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+# Hector 仿真项目分析报告
+
+## 项目概述
+
+**项目名称**: HECTOR - Humanoid for Enhanced ConTrol and Open-source Research (增强控制和开源研究人形机器人)
+
+**开发单位**: USC Dynamic Robotics and Control Laboratory (南加州大学动态机器人与控制实验室)
+
+**项目类型**: MATLAB/Simulink 双足人形机器人仿真软件
+
+**许可证**: 3-Clause BSD License (开源)
+
+## 核心功能
+
+本项目是一个基于 MATLAB/Simulink 的人形机器人完整仿真系统，主要用于:
+1. 双足机器人的动力学仿真
+2. 基于力和力矩的模型预测控制 (Force-and-Moment-based MPC)
+3. 高动态步态控制与规划
+4. 机器人行走、跳跃、跑步等运动模式的研究
+
+## 技术架构
+
+### 1. 核心依赖
+
+- **MATLAB & Simulink 2023a+**: 主要开发平台
+- **Simscape Multibody**: 物理引擎和机械系统建模
+- **CasADi**: 符号计算和优化框架
+- **qpOASES**: 二次规划求解器（用于 MPC 实时优化）
+
+### 2. 系统要求
+
+- 推荐 Windows 10 及以上系统
+- Linux 系统可运行但可能需要调整路径定义
+
+## 项目结构
+
+```
+Hector_Simulation-Matlab_Simulation/
+├── Hector_Simulation.slx          # 主 Simulink 仿真模型
+├── Initiate_Simulation.m          # 仿真初始化脚本
+├── Functions/                      # 核心控制算法库
+│   ├── LocomotionMPC_qpoases.m    # MPC 控制器实现
+│   ├── Swing_PD.m                 # 摆动腿 PD 控制
+│   ├── JacobianMapping.m          # 雅可比映射
+│   ├── Formulate_Contact_Jacobian.m  # 接触雅可比计算
+│   ├── Arm_Controller.m           # 手臂控制器
+│   ├── AssignMPCStage.m          # MPC 阶段分配
+│   └── misc/                      # 辅助函数
+│       ├── foot_to_joint.m       # 足端到关节映射
+│       ├── Rx.m, Ry.m, Rz.m      # 旋转矩阵
+├── Readme.md                      # 英文说明文档
+└── License.md                     # BSD 许可证
+
+```
+
+## 核心算法详解
+
+### 1. 模型预测控制 (MPC) - `LocomotionMPC_qpoases.m`
+
+**算法特点**:
+- 基于力和力矩的 MPC 框架
+- 预测时域: 10 步
+- 使用 qpOASES 进行实时二次规划求解
+- 支持多种步态模式（站立、行走、跳跃）
+
+**关键参数**:
+- 步态周期: 0.4 秒 (可调)
+- MPC 采样时间: 0.04 秒
+- 优化变量: 12×h (h=10 个预测步)
+- 约束数量: 34×h
+
+**实现的功能**:
+- 质心位置和速度跟踪
+- 姿态稳定控制
+- 接触力优化
+- 欧拉角连续性处理（处理 2π=0 关系）
+
+### 2. 摆动腿控制 - `Swing_PD.m`
+
+**控制策略**:
+- 基于启发式足部落点策略
+- 自适应频率步态规划
+- PD 反馈控制
+
+**关键功能**:
+- 足部轨迹规划（抬腿高度: 0.12m）
+- 步态调度器（walking/hopping/running）
+- 速度反馈补偿
+- 机体姿态补偿
+
+**PD 增益**:
+```matlab
+Kp = diag([100 100 100 100 5])  % 位置增益
+Kd = diag([2 2 2 2 0.1])        # 速度增益
+```
+
+### 3. 接触雅可比计算 - `Formulate_Contact_Jacobian.m`
+
+**功能**: 
+- 计算足部接触点的雅可比矩阵
+- 建立广义接触力到关节力矩的映射
+
+**输出**:
+- Contact_Jacobian: [12×5] 雅可比矩阵
+- Rotm_foot: 足端姿态矩阵
+
+**机器人腿部配置**:
+- 5 个关节每条腿: hip_yaw, hip_roll, hip_pitch, knee, ankle
+- 使用符号计算 (CasADi) 自动求导
+
+### 4. 雅可比映射 - `JacobianMapping.m`
+
+**功能**: 将 MPC 输出的接触力和力矩映射为关节驱动力矩
+
+**映射关系**:
+```
+τ = J_c^T × (-u)
+```
+其中:
+- τ: 关节力矩向量
+- J_c: 接触雅可比
+- u: MPC 输出的广义力
+
+### 5. 手臂控制器 - `Arm_Controller.m`
+
+**控制模式**:
+1. 启发式摆臂: 手臂运动与对侧腿部协调
+2. 固定位置: 手臂保持固定姿态
+
+**关节配置**:
+- 每个手臂 3 个关节: shoulder_roll, shoulder_pitch, elbow
+- PD 控制增益: Kp=50, Kd=2
+
+## 机器人模型参数
+
+### 物理参数
+
+**初始状态**:
+- 初始高度: 0.525m
+- 初始速度: [0, 0, 0] m/s
+- 初始姿态: [0, 0, 0] deg
+
+**关节限位**:
