diff --git a/_data/papers.json b/_data/papers.json
index 3089f43..8172f07 100644
--- a/_data/papers.json
+++ b/_data/papers.json
@@ -2138,6 +2138,17 @@
"zhname": "FastStair:让人形机器人快速跑上楼梯",
"zh_title": "FastStair:让人形机器人快速跑上楼梯"
},
+ {
+ "title": "Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds",
+ "path": "papers/05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds.md",
+ "url": "/papers/05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds.html",
+ "dir": "Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds",
+ "arxiv": "2601.06286",
+ "published_date_zh": "2026年1月9日(arXiv)",
+ "published_date_en": "Jan 9, 2026 (arXiv)",
+ "zhname": "Walk the PLANC:受约束落脚点上的物理引导人形敏捷行走",
+ "zh_title": "Walk the PLANC:受约束落脚点上的物理引导人形敏捷行走"
+ },
{
"title": "Extreme Parkour with Legged Robots",
"path": "papers/05_Locomotion/Extreme_Parkour_with_Legged_Robots/Extreme_Parkour_with_Legged_Robots.md",
diff --git a/papers/05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds.md b/papers/05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds.md
new file mode 100644
index 0000000..e7d075a
--- /dev/null
+++ b/papers/05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds.md
@@ -0,0 +1,187 @@
+---
+layout: paper
+paper_order: 13
+title: "Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds"
+zhname: "Walk the PLANC:受约束落脚点上的物理引导人形敏捷行走"
+category: "Locomotion"
+arxiv: "2601.06286"
+---
+
+# Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds
+**用一个降阶(LIP)落脚规划器在线生成「动力学一致」的参考轨迹,再用控制李雅普诺夫函数(CLF)奖励把 RL 训练引导到这条物理可行的参考上——在踏脚石/稀疏落脚点这类受约束地形上,让 Unitree G1 既敏捷又可靠地精准落脚(真机验证)**
+
+> 📅 阅读日期: 2026-06-30
+>
+> 🏷️ 板块: 05 Locomotion · 踏脚石行走 / 受约束落脚点 / 降阶模型规划 / CLF 引导 RL / 师生蒸馏
+>
+> 🔁 推进轨: 模块轮转(04_WBC → **05_Locomotion**)
+
+---
+
+## 📋 基本信息
+
+| 项目 | 链接 |
+|---|---|
+| arXiv | [2601.06286](https://arxiv.org/abs/2601.06286) |
+| HTML | [arXiv HTML](https://arxiv.org/html/2601.06286) |
+| PDF | [arXiv PDF](https://arxiv.org/pdf/2601.06286) |
+| 项目主页 | [caltech-amber.github.io/planc](https://caltech-amber.github.io/planc/) |
+| 视频 | [YouTube 演示](https://youtu.be/D_CZ_FRYjtc) |
+| 源码 | [匿名仓库 anonymous.4open.science](https://anonymous.4open.science/r/robot_rl-E4FF)(以项目页后续正式开源为准) |
+| **发布时间** | 2026-01-09 (arXiv) |
+| 作者 | Min Dai, William D. Compton, Junheng Li, Lizhi Yang, Aaron D. Ames |
+| 机构 | Caltech AMBER Lab(加州理工) |
+| 平台 | Unitree G1 人形机器人(21 自由度) |
+| 仿真 | IsaacLab / NVIDIA Isaac Sim 训练 → MuJoCo sim-to-sim → G1 真机零样本部署 |
+
+---
+
+## 🎯 一句话总结
+
+> 踏脚石/稀疏落脚点上的人形行走,最难的是**「敏捷」和「精准落脚」要同时满足**:纯 model-free RL 在这种离散、受约束地形上很难学,常常退化成原地站着不动;纯模型法(落脚规划)落脚精准但动作保守、对未建模动力学不鲁棒。**PLANC** 把两者缝起来——用一个 **降阶 LIP 落脚规划器**实时生成「动力学一致」的全状态参考轨迹,再用 **控制李雅普诺夫函数(CLF)奖励**把 RL 策略**引导**到这条物理可行的参考上,最终在 Unitree G1 上实现既快又准、可真机部署的踏脚石行走。
+
+---
+
+## 📌 英文缩写速查
+
+| 缩写 | 全称 | 解释 |
+|---|---|---|
+| LIP | Linear Inverted Pendulum | 线性倒立摆,双足步态规划的经典降阶模型 |
+| HLIP | Hybrid / Horizontal LIP | LIP 的混合系统变体,用于步态周期落脚预测 |
+| RoM | Reduced-order Model | 降阶模型,相对全身动力学的简化表示 |
+| CLF | Control Lyapunov Function | 控制李雅普诺夫函数,用 V(η) 度量输出跟踪误差并约束其衰减 |
+| PPO | Proximal Policy Optimization | 近端策略优化,本文 RL 训练算法 |
+| MPC | Model Predictive Control | 模型预测控制,对比的传统模型法 |
+| DoF | Degree of Freedom | 自由度;G1 共 21 个驱动自由度 |
+
+---
+
+## ❓ 论文要解决什么问题?
