Friction Margin: From Climbing to DexHands

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Why climbers care about friction (and why robots should too)

Core idea: estimate the friction margin, not “the friction”

Watching Alex Honnold climb, the key mental model is simple: continuously estimate how much friction budget you have left. In mechanics, the contact constraint is ‖Ft‖ ≤ μN. The actionable quantity is the margin: m = μeffN − ‖Ft‖.

For dexterous hands, “robust grasping” is mostly “keep m positive under uncertainty”.

Friction cone Margin Uncertainty Pre-slip

From rock to robot: what changes?

  • μ is not a constant: surface films (dust/oil/water), temperature, speed, and material compliance all change μeff.
  • Slip is not binary: incipient slip starts locally (edges), then propagates. Early warnings matter.
  • Contact area and pressure distribution change the effective constraint (smearing vs edging in climbing; soft pad vs hard edge in hands).

What sensing should optimize for

Design the sensing stack around three questions:

  • Can we estimate N and Ft (or their proxies) at the contact?
  • Can we detect incipient slip before macroscopic slip?
  • Can we update μeff online (even roughly) to keep margin under control?
Minimal friction-aware loop

  Sensors:
    N (normal) + Ft (shear proxy) + pre-slip cue (micro-slip/vibration)

  Estimator:
    mu_eff <- online update (filtered / Bayesian / probe)
    margin m = mu_eff * N - |Ft|

  Controller:
    keep m >= m_min by adjusting:
      - normal force (grip)
      - contact area / pose (regrasp, roll)
      - tangential load (trajectory / impedance)

Sensing options that map to “climbing friction”

  • Force/torque: fingertip normal + wrist 6D F/T (best if you can afford it).
  • Shear + micro-slip: shear taxels, or infer shear from deformation field (visuotactile).
  • Vibration / stick-slip: small IMU near fingertip, or vibro-acoustic pickup on the structure.
  • Contact patch: contact area + pressure distribution to predict where slip will start.
  • Surface state proxies: temperature / humidity / contamination class (even coarse helps explain μ drift).

Rate-and-state friction as a useful mental model

In many real contacts, μ depends on sliding speed and “state” (aging / film / contact history). You don’t need the full theory to benefit: treat μeff as a latent variable with slow drift, and update it when your pre-slip cues and force balance disagree.

Practical evaluation: what to measure in experiments

  • Margin tracking: how often m crosses below 0 before recovery?
  • Pre-slip lead time: how early can you detect slip onset (ms) at given loads?
  • Robustness: performance across surface changes (dry/wet/dusty), temperature, and object materials.
  • Data usefulness: can logged signals support learning a reusable μ estimator?

把攀岩的“摩擦估算”借给灵巧手

核心不是“摩擦系数是多少”，而是“还剩多少摩擦裕度”

看 Alex Honnold 攀岩，最关键的能力其实是：在不确定接触面上实时估算“我还能靠摩擦撑多久”。 物理约束是 ‖Ft‖ ≤ μN。对机器人最有用的量是摩擦裕度： m = μeffN − ‖Ft‖。

灵巧手的稳定抓取，本质上就是：在 μ 不确定时，仍然让 m 保持为正，并且能够提前发现 m 在变小。

摩擦锥 摩擦裕度 不确定性 预滑

攀岩摩擦学对灵巧手的三条迁移

  • μ 不是常数：粉尘/油膜/水膜、温度、速度、材料粘弹性都会改变 μeff。
  • 滑移不是二元事件：通常从局部（边缘微滑）开始，再扩展成宏观滑移。
  • 接触面积与压力分布很重要：攀岩的 smearing/edging，等价于机器人里“软指腹贴合 vs 硬边点接触”。

传感方案应该围绕三个问题来设计

  • 能否测到 N 和 Ft（或可靠代理量）？
  • 能否在宏观滑移前发现预滑（微滑/振动/接触斑点变化）？
  • 能否在线更新 μeff（哪怕粗糙），从而直接控制摩擦裕度 m？
最小“摩擦感知”闭环

  传感：
    N(法向) + Ft(切向代理) + 预滑线索(微滑/振动/接触斑点位移)

  估计：
    mu_eff <- 在线更新(滤波/贝叶斯/小幅主动探测)
    m = mu_eff * N - |Ft|

  控制：
    让 m >= m_min，通过：
      - 调整法向力(抓紧/放松)
      - 调整接触面积/姿态(滚动/复抓)
      - 调整切向载荷(轨迹/阻抗)

对应到传感器：哪些东西最“像攀岩”

  • 法向 + 切向：指尖法向力 +（最好有）腕部 6D F/T。
  • 剪切/预滑：剪切 taxel，或用视触觉从形变场推断切向载荷与微滑。
  • 振动谱 / stick–slip：指尖附近 IMU，或结构声学拾音（对粘着-滑移很敏感）。
  • 接触斑点：接触面积与压力分布，预测“从哪里先滑”。
  • 表面状态代理：温度/湿度/污染等级（哪怕粗略，也能解释 μ 漂移）。

可借用的理论：速率-状态摩擦（rate-and-state）

很多真实接触里，摩擦取决于速度与“状态”（接触老化/表面膜/历史）。 工程上不必完整复刻：把 μeff 当作缓慢漂移的隐变量，用预滑线索与力平衡残差来校正它， 就能把“摩擦不确定”变成“可控的不确定”。

怎么评测：不要只测“有没有滑”，要测“裕度控制得好不好”

  • 裕度穿越率：m 变成负之前，系统是否能触发恢复？频率多高？
  • 预滑提前量：在给定载荷下，能提前多少毫秒发现滑移趋势？
  • 跨表面鲁棒性：干/湿/粉尘、不同材料、温度变化下是否稳定？
  • 数据可学习性：记录的信号是否足以训练通用的 μ 估计器？