+- Hip Yaw: ±30°
+- Hip Roll: ±18°
+- Hip Pitch: -120° ~ 120°
+- Knee: -160° ~ -15°
+- Ankle: -75° ~ 75°
+
+**接触参数**:
+- 地面刚度: 1×10^5 N/m
+- 地面阻尼: 1×10^3 N·s/m
+- 摩擦系数: μ_s = μ_k = 1.0
+- 接触点配置: 每只脚 15 个点（3 排 × 5 点）
+
+### 控制参数
+
+**步态参数**:
+- 步态模式: 0=站立, 1=行走, 2=跳跃, 3=跑步
+- 默认步态周期: 0.4 秒
+- 预测时域: 10 步
+- 步长反馈系数: K_step = 0.03
+
+## 主要学术贡献
+
+本项目实现了以下论文的算法:
+
+**论文标题**: "Force-and-moment-based model predictive control for achieving highly dynamic locomotion on bipedal robots"
+
+**作者**: Junheng Li, Quan Nguyen
+
+**发表**: 2021 IEEE Conference on Decision and Control (CDC)
+
+**核心创新**:
+1. 基于力和力矩的 MPC 框架，突破传统 ZMP 方法限制
+2. 实现了高动态双足运动（包括跑步、跳跃）
+3. 开源实现，便于研究复现和扩展
+
+**相关研究**:
+- 自适应频率 MPC 用于不平整地形行走
+- 动态步态切换
+- 鲁棒性控制设计
+
+## 使用方法
+
+### 安装步骤
+
+1. 下载并解压本仿真软件到指定目录
+2. 下载 CasADi MATLAB 库到同一目录
+3. 安装 MATLAB 2023a 或更高版本
+
+### 运行流程
+
+1. 启动 MATLAB 2023a+
+2. 将整个仿真文件夹和 CasADi 库添加到 MATLAB 路径
+3. 运行 `Initiate_Simulation.m` 加载模型和参数
+4. 打开 `Hector_Simulation.slx` 并根据需要修改
+5. 按 Ctrl+D 构建模型
+6. 在 Mechanics Explorer 中运行仿真（非实时）
+7. 可选：注释/取消注释手臂模块
+
+### 可配置参数
+
+在 `Initiate_Simulation.m` 中可以修改:
+
+**步态参数**:
+```matlab
+gait = 1;            % 步态模式选择
+gaitcycle = 0.4;     % 步态周期
+lift_height = 0.12;  % 抬腿高度
+```
+
+**MPC 参数**:
+```matlab
+h = 10;                    % 预测时域
+dt_MPC = gaitcycle/10;     % MPC 采样时间
+```
+
+**物理参数**:
+```matlab
+contact_stiffness = 1e5;   % 接触刚度
+contact_damping = 1e3;     % 接触阻尼
+mu_s = 1.0;                % 静摩擦系数
+```
+
+**初始状态**:
+```matlab
+body_z0 = 0.525;           % 初始高度
+body_v0 = [0 0 0];         % 初始速度
+```
+
+## 扩展功能
+
+### 1. 不平整地形支持
+
+代码中包含网格地形定义功能:
+```matlab
+x_grid = -1:0.01:5;
+y_grid = -1:0.01:1;
+[X,Y] = meshgrid(x_grid,y_grid);
+z_heights = [0.05*cos(2*pi*X)-0.05]';
+```
+
+使用时需在 Simulink 模型中切换到 "Mesh Grid Surface"
+
+### 2. 变步长 MPC
+
+支持自适应采样时间的 MPC，通过 `AssignMPCStage.m` 实现:
+- 可根据步态阶段动态调整 MPC 采样时间
+- 适用于自适应频率步态控制
+
+### 3. 可选手臂模块
+
+通过设置 `addArm` 变量控制:
+```matlab
+addArm = 0;  % 不包含手臂
+addArm = 1;  % 包含手臂
+```
+
+## 技术优势
+
+1. **完整开源**: 提供完整的仿真和控制代码
+2. **高动态性能**: 支持跑步、跳跃等高难度动作
+3. **先进算法**: 基于最新的力-力矩 MPC 框架
+4. **易于扩展**: 模块化设计，便于添加新功能
+5. **学术支持**: 有对应的学术论文和理论支撑
+6. **可视化**: 使用 Simscape Multibody 提供 3D 可视化
+
+## 应用场景
+
+1. **研究**: 双足机器人控制算法研究
+2. **教学**: 机器人学、控制理论课程教学
+3. **开发**: 人形机器人控制器设计和测试
+4. **验证**: 控制算法在实际机器人前的仿真验证
+
+## 潜在改进方向
+
+1. **实时性优化**: 当前仿真非实时，可优化求解速度
+2. **鲁棒性增强**: 添加外力扰动处理
+3. **地形感知**: 集成视觉/感知系统
+4. **学习方法**: 结合机器学习优化步态
+5. **硬件接口**: 添加与真实机器人的接口
+
+## 联系信息
+
+**项目负责人**: Junheng Li
+**邮箱**: junhengl@usc.edu
+
+**致谢**: 
+- Zhanhao Le
+- Han Gong
+
+对开源软件的贡献。
+
+## 引用格式
+
+如果使用本软件进行研究，请引用:
+
+```bibtex
+@inproceedings{li2021force,
+  title={Force-and-moment-based model predictive control for achieving highly dynamic locomotion on bipedal robots},