+
+1. **受约束落脚点难学**:踏脚石、稀疏/离散落脚点要求脚必须落在指定可行区域,纯 model-free RL 探索效率低,常退化为保守的「原地踏步/站立」。
+2. **敏捷 vs. 精准的矛盾**:既要动态、敏捷地迈步跨越,又要每一步都精准落到目标点,奖励整形很难两全。
+3. **模型法太保守、RL 太脆弱**:传统降阶模型规划落脚精准但对未建模动力学鲁棒性差、动作保守;端到端 RL 鲁棒但缺乏物理结构、训练不稳定。
+
+**目标**:让降阶模型的「物理结构与落脚精度」去引导 RL 的「鲁棒性与动态能力」,在受约束地形上又快又准地行走。
+
+---
+
+## 🔧 方法详解
+
+### 核心:降阶落脚规划器 + CLF 奖励引导 RL
+
+- **降阶 LIP 落脚规划器(实时参考生成器)**:基于线性倒立摆模型,在每个时间步输出一条**动力学一致的全状态参考轨迹**:
+ - **步时(step timing)**:由 LIP 动力学解析计算,使落脚刚好到达目标落脚点;
+ - **质心(CoM)轨迹**:三次样条生成,并通过竖直速度控制做动量调节;
+ - **摆动脚落点**:贝塞尔多项式插值,精确命中受约束的目标落脚点;
+ - **轨道能量调节**:维持期望能量水平(E* ≈ 0.6)以保证持续向前推进。
+- **CLF 引导奖励**:用控制李雅普诺夫函数 V(η) 度量「实际输出 vs. 期望输出」的误差,奖励项鼓励满足衰减条件 V̇(η) ≤ −cV(η),从而把策略学习**塑形到物理一致的轨迹周围**,而不是仅靠手工奖励硬调。
+
+### 师生蒸馏三阶段管线
+
+1. **教师策略**:用特权信息(真值地形高度、接触相位等)训练,先学会高质量的受约束落脚。
+2. **学生蒸馏**:行为克隆把教师蒸馏到不依赖特权信息的学生,去掉对真值的依赖。
+3. **学生微调**:在噪声与部分可观测条件下用 PPO 继续微调,提升真机可部署性与鲁棒性。
+
+### 训练与部署设置
+
+- **仿真**:IsaacLab(NVIDIA Isaac Sim 物理引擎)训练;真机用动捕系统 + 射线投射高程图获取落脚点。
+- **迁移链路**:IsaacLab 训练 → MuJoCo sim-to-sim(楼梯、变高踏脚石、稀疏落脚点的混合地形)→ Unitree G1 真机零样本部署。
+- **平台**:Unitree G1(21 DoF)。
+
+---
+
+## 🧭 整体流程(mermaid)
+
+
+flowchart TB
+ subgraph PLAN["🧮 降阶 LIP 落脚规划器(实时参考)"]
+ TIMING["步时解析
命中目标落脚点"]
+ COM["CoM 样条 + 动量调节"]
+ SWING["摆动脚 Bézier 落点"]
+ ENERGY["轨道能量调节 E*≈0.6"]
+ end
+
+ subgraph TRAIN["🎓 CLF 引导 RL + 师生蒸馏 (IsaacLab)"]
+ CLF["CLF 奖励
V̇(η) ≤ −cV(η) 引导到物理参考"]
+ TEACHER["① 教师: 特权信息训练"]
+ STUDENT["② 学生: 行为克隆去特权"]
+ FINETUNE["③ PPO 微调: 噪声 + 部分可观测"]
+ end
+
+ subgraph DEPLOY["🚀 迁移与部署: Unitree G1 (21 DoF)"]
+ S2S["MuJoCo sim-to-sim
楼梯 / 变高踏脚石 / 稀疏落脚"]
+ REAL["真机零样本
未见石块深度泛化 + 抗扰"]
+ end
+
+ PLAN -->|动力学一致参考轨迹| CLF
+ CLF --> TEACHER
+ TEACHER --> STUDENT
+ STUDENT --> FINETUNE
+ FINETUNE --> S2S
+ S2S --> REAL
+
+ style PLAN fill:#e8eef8,stroke:#2c3e80,color:#1a2452
+ style TRAIN fill:#e8f8e8,stroke:#27ae60,color:#1b5e20
+ style DEPLOY fill:#fff3e0,stroke:#fb8c00,color:#4e342e
+
+
+---
+
+## 💡 核心贡献
+
+1. **物理引导而非纯奖励整形**:用降阶 LIP 规划器在线生成动力学一致的参考,再以 CLF 奖励把 RL 引导到该参考上,兼得模型法的落脚精度与 RL 的鲁棒性。
+2. **CLF 作为可学习的稳定性塑形信号**:把控制李雅普诺夫函数的衰减条件写进奖励,使训练围绕物理一致轨迹收敛,显著优于纯 model-free 基线(后者在难地形上退化为站立)。
+3. **师生蒸馏 + PPO 微调**:从特权教师蒸馏到无特权学生,再在噪声/部分可观测下微调,打通从特权训练到真机部署的链路。
