嘈杂地形上的帧编码腿式运动
Frame-Coded Legged Locomotion over Noisy Terrain
- Stony Brook University（石溪大学）
- AI Innovation Institute（人工智能创新研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文将腿式运动建模为带擦除的量化有限帧编码，证明等范数Parseval帧在接触缺失时最优，并建立信息-运动不等式与帧编码定理，揭示冗余与鲁棒性的基本极限。
AI中文摘要：
开放循环的多足运动在粗糙地形上已被解释为通过嘈杂信道的物质传输：腿-地面相互作用是离散的基本主动接触，地形删除或扰动这些接触，空间冗余集中了由此产生的推力和到达时间。这种构造类似于重复，因为每个模块都承载相同的标量运动任务。因此，它既不提供正的传输速率，也不提供随幸存接触集变化的解码器。这里我们改为将运动表述为带擦除的量化有限帧展开。一个d维身体级命令被映射到N>d个异构局部接触命令。粗糙地形擦除或破坏帧系数，而接触门控的柔顺形态在物理上实现了加权活动子帧解码器。对于线性高斯模型，机械平衡恰好是后验均值，切线刚度是后验精度，机械柔顺是后验协方差。等范数Parseval帧被证明在缺失一个接触时是最小最大最优的，两个接触的鲁棒性由帧相干性控制，而调和帧给出了可直接实现的步态族。对于独立幸存接触概率q，随机高斯帧在模拟维度速率R<q时允许精确重建，具有二项可靠性指数，而R>q时任意命令的重建是不可能的。残余接触噪声产生渐近每模放大1/(q-R)和阈值处的消失机械刚度裕度。一个信息-运动不等式和一个精确的增量冗余规则将下一个步态分量引向最软的任务相关未解析模式。由此产生的模拟帧编码定理建立了有限相对冗余和逆定理，作为腿式运动基本极限理论的一部分。
英文摘要：
Open-loop multilegged locomotion over rough terrain has been interpreted as matter transport over a noisy channel: leg-ground interactions are discrete basic active contacts, terrain deletes or perturbs those contacts, and spatial redundancy concentrates the resulting thrust and arrival time. That construction is repetition-like because every module carries the same scalar locomotion task. It consequently provides neither a positive task rate nor a decoder that changes with the surviving contact set. Here we formulate locomotion instead as a quantized finite-frame expansion with erasures. A d-dimensional body-level command is mapped into N>d heterogeneous local contact commands. Rough terrain erases or corrupts frame coefficients, while a contact-gated compliant morphology physically realizes the weighted active-subframe decoder. For a linear-Gaussian model, mechanical equilibrium is exactly the posterior mean, tangent stiffness is posterior precision, and mechanical compliance is posterior covariance. Equal-norm Parseval frames are shown to be minimax optimal against one missing contact, two-contact robustness is governed by frame coherence, and a harmonic frame gives a directly realizable gait family. For independently surviving contacts of probability q, random Gaussian gait frames admit exact reconstruction at every analog dimension rate R<q, with a binomial reliability exponent, whereas recovery of arbitrary commands is impossible for R>q. Residual contact noise yields an asymptotic per-mode amplification 1/(q-R) and a vanishing mechanical stiffness margin at the threshold. An information-locomotion inequality and an exact incremental-redundancy rule direct the next gait component toward the softest task-relevant unresolved mode. The resulting analog frame-coding theorem establishes a finite relative redundancy and converse as part of a fundamental limit theory of legged locomotion.