+  author={Li, Junheng and Nguyen, Quan},
+  booktitle={2021 60th IEEE Conference on Decision and Control (CDC)},
+  pages={1024--1030},
+  year={2021},
+  organization={IEEE}
+}
+```
+
+## 总结
+
+Hector 仿真项目是一个功能完整、技术先进的双足人形机器人仿真平台。它不仅实现了最新的力-力矩 MPC 控制算法，还提供了完整的开源代码和详细的文档，非常适合机器人控制领域的研究人员和学生使用。
+
+**主要特点**:
+- ✅ 完整的双足机器人动力学模型
+- ✅ 先进的 MPC 控制框架
+- ✅ 多种步态模式（站立/行走/跳跃/跑步）
+- ✅ 模块化、可扩展的代码结构
+- ✅ 完整的开源和学术支持
+- ✅ 3D 可视化仿真环境
+
+**适用人群**:
+- 机器人学研究人员
+- 控制理论研究者
+- 机器人工程专业学生
+- 人形机器人开发者
+
+本项目为双足机器人控制研究提供了一个优秀的起点和参考实现。
diff --git a/PROJECT_ANALYSIS_EN.md b/PROJECT_ANALYSIS_EN.md
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+# Hector Simulation Project Analysis Report
+
+## Project Overview
+
+**Project Name**: HECTOR - Humanoid for Enhanced ConTrol and Open-source Research
+
+**Developer**: USC Dynamic Robotics and Control Laboratory
+
+**Project Type**: MATLAB/Simulink Bipedal Humanoid Robot Simulation Software
+
+**License**: 3-Clause BSD License (Open Source)
+
+## Core Functionality
+
+This project is a complete humanoid robot simulation system based on MATLAB/Simulink, primarily used for:
+1. Bipedal robot dynamics simulation
+2. Force-and-Moment-based Model Predictive Control (MPC)
+3. Highly dynamic gait control and planning
+4. Research on robot walking, hopping, running, and other locomotion modes
+
+## Technical Architecture
+
+### 1. Core Dependencies
+
+- **MATLAB & Simulink 2023a+**: Main development platform
+- **Simscape Multibody**: Physics engine and mechanical system modeling
+- **CasADi**: Symbolic computation and optimization framework
+- **qpOASES**: Quadratic programming solver (for MPC real-time optimization)
+
+### 2. System Requirements
+
+- Recommended: Windows 10 and above
+- Linux systems can run but may require path adjustments
+
+## Project Structure
+
+```
+Hector_Simulation-Matlab_Simulation/
+├── Hector_Simulation.slx          # Main Simulink simulation model
+├── Initiate_Simulation.m          # Simulation initialization script
+├── Functions/                      # Core control algorithm library
+│   ├── LocomotionMPC_qpoases.m    # MPC controller implementation
+│   ├── Swing_PD.m                 # Swing leg PD control
+│   ├── JacobianMapping.m          # Jacobian mapping
+│   ├── Formulate_Contact_Jacobian.m  # Contact Jacobian calculation
+│   ├── Arm_Controller.m           # Arm controller
+│   ├── AssignMPCStage.m          # MPC stage assignment
+│   └── misc/                      # Utility functions
+│       ├── foot_to_joint.m       # Foot to joint mapping
+│       ├── Rx.m, Ry.m, Rz.m      # Rotation matrices
+├── Readme.md                      # Documentation
+└── License.md                     # BSD License
+```
+
+## Core Algorithm Details
+
+### 1. Model Predictive Control (MPC) - `LocomotionMPC_qpoases.m`
