add mujoco simulation section

Author: wanxinjin

.DS_Store

@@ -0,0 +1,176 @@
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_build/.doctrees/environment.pickle

@@ -71,14 +71,14 @@ kinematic chain is closed when a sequence of links forms a loop. This course mai
 
 MuJoCo (Multi-Joint dynamics with Contact) is a physics engine designed for the simulation and control of robots and other articulated mechanisms. It is widely used in robotics research for its speed, accuracy, and support for advanced features such as soft contacts and complex constraints.
 
-**Key Features:**
+### Key Features
 
 - Fast and accurate simulation of rigid body dynamics
 - Support for soft and hard contacts
 - Flexible model specification using XML
 - Widely used in reinforcement learning and robotics research
 
-**Getting Started:**
+### Getting Started
 
 To use MuJoCo, you need to:
 
@@ -88,9 +88,6 @@ To use MuJoCo, you need to:
 
 
 
-
-```
-
 # Configuration
 
 ```{important}

_build/.doctrees/lec2-dof/configuration.doctree

@@ -52,6 +52,40 @@ chosen in the approach direction to the object, $\boldsymbol{s}_{e}$ is
 chosen in the sliding plane of the jaws,
 and $\boldsymbol{n}_{e}$ is chosen to complete the right-handed rule.
 
+```{admonition} MuJoCo Simulation of Franka Robot Arm
+:class: tip
+
+To run the Franka Emika Panda forward kinematics simulation locally:
+
+1. **Download the FK code files:**
+  - [Download franka_emika_panda.zip](./fk_code/franka_emika_panda.zip)
+  - Unzip the file to any folder of your choice on your local system.
+
+2. **Install MuJoCo and its Python bindings:**
+  - Make sure you have Python installed.
+  - Install MuJoCo and the Python package:
+    ```sh
+    pip install mujoco
+    ```
+
+
+3. **Run the simulation:**
+   - Open the `demo.py` script in your code editor.
+   - Set the `MODEL_PATH` variable in `demo.py` to the correct path of the `scene.xml` file in your local system. For example:
+     ```python
+     MODEL_PATH = "/path/to/your/franka_emika_panda/scene.xml"  # Use the provided scene.xml file
+     model = mujoco.MjModel.from_xml_path(MODEL_PATH)
+     ```
+   - Save the changes to `demo.py`.
+   - In your terminal, navigate to the folder containing `demo.py` and run:
+     ```sh
+     python demo.py
+     ```
+
+You should see a window displaying the Franka Emika Panda robot simulation. Press ESC in the viewer window to exit.
+```
+
+
 # Notation Convention
 
 
@@ -84,6 +118,9 @@ end-effector frame with respect to Frame $n$, respectively.
 Question: how to choose frame for each link to faciliate the computation of
 $\boldsymbol{T}_{i}^{i-1}\left(q_{i}\right)$? 
 
+
+
+
 # Denavit-Hartenberg (DH) Convention
 
 DH Convention is to systematically and recursively
@@ -533,5 +570,7 @@ width: 50%
 name: cover
 ---
 Panda's kinematic chain (from Peter Corke's
-Tutorial
+Tutorial)
 ```
+
+

_build/.doctrees/lec4-fk/fk.doctree

@@ -0,0 +1,57 @@
+# Franka Emika Panda Description (MJCF)
+
+Requires MuJoCo 2.3.3 or later.
+
+## Overview
+
+This package contains a simplified robot description (MJCF) of the [Franka Emika
+Panda](https://www.franka.de/) developed by [Franka
+Emika](https://www.franka.de/company). It is derived from the [publicly
+available URDF
+description](https://github.com/frankaemika/franka_ros/tree/develop/franka_description).
+
+<p float="left">
+  <img src="panda.png" width="400">
+</p>
+
+## URDF → MJCF derivation steps
+
+1. Converted the DAE [mesh
+   files](https://github.com/frankaemika/franka_ros/tree/develop/franka_description/meshes/visual)
+   to OBJ format using [Blender](https://www.blender.org/).
+2. Processed `.obj` files with [`obj2mjcf`](https://github.com/kevinzakka/obj2mjcf).
+3. Eliminated the perfectly flat `link0_6` from the resulting submeshes created for `link0`.
+4. Created a convex decomposition of the STL collision [mesh
+   file](https://github.com/frankaemika/franka_ros/tree/develop/franka_description/meshes/collision)
+   for `link5` using [V-HACD](https://github.com/kmammou/v-hacd).
+5. Added `<mujoco> <compiler discardvisual="false"/> </mujoco>` to the
+   [URDF](https://github.com/frankaemika/franka_ros/tree/develop/franka_description/robots)'s
+   `<robot>` clause in order to preserve visual geometries.
+6. Loaded the URDF into MuJoCo and saved a corresponding MJCF.
+7. Matched inertial parameters with [inertial.yaml](
+   https://github.com/frankaemika/franka_ros/blob/develop/franka_description/robots/common/inertial.yaml).
+8. Added a tracking light to the base.
+9. Manually edited the MJCF to extract common properties into the `<default>` section.
+10. Added `<exclude>` clauses to prevent collisions between `link7` and `link8`.
+11. Manually designed collision geoms for the fingertips.
+12. Added position-controlled actuators for the arm.
+13. Added an equality constraint so that the left finger mimics the position of the right finger.
+14. Added a tendon to split the force equally between both fingers and a
+    position actuator acting on this tendon.
+15. Added `scene.xml` which includes the robot, with a textured groundplane, skybox, and haze.
+
+### MJX
+
+A version of the Franka Emika Panda environment was created for MJX. Steps:
+
+1. Added `mjx_panda.xml`, forked from `panda.xml`.
+2. Added `mjx_scene.xml` and `mjx_single_cube.xml`, forked from `scene.xml`.
+3. Gripper collision geometries were modified to contain less geoms. A capsule collision geom was added to the hand.
+4. Solver parameters were tuned for performance.
+5. Actuator `kp` and `kv` were reduced for more stable simulation.
+6. Added a `site` to the gripper.
+7. Removed tendon and added position actuator for the gripper. Changed gripper `ctrlrange`.
+
+## License
+
+This model is released under an [Apache-2.0 License](LICENSE).