Steven Man

Naomi Oke, Aja Carter, Ben Gu et al.

Scaling the design of robots up or down remains a fundamental challenge. While biological systems follow well-established isometric and allometric scaling laws relating mass, stride frequency, velocity, and torque, it is unclear how these relationships translate to robotic systems. In this paper, we generate similar allometric scaling laws for bipedal robots across three orders of magnitude in leg length. First, we conduct a review of legged robots from the literature and extract empirical relationships between leg length (L), body length, mass, and speed. These data show that robot mass scales more closely to L^2, in contrast to the L^3 scaling predicted by isometric scaling. We then perform controlled simulation studies in Drake using three variants of real quasi-passive, hip-actuated walkers with different foot geometries and control strategies. We evaluate the performance of each design scaled with leg length, L. Across all robots, walking velocity follows the expected L^(1/2) trend from dynamic similarity. Minimum required torque scales more closely with m*L than the isometric model of m*L^2. Foot geometry scaled proportionally with L^1. These results provide new insight into how robot designs allometrically scale to different sizes, and how that scaling is different from isometric or biological scaling laws.

Kensuke Nakamura, Arun L. Bishop, Steven Man et al.

Latent safety filters extend Hamilton-Jacobi (HJ) reachability to operate on latent state representations and dynamics learned directly from high-dimensional observations, enabling safe visuomotor control under hard-to-model constraints. However, existing methods implement "least-restrictive" filtering that discretely switch between nominal and safety policies, potentially undermining the task performance that makes modern visuomotor policies valuable. While reachability value functions can, in principle, be adapted to be control barrier functions (CBFs) for smooth optimization-based filtering, we theoretically and empirically show that current latent-space learning methods produce fundamentally incompatible value functions. We identify two sources of incompatibility: First, in HJ reachability, failures are encoded via a "margin function" in latent space, whose sign indicates whether or not a latent is in the constraint set. However, representing the margin function as a classifier yields saturated value functions that exhibit discontinuous jumps. We prove that the value function's Lipschitz constant scales linearly with the margin function's Lipschitz constant, revealing that smooth CBFs require smooth margins. Second, reinforcement learning (RL) approximations trained solely on safety policy data yield inaccurate value estimates for nominal policy actions, precisely where CBF filtering needs them. We propose the LatentCBF, which addresses both challenges through gradient penalties that lead to smooth margin functions without additional labeling, and a value-training procedure that mixes data from both nominal and safety policy distributions. Experiments on simulated benchmarks and hardware with a vision-based manipulation policy demonstrate that LatentCBF enables smooth safety filtering while doubling the task-completion rate over prior switching methods.