+
+**Algorithm Features**:
+- Force-and-moment-based MPC framework
+- Prediction horizon: 10 steps
+- Real-time quadratic programming using qpOASES
+- Multiple gait mode support (standing, walking, hopping)
+
+**Key Parameters**:
+- Gait cycle: 0.4 seconds (adjustable)
+- MPC sampling time: 0.04 seconds
+- Optimization variables: 12×h (h=10 prediction steps)
+- Constraint count: 34×h
+
+**Implemented Features**:
+- Center of mass position and velocity tracking
+- Attitude stabilization control
+- Contact force optimization
+- Euler angle continuity handling (2π=0 relation)
+
+### 2. Swing Leg Control - `Swing_PD.m`
+
+**Control Strategy**:
+- Heuristic foot placement policy
+- Adaptive frequency gait planning
+- PD feedback control
+
+**Key Functions**:
+- Foot trajectory planning (lift height: 0.12m)
+- Gait scheduler (walking/hopping/running)
+- Velocity feedback compensation
+- Body attitude compensation
+
+**PD Gains**:
+```matlab
+Kp = diag([100 100 100 100 5])    # Position gains
+Kd = diag([2 2 2 2 0.1])          # Velocity gains
+```
+
+### 3. Contact Jacobian Calculation - `Formulate_Contact_Jacobian.m`
+
+**Functionality**: 
+- Computes Jacobian matrix for foot contact points
+- Establishes mapping from generalized contact forces to joint torques
+
+**Outputs**:
+- Contact_Jacobian: [12×5] Jacobian matrix
+- Rotm_foot: Foot orientation matrix
+
+**Robot Leg Configuration**:
+- 5 joints per leg: hip_yaw, hip_roll, hip_pitch, knee, ankle
+- Symbolic computation using CasADi for automatic differentiation
+
+### 4. Jacobian Mapping - `JacobianMapping.m`
+
+**Functionality**: Maps MPC output contact forces and moments to joint actuation torques
+
+**Mapping Relation**:
+```
+τ = J_c^T × (-u)
+```
+Where:
+- τ: Joint torque vector
+- J_c: Contact Jacobian
+- u: MPC output generalized forces
+
+### 5. Arm Controller - `Arm_Controller.m`
+
+**Control Modes**:
+1. Heuristic arm swing: Arm motion coordinated with opposite leg
+2. Fixed position: Arms maintain fixed posture
+
+**Joint Configuration**:
+- 3 joints per arm: shoulder_roll, shoulder_pitch, elbow
+- PD control gains: Kp=50, Kd=2
+
+## Robot Model Parameters
+
+### Physical Parameters
+
+**Initial State**:
+- Initial height: 0.525m
+- Initial velocity: [0, 0, 0] m/s
+- Initial attitude: [0, 0, 0] deg
+
+**Joint Limits**:
+- Hip Yaw: ±30°
+- Hip Roll: ±18°
+- Hip Pitch: -120° ~ 120°
+- Knee: -160° ~ -15°
+- Ankle: -75° ~ 75°
+
+**Contact Parameters**:
+- Ground stiffness: 1×10^5 N/m
+- Ground damping: 1×10^3 N·s/m
+- Friction coefficient: μ_s = μ_k = 1.0
+- Contact point configuration: 15 points per foot (3 rows × 5 points)
+
+### Control Parameters
+
+**Gait Parameters**:
+- Gait modes: 0=standing, 1=walking, 2=hopping, 3=running