+4. **真机验证的受约束行走**:Unitree G1 上实现踏脚石/稀疏落脚点的敏捷精准行走,对未见石块深度零样本泛化,并能抵抗 ±100 Nm / 0.2s 的外部推力扰动。
+
+---
+
+## 📊 关键实验结果(结构性总结)
+
+| 地形 / 设置 | model-free 基线 | PLANC(本文) |
+|---|---|---|
+| 平面踏脚石(高难度) | 57.6% | **100%** |
+| 变高踏脚石(中难度) | 0% | **99.2%** |
+| 变高踏脚石(高难度) | 0% | **97.2%** |
+| 端到端 RL 无模型引导 | 退化为原地站立 | — |
+| 抗扰 | — | 抵抗 ±100 Nm / 0.2s 推力 |
+| 真机 | — | G1 零样本,泛化到未见石块深度 |
+
+> ⚠️ 消融实验表明:去掉步时自适应或动量调节都会明显掉点,证实两者均必要。详细数值以 arXiv [2601.06286](https://arxiv.org/abs/2601.06286) 论文正文为准。
+
+---
+
+## 🤖 工程价值
+
+- **「规划器当参考 + CLF 当引导」是可迁移范式**:把降阶模型的物理结构作为 RL 的软引导,而非硬约束,适用于踏脚石、沟壑、稀疏落脚点等强离散接触地形。
+- **CLF 奖励提供物理可解释的塑形**:相比堆砌手工奖励项,CLF 衰减条件给出明确的稳定性目标,训练更稳、更不易退化。
+- **师生蒸馏打通部署**:特权教师 → 无特权学生 → PPO 抗噪微调,是从仿真特权信息走向真机的成熟工程路线。
+- **限制**:LIP 是降阶近似,复杂富接触/三维地形下可能损失最优性;真机依赖动捕 + 高程图获取落脚点,野外感知尚未完全自洽;评测以踏脚石/稀疏落脚为主,更广义地形泛化待验证。
+
+---
+
+## 🎤 面试参考
+
+**Q:为什么纯 model-free RL 在踏脚石上会「退化成站着不动」?**
+A:受约束落脚点是强离散、稀疏奖励的探索难题,随机探索很难偶然踩中可行落脚序列;在缺乏物理引导时,策略容易收敛到「不动也不摔」的保守局部最优。PLANC 用降阶规划器提供动力学一致的落脚参考,把探索方向锚定到可行解附近,从而跳出这个退化解。
+
+**Q:CLF 奖励和普通跟踪奖励有什么区别?**
+A:普通跟踪奖励只惩罚瞬时误差;CLF 奖励鼓励满足李雅普诺夫衰减条件 V̇ ≤ −cV,即要求误差**按指数收敛**,提供了带稳定性保证语义的塑形信号,让策略学到的是「能把误差拉回去」的行为,而不只是某一时刻贴近参考。
+
+**Q:降阶 LIP 规划器具体生成哪些参考量?**
+A:解析步时(保证按时落到目标点)、三次样条质心轨迹(含竖直速度的动量调节)、贝塞尔摆动脚落点(命中受约束目标)、以及轨道能量调节(维持 E*≈0.6 保证前进),合起来是一条每步刷新的全状态动力学一致参考。
+
+---
+
+## 🔗 相关阅读
+
+- [FastStair: Learning to Run Up Stairs with Humanoid Robots (2601.10365)](https://arxiv.org/abs/2601.10365) — 同样把基于模型的落脚规划器塞进 RL 回路,面向楼梯攀爬
+- [BeamDojo: Learning Agile Humanoid Locomotion on Sparse Footholds (2502.10363)](https://arxiv.org/abs/2502.10363) — 稀疏落脚点上的敏捷人形运动,另一条路线
+- [APEX: Learning Adaptive High-Platform Traversal for Humanoid Robots (2602.11143)](https://arxiv.org/abs/2602.11143) — 高平台攀爬,富接触多技能编排
+- [Chasing Stability: Humanoid Running via Control Lyapunov Function Guided RL (2509.19573)](https://arxiv.org/abs/2509.19573) — 同样用 CLF 引导 RL,面向人形奔跑
+
+---
+
+> 备注:本笔记基于 arXiv 摘要、[arXiv HTML 正文](https://arxiv.org/html/2601.06286)、[项目主页](https://caltech-amber.github.io/planc/)与公开搜索结果整理;具体数值、奖励权重与网络细节以 arXiv [2601.06286](https://arxiv.org/abs/2601.06286) 论文正文为准。
+
diff --git a/papers/DAILY_SUMMARY_LOG.md b/papers/DAILY_SUMMARY_LOG.md
