# MuJoCo Hopper Environment Documentation

## Environment Overview
The hopper is a two-dimensional one-legged figure consisting of four main body parts - the torso at the top, the thigh in the middle, the leg at the bottom, and a single foot on which the entire body rests.
The hopper is capable of performing various locomotion tasks by applying torque to the three hinges that connect the four body parts.

## Technical Specifications

### State Space
The environment state is represented as a 1-dimensional NumPy array of shape `(11,)`, containing comprehensive information about the hopper's current configuration:

#### 1. Position and Angle
- `state[0:2]`: Position (state[0]) and angle (state[1]) of the torso
  - `state[0]`: z-coordinate of the torso (height of hopper) in meters (1.25 when spawned).  
  - `state[1]`: angle of the torso in radians (0 when spawned).  

#### 2. Joint Angles
- `state[2:5]`: Angles of joints
  - `state[2]`: angle of the thigh joint in radians.  
  - `state[3]`: angle of the leg joint in radians.  
  - `state[4]`: angle of the foot joint in radians. 

### Action Space
The action space consists of a 1-dimensional NumPy array of shape `(3,)`, controlling the torques applied to each of the hopper's actuated joints.

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

**Control mapping**:
- `action[0]`: Torque applied on the thigh rotor.  
- `action[1]`: Torque applied on the leg rotor.  
- `action[2]`: Torque applied on the foot rotor.