Hardware-as-Regularization

Low-cost passive leader arms enable scalable data collection for imitation learning, but their lack of restoring forces leaves redundant joints unconstrained, yielding highly inconsistent joint-space trajectories. We address this with a low-cost passive joint module (an adjustable mechanical clutch and a 3D-printed spiral spring) that pulls each joint toward a user-defined neutral posture. This passive restoring force acts as a physical prior equivalent to joint-space $L_2$ regularization (“Hardware-as-Regularization”), improving kinematic consistency with shorter completion time than an unregularized arm and preserved movement smoothness.

Experiments show substantial variance reduction over a naive passive arm, trajectory consistency on par with an active virtual spring of the same actuator class, and substantially higher downstream success rates (e.g., 73.3% vs. 36.7% on Block Stacking); a stiffness sweep shows consistency degrading monotonically as stiffness decreases, confirming that mechanical stiffness behaves like a regularization weight.

We add a purely mechanical joint module — a 3D-printed spiral spring with an adjustable Hirth-coupling clutch — that pulls each joint toward a user-defined neutral posture $q_0$. Assuming the operator minimizes physical exertion, teleoperation becomes $$ \min_{q} \; \frac{1}{2} (q - q_0)^T K (q - q_0) \quad \text{subject to} \quad f(q) = x_d, $$ where $K$ is the spring stiffness, $f$ the forward kinematics, and $x_d$ the target pose. This is Tikhonov ($L_2$) regularization in joint space: the problem is strongly convex, so the arm settles into a unique posture. The hardware thus acts as a passive, zero-latency prior that makes demonstrations consistent.

The module uses only 3D-printed parts (PC spring, ABS body), screws, bearings, and a magnetic encoder — about \$100 per arm, vs. ∼\$200 for a naive GELLO and >\$700 for a virtual-spring setup.

• The planar spiral spring deflects in both directions and is well suited to FDM printing.
• Stiffness follows $K = Ebt^3/(12L)$: measured 0.0330 Nm/rad (theory 0.025), consistent across prints (0.0322–0.0335) and after 1,000 cycles. Gravity-loaded J2/J4 use stiffer springs.

With the expert alone, consistency improves monotonically with stiffness ($K=0$ (naive) $\rightarrow K/2 \rightarrow K$). The virtual spring tuned to $K$ is worse than even $K/2$, consistent with the backlash and dead zones of its geared motor.