class_docstr: ### Description
  
  This environment originates from control theory and builds on the cartpole
  environment based on the work done by Barto, Sutton, and Anderson in
  ["Neuronlike adaptive elements that can solve difficult learning control problems"](https://ieeexplore.ieee.org/document/6313077),
  powered by the Mujoco physics simulator - allowing for more complex experiments
  (such as varying the effects of gravity or constraints). This environment involves a cart that can
  moved linearly, with a pole fixed on it and a second pole fixed on the other end of the first one
  (leaving the second pole as the only one with one free end). The cart can be pushed left or right,
  and the goal is to balance the second pole on top of the first pole, which is in turn on top of the
  cart, by applying continuous forces on the cart.
  
  ### Action Space
  The agent take a 1-element vector for actions.
  The action space is a continuous `(action)` in `[-1, 1]`, where `action` represents the
  numerical force applied to the cart (with magnitude representing the amount of force and
  sign representing the direction)
  
  | Num | Action                    | Control Min | Control Max | Name (in corresponding XML file) | Joint | Unit      |
  |-----|---------------------------|-------------|-------------|----------------------------------|-------|-----------|
  | 0   | Force applied on the cart | -1          | 1           | slider                           | slide | Force (N) |
  
  ### Observation Space
  
  The state space consists of positional values of different body parts of the pendulum system,
  followed by the velocities of those individual parts (their derivatives) with all the
  positions ordered before all the velocities.
  
  The observation is a `ndarray` with shape `(11,)` where the elements correspond to the following:
  
  | Num | Observation                                                       | Min  | Max | Name (in corresponding XML file) | Joint | Unit                     |
  | --- | ----------------------------------------------------------------- | ---- | --- | -------------------------------- | ----- | ------------------------ |
  | 0   | position of the cart along the linear surface                     | -Inf | Inf | slider                           | slide | position (m)             |
  | 1   | sine of the angle between the cart and the first pole             | -Inf | Inf | sin(hinge)                       | hinge | unitless                 |
  | 2   | sine of the angle between the two poles                           | -Inf | Inf | sin(hinge2)                      | hinge | unitless                 |
  | 3   | cosine of the angle between the cart and the first pole           | -Inf | Inf | cos(hinge)                       | hinge | unitless                 |
  | 4   | cosine of the angle between the two poles                         | -Inf | Inf | cos(hinge2)                      | hinge | unitless                 |
  | 5   | velocity of the cart                                              | -Inf | Inf | slider                           | slide | velocity (m/s)           |
  | 6   | angular velocity of the angle between the cart and the first pole | -Inf | Inf | hinge                            | hinge | angular velocity (rad/s) |
  | 7   | angular velocity of the angle between the two poles               | -Inf | Inf | hinge2                           | hinge | angular velocity (rad/s) |
  | 8