# MuJoCo HalfCheetah Environment Documentation

## Environment Overview
The HalfCheetah is a 2-dimensional robot consisting of 9 body parts and 8 joints connecting them (including two paws).
The cheetah’s head is fixed to its torso. 
The HalfCheetah is capable of performing various locomotion tasks by applying torque to 6 joints over the front and back thighs (which connect to the torso), the shins (which connect to the thighs), and the feet (which connect to the shins).

## Technical Specifications

### State Space
The environment state is represented as a 1-dimensional NumPy array of shape `(17,)`, containing comprehensive information about the HalfCheetah's current configuration:

#### 1. Position and Angle
- `state[0:2]`: Position (state[0]) and angle (state[1]) of head fixed to its torso
  - `state[0]`: z-coordinate of the head in meters (0 when spawned).  
  - `state[1]`: angle of the head in radians (0 when spawned).  

#### 2. Joint Angles
- `state[2:8]`: Angles of joint in back leg (state[2:5]) and front leg(state[5:8])
  - `state[2]`: angle of the back thigh in radians.  
  - `state[3]`: angle of the back shin in radians.  
  - `state[4]`: angle of the back foot in radians. 
  - `state[5]`: angle of the front thigh in radians.  
  - `state[6]`: angle of the front shin in radians.  
  - `state[7]`: angle of the front foot in radians.  

### Action Space
The action space consists of a 1-dimensional NumPy array of shape `(6,)`, controlling the torques applied to each of the HalfCheetah's actuated joints.

**Range**: All actions are bounded between [-1, 1]

**Control mapping**:
- `action[0]`: Torque applied on the back thigh rotor.  
- `action[1]`: Torque applied on the back shin rotor.  
- `action[2]`: Torque applied on the back foot rotor.  
- `action[3]`: Torque applied on the front thigh rotor.  
- `action[4]`: Torque applied on the front shin rotor.  
- `action[5]`: Torque applied on the front foot rotor.