index a8ac0ad..75cc579 100644
--- a/papers/DAILY_SUMMARY_LOG.md
+++ b/papers/DAILY_SUMMARY_LOG.md
@@ -309,6 +309,7 @@
| — | InterPrior: Scaling Generative Control for Physics-Based Human-Object Interactions | 13_Physics-Based_Animation | ✅ 已完成(2026-06-27) |
| 485 | GENMO: A Generalist Model for Human Motion | 14_Human_Motion | ✅ 已完成(2026-06-28) |
| 64 | PvP: Data-Efficient Humanoid Robot Learning with Proprioceptive-Privileged Contrastive Representations | 04_Loco-Manipulation_and_WBC | ✅ 已完成(2026-06-29) |
-| ? | (下一篇:05_Locomotion 模块首个未完成论文;按 04 → 05 → 06 → 07 → 08 → 09 → 10 → 11 → 12 → 13 → 14 → 04 顺序循环) | 05_Locomotion | ⏭️ 下一篇候选 |
+| 197 | Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds | 05_Locomotion | ✅ 已完成(2026-06-30) |
+| ? | (下一篇:06_Manipulation 模块首个未完成且无笔记的论文;按 04 → 05 → 06 → 07 → 08 → 09 → 10 → 11 → 12 → 13 → 14 → 04 顺序循环) | 06_Manipulation | ⏭️ 下一篇候选 |
> 实际推进时会按当天轮转到的模块在 `papers` 列表中扫描,跳过已有内容的笔记。
diff --git a/papers/PROGRESS.md b/papers/PROGRESS.md
index 143a9ab..56ee4ef 100644
--- a/papers/PROGRESS.md
+++ b/papers/PROGRESS.md
@@ -282,7 +282,7 @@
| 194 | [CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrains](https://arxiv.org/abs/2602.03511) ✅ [笔记](05_Locomotion/CMR__Contractive_Mapping_Embeddings_for_Robust_Humanoid_Locomotion/CMR__Contractive_Mapping_Embeddings_for_Robust_Humanoid_Locomotion.md) | 2026.02 | | ✅ 已总结 |
| 195 | [RPL: Learning Robust Humanoid Perceptive Locomotion on Challenging Terrains](https://arxiv.org/abs/2602.03002) ✅ [笔记](05_Locomotion/RPL__Learning_Robust_Humanoid_Perceptive_Locomotion_on_Challenging_Terrains/RPL__Learning_Robust_Humanoid_Perceptive_Locomotion_on_Challenging_Terrains.md) | 2026.02 | | ✅ 已总结 |
| 196 | [FastStair: Learning to Run Up Stairs with Humanoid Robots](https://arxiv.org/abs/2601.10365) ✅ [笔记](05_Locomotion/FastStair__Learning_to_Run_Up_Stairs_with_Humanoid_Robots/FastStair__Learning_to_Run_Up_Stairs_with_Humanoid_Robots.md) | 2026-06-21 | | ✅ 已总结 |
-| 197 | [Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds](https://arxiv.org/abs/2601.06286) | 2026.01 | | ⏳ 待读 |
