EquivDP3: A SIM(3)-Invariant Point-Cloud Encoder for Data-Efficient Humanoid Loco-Manipulation

Visuomotor policies for humanoid loco-manipulation must generalize across object poses and lighting from only a handful of demonstrations. 3D Diffusion Policy (DP3) conditions a diffusion-based action generator on point-cloud features, but its PointNet-style encoder has no built-in equivariance to the rotations, translations, and scalings (SIM(3)) that manipulation tasks respect. EquiBot closed this gap for wheeled manipulators with a SIM(3)-equivariant Vector Neuron Network (VNN) encoder. We extend this to a substantially more complex embodiment, the 43-joint Unitree G1 humanoid, and propose EquivDP3: a two-stage policy where a high-level diffusion planner with a SIM(3)-equivariant VNN encoder emits 6 Hz whole-body command chunks, executed at 50 Hz by a frozen, pre-trained RL locomotion policy and a differential inverse-kinematics module for the arms, trained end-to-end by behavior cloning. Across two simulated IsaacLab benchmarks and four non-equivariant baselines (5-100 demonstrations, in- and out-of-distribution), EquivDP3's advantage concentrates in the low-data regime: at 5-10 demonstrations it reaches 67.1% success versus 38.2-52.4% for the baselines, while by 50-100 all encoders converge (74.3-85.2%) and the ordering is no longer meaningful. A proprioception-only control confirms this gap is genuinely perceptual: with the point cloud removed, success drops to 31% vs. 60% (EquivDP3) at 5 demonstrations and 78% vs. 99% at 10, but vanishes by 50-100, showing the high-data plateau reflects a benchmark ceiling, not five encoders learning the same invariance. The encoder costs only 0.8 ms of extra latency per action chunk over the PointNet encoder it replaces. Baking geometric symmetry into a hierarchical diffusion policy's perception backbone is a practical, nearly free way to improve data efficiency for humanoid loco-manipulation when demonstrations are scarce.