# MuJoCo Humanoid Environment Documentation

## Environment Overview
The humanoid is the 3D bipedal robot designed to simulate a human.
It has a torso (abdomen) with a pair of legs and arms, and a pair of tendons connecting the hips to the knees.
The legs each consist of three body parts (thigh, shin, foot), and the arms consist of two body parts (upper arm, forearm).
The humanoid is capable of performing various locomotion tasks by applying torque to the hinges that connect its body parts.

## Technical Specifications

### State Space
The environment state is represented as a 1-dimensional NumPy array of shape `(67,)`, containing comprehensive information about the humanoid's current configuration:

#### 1. Joint Angles
- `state[0:21]`: Joint angle information in radians
  - `state[0]`: z-angle of the abdomen (in lower_waist) in radians.  
  - `state[1]`: y-angle of the abdomen (in lower_waist) in radians.  
  - `state[2]`: x-angle of the abdomen (in pelvis) in radians.  
  - `state[3]`: x-coordinate of angle between pelvis and right hip (in right_thigh) in radians.  
  - `state[4]`: z-coordinate of angle between pelvis and right hip (in right_thigh) in radians.  
  - `state[5]`: y-coordinate of angle between pelvis and right hip (in right_thigh) in radians.  
  - `state[6]`: angle between right hip and the right shin (in right_knee) in radians. 
  - `state[7]`: x-coordinate of right ankle in radians.  
  - `state[8]`: y-coordinate of right ankle in radians.  
  - `state[9]`: x-coordinate of angle between pelvis and left hip (in left_thigh) in radians.  
  - `state[10]`: z-coordinate of angle between pelvis and left hip (in left_thigh) in radians.  
  - `state[11]`: y-coordinate of angle between pelvis and left hip (in left_thigh) in radians.  
  - `state[12]`: angle between left hip and the left shin (in left_knee) in radians.  
  - `state[13]`: x-coordinate of left ankle in radians.  
  - `state[14]`: y-coordinate of left ankle in radians.  
  - `state[15]`: coordinate-1 (multi-axis) angle between torso and right arm (in right_upper_arm) in radians.  
  - `state[16]`: coordinate-2 (multi-axis) angle between torso and right arm (in right_upper_arm) in radians.  
  - `state[17]`: angle between right upper arm and right_lower_arm in radians.  
  - `state[18]`: coordinate-1 (multi-axis) angle between torso and left arm (in left_upper_arm) in radians.  
  - `state[19]`: coordinate-2 (multi-axis) angle between torso and left arm (in left_upper_arm) in radians.  
  - `state[20]`: angle between left upper arm and left_lower_arm in radians. 

#### 2. Head Positions
  - `state[21]`: z-coordinate of the head in meters (1.6 when standing).  

#### 3. Orientation of Torso
  - `state[34]`: Alignment of the torso to x-axis (0~1).
  - `state[35]`: Alignment of the torso to y-axis (0~1).
  - `state[36]`: Alignment of the torso to z-axis (0~1).

### Action Space
The action space consists of a 1-dimensional NumPy array of shape `(17,)`, controlling the torques applied to each of the humanoid's actuated joints.

**Range**: All actions are bounded between [-1.0, 1.0]

**Control mapping**:
- `action[0]`: Torque applied on the hinge in the y-coordinate of the abdomen.
- `action[1]`: Torque applied on the hinge in the z-coordinate of the abdomen. 
- `action[2]`: Torque applied on the hinge in the x-coordinate of the abdomen.
- `action[3]`: Torque applied on the rotor between torso/abdomen and the right hip (x-coordinate).
- `action[4]`: Torque applied on the rotor between torso/abdomen and the right hip (z-coordinate).
- `action[5]`: Torque applied on the rotor between torso/abdomen and the right hip (y-coordinate).
- `action[6]`: Torque applied on the rotor between the right hip/thigh and the right shin.
- `action[7]`: Torque applied on the right ankle (x-coordinate).
- `action[8]`: Torque applied on the right ankle (y-coordinate).
- `action[9]`: Torque applied on the rotor between torso/abdomen and the left hip (x-coordinate).
- `action[10]`: Torque applied on the rotor between torso/abdomen and the left hip (z-coordinate).
- `action[11]`: Torque applied on the rotor between torso/abdomen and the left hip (y-coordinate).
- `action[12]`: Torque applied on the rotor between the left hip/thigh and the left shin.
- `action[13]`: Torque applied on the left ankle (x-coordinate).
- `action[14]`: Torque applied on the left ankle (y-coordinate).
- `action[15]`: Torque applied on the rotor between the torso and right upper arm (coordinate -1).
- `action[16]`: Torque applied on the rotor between the torso and right upper arm (coordinate -2).
- `action[17]`: Torque applied on the rotor between the right upper arm and right lower arm.
- `action[18]`: Torque applied on the rotor between the torso and left upper arm (coordinate -1).
- `action[19]`: Torque applied on the rotor between the torso and left upper arm (coordinate -2).
- `action[20]`: Torque applied on the rotor between the left upper arm and left lower arm.