes to unseen tasks, achieving 100% success in multi-geometry peg-in-hole insertion.
Teleoperated Data Collection for Model Training
Teleoperation is used to guide the robot through physical obstacles, enabling the model to learn how interaction forces vary with pose and context.
Teleoperation is used to record additionally data of patient movements with varying levels of support, enabling the model to learn the dynamic relationship between force and motion.
Model Deployment in Real-World Contact Tasks
For both experiments, the nominal Zero-Force Trajectories (ZFTs) were generated through kinesthetic teaching. The operator manually guided the robot while the robot was in gravity-compensated mode. At relevant configurations, a button on the robot flange was pressed to record the current joint pose. These recorded key configurations were then used to generate smooth nominal trajectories by interpolating between poses using minimum-jerk trajectories and SLERP for orientation. In the parkour task (video left), several key poses defined a trajectory that intentionally passed through the obstacles while maintaining table contact. In the peg-in-hole task (video right), three key poses (start, touch, and insertion) were recorded and interpolated to define the nominal ZFT.
Parkour: kinesthetic teaching of key poses
Peg-in-hole: 3 key poses (start/touch/insert)
These videos compare the robot using constant stiffness parameters (left) versus diffusion-based adaptive impedance (right). With constant stiffness, the robot fails to complete the task due to speed and force limitations. With adaptive impedance, the robot successfully completes the task, smoothly traversing all obstacles.
The robot performs peg insertion tasks with cylindrical, square, and star-shaped pegs using constant stiffness parameters. The cylindrical peg was inserted successfully in 30/30 trials, the square peg in 4/30 trials, and the star peg in none of the 30 trials. These trials highlight the difficulty of choosing feasible fixed impedance in contact-rich environments.
Diffusion-Based Impedance Learning achieved a 30/30 success rate for all three peg types. These results highlight that with increasing insertion complexity, more advanced strategies such as our diffusion-based approach become essential. The outcome is particularly notable because the training data included only parkour and upper-limb rehabilitation data and no peg-in-hole demonstrations.
We performed an ablation study to isolate the contributions of the reconstructed sZFT by the Diffusion Model and the directional impedance adaptation. Therefore, we evaluated the effect of directional stiffness adaptation directly from the nominal ZFT. The results confirm that directional adaptation alone is insufficient if it is derived from the nominal ZFT. Uniform stiffness (high, medium, and low) values failed throughout the experiments.
Diffusion-based Impedance Learning (30/30)
Directional stiffness adaptation from nominal ZFT (0/30)