Diffusion-Based Impedance Learning for Contact-Rich Manipulation Tasks

TL;DR

Diffusion-Based Impedance Learning, a framework that bridges generative modeling with energy-consistent impedance control, is presented, achieving 100% success in multi-geometry peg-in-hole insertion.

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 realtime 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.

Figures (14)

• Figure 1: Diffusion overview. Bottom: dashed arrows depict the forward process $q(z_t\!\mid\!z_{t-1})$ which gradually corrupts a clean trajectory $z_0$. Top: solid arrows depict the reverse process $p_\theta(z_{t-1}\!\mid\!z_t)$ which is learned to reconstruct structured robotic behavior. Figure adapted from Janner2022.
• Figure 2: Norton equivalent network to represent physical interaction as the combination of a virtual motion source and an impedance source. The displacement $\Delta \bm{x}$ is coupled to stiffness $\bm{K}$ to generate wrench, while the environment contributes external wrenches.
• Figure 3: Diffusion-based reconstruction of the simulated Zero-Force Trajectory (sZFT). The observed pose $\{ \bm{p}, \bm{Q} \}$ together with the external wrench $\bm{F}_{\text{ext}}$ is treated as noise relative to the equilibrium $\{ \bm{p}_0, \bm{Q}_0 \}$. The Diffusion Model iteratively denoises this input to reconstruct the equilibrium trajectory, which is then used in energy-based stiffness estimation.
• Figure 4: Illustration of the nominal Zero-Force Trajectory during deployment (ZFT, light blue) and the reconstructed simulated Zero-Force Trajectory (sZFT, skin color), generated by the Diffusion Model. The ground truth sZFT was created by teleoperation, which tracked the wrist frame {W} and serves as an input to the robot controller to move the end-effector frame {EE}. In the illustration, the ZFT is just a straight line. However, due to the external wrench during contact, the Diffusion Model will reconstruct the sZFT to imitate the demonstrated behavior. Autonomously, the robot will adapt its compliant behavior through impedance to smoothly go over the obstacle.
• Figure 5: Rotational noise scheduling with Spherical Linear Interpolation (SLERP) Shoemake1985. Perturbed quaternions stay on the unit sphere, enabling geometry-consistent noise injection and removal.