+| 197 | [Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds](https://arxiv.org/abs/2601.06286) ✅ [笔记](05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds.md) | 2026-06-30 | | ✅ 已总结 |
| 198 | [SKATER: Synthesized Kinematics for Advanced Traversing Efficiency on a Humanoid Robot via Roller Skate Swizzles](https://arxiv.org/abs/2601.04948) | 2026.01 | | ⏳ 待读 |
| 199 | Walk the PLANC: Physics‑Guided RL for Agile Humanoid LocomotioN on Constrained Footholds | 2026.01 | | ⏳ 待读 |
| 200 | [Do You Have Freestyle? Expressive Humanoid Locomotion via Audio Control](https://arxiv.org/abs/2512.23650) | 2025.12 | | ⏳ 待读 |
diff --git a/progress.json b/progress.json
index 78aa58e..74baef8 100644
--- a/progress.json
+++ b/progress.json
@@ -41,16 +41,25 @@
"13_Physics-Based_Animation",
"14_Human_Motion"
],
- "last_module": "04_Loco-Manipulation_and_WBC",
- "last_index": 64,
- "last_title": "PvP: Data-Efficient Humanoid Robot Learning with Proprioceptive-Privileged Contrastive Representations (arXiv:2512.13093)",
- "next_module": "05_Locomotion"
- },
- "last_summary_index": 64,
- "last_summary_date": "2026-06-29",
- "last_summary_title": "PvP: Data-Efficient Humanoid Robot Learning with Proprioceptive-Privileged Contrastive Representations",
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+ "last_index": 197,
+ "last_title": "Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds (arXiv:2601.06286)",
+ "next_module": "06_Manipulation"
+ },
+ "last_summary_index": 197,
+ "last_summary_date": "2026-06-30",
+ "last_summary_title": "Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds",
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"log": [
+ {
+ "date": "2026-06-30",
+ "index": 197,
+ "title": "Walk the PLANC: Physics-Guided RL for Agile Humanoid Locomotion on Constrained Footholds",
+ "folder": "papers/05_Locomotion/Walk_the_PLANC__Physics-Guided_RL_for_Agile_Humanoid_Locomotion_on_Constrained_Footholds",
+ "module": "05_Locomotion",
+ "arxiv": "2601.06286",
+ "source": "匿名仓库 anonymous.4open.science/r/robot_rl-E4FF(待正式开源)· 项目页 caltech-amber.github.io/planc · Unitree G1 21-DoF 真机 · 模块轮转(04_Loco-Manipulation_and_WBC → 05_Locomotion)"
+ },
{
"date": "2026-06-29",
"index": 64,