+- Default gait cycle: 0.4 seconds
+- Prediction horizon: 10 steps
+- Step feedback coefficient: K_step = 0.03
+
+## Key Academic Contributions
+
+This project implements algorithms from the following paper:
+
+**Paper Title**: "Force-and-moment-based model predictive control for achieving highly dynamic locomotion on bipedal robots"
+
+**Authors**: Junheng Li, Quan Nguyen
+
+**Published**: 2021 IEEE Conference on Decision and Control (CDC)
+
+**Core Innovations**:
+1. Force-and-moment-based MPC framework, breaking traditional ZMP method limitations
+2. Achievement of highly dynamic bipedal locomotion (including running, hopping)
+3. Open-source implementation for research reproduction and extension
+
+**Related Research**:
+- Adaptive frequency MPC for uneven terrain walking
+- Dynamic gait transitions
+- Robust control design
+
+## Usage Instructions
+
+### Installation Steps
+
+1. Download and extract the simulation software to desired directory
+2. Download CasADi MATLAB library to the same directory
+3. Install MATLAB 2023a or later version
+
+### Running Procedure
+
+1. Launch MATLAB 2023a+
+2. Add entire simulation folder and CasADi library to MATLAB path
+3. Run `Initiate_Simulation.m` to load model and parameters
+4. Open `Hector_Simulation.slx` and modify as needed
+5. Press Ctrl+D to build model
+6. Run simulation in Mechanics Explorer (note: not real-time)
+7. Optional: Comment/uncomment arm assembly and control
+
+### Configurable Parameters
+
+In `Initiate_Simulation.m`, you can modify:
+
+**Gait Parameters**:
+```matlab
+gait = 1;            % Gait mode selection
+gaitcycle = 0.4;     % Gait cycle period
+lift_height = 0.12;  % Foot lift height
+```
+
+**MPC Parameters**:
+```matlab
+h = 10;                    % Prediction horizon
+dt_MPC = gaitcycle/10;     % MPC sampling time
+```
+
+**Physical Parameters**:
+```matlab
+contact_stiffness = 1e5;   % Contact stiffness
+contact_damping = 1e3;     % Contact damping
+mu_s = 1.0;                % Static friction coefficient
+```
+
+**Initial State**:
+```matlab
+body_z0 = 0.525;           % Initial height
+body_v0 = [0 0 0];         % Initial velocity
+```
+
+## Extended Features
+
+### 1. Uneven Terrain Support
+
+Code includes grid terrain definition functionality:
+```matlab
+x_grid = -1:0.01:5;
+y_grid = -1:0.01:1;
+[X,Y] = meshgrid(x_grid,y_grid);
+z_heights = [0.05*cos(2*pi*X)-0.05]';
+```
+
+To use, switch to "Mesh Grid Surface" in Simulink model
+
+### 2. Variable-Step MPC
+
+Supports adaptive sampling time MPC, implemented via `AssignMPCStage.m`:
+- Can dynamically adjust MPC sampling time based on gait phase
+- Applicable for adaptive frequency gait control
+
+### 3. Optional Arm Module
+
+Controlled by setting `addArm` variable:
+```matlab
+addArm = 0;  % Without arms
+addArm = 1;  % With arms
+```
+
+## Technical Advantages
+
+1. **Fully Open Source**: Complete simulation and control code provided
+2. **High Dynamic Performance**: Supports challenging motions like running and hopping
+3. **Advanced Algorithms**: Based on latest force-moment MPC framework
+4. **Easy to Extend**: Modular design facilitates adding new features
+5. **Academic Support**: Backed by corresponding academic papers and theory
+6. **Visualization**: 3D visualization using Simscape Multibody
+
+## Application Scenarios
+
+1. **Research**: Bipedal robot control algorithm research
+2. **Education**: Robotics and control theory course teaching
+3. **Development**: Humanoid robot controller design and testing
+4. **Validation**: Controller algorithm simulation before real robot deployment
+
+## Potential Improvement Directions
+
+1. **Real-time Optimization**: Current simulation is non-real-time, can optimize solver speed
+2. **Robustness Enhancement**: Add external force disturbance handling
+3. **Terrain Awareness**: Integrate vision/perception systems
+4. **Learning Methods**: Combine machine learning for gait optimization
+5. **Hardware Interface**: Add interface to real robots
+
+## Contact Information
+
+**Project Lead**: Junheng Li
+**Email**: junhengl@usc.edu
+
+**Acknowledgments**: 
+- Zhanhao Le
+- Han Gong
+
+For contributions to the open-source software.
+
+## Citation Format
+
+If using this software for research, please cite:
+
+```bibtex
+@inproceedings{li2021force,
+  title={Force-and-moment-based model predictive control for achieving highly dynamic locomotion on bipedal robots},
+  author={Li, Junheng and Nguyen, Quan},
+  booktitle={2021 60th IEEE Conference on Decision and Control (CDC)},
+  pages={1024--1030},
+  year={2021},
+  organization={IEEE}
+}
+```
+
+## Summary
+
+The Hector simulation project is a fully-featured, technically advanced bipedal humanoid robot simulation platform. It not only implements the latest force-moment MPC control algorithm but also provides complete open-source code and detailed documentation, making it ideal for researchers and students in the field of robot control.
+
+**Key Features**:
+- ✅ Complete bipedal robot dynamics model
+- ✅ Advanced MPC control framework
+- ✅ Multiple gait modes (standing/walking/hopping/running)
+- ✅ Modular, extensible code structure
+- ✅ Complete open-source and academic support
+- ✅ 3D visualization simulation environment
+
+**Target Audience**:
+- Robotics researchers
+- Control theory researchers
+- Robotics engineering students
+- Humanoid robot developers
+
+This project provides an excellent starting point and reference implementation for bipedal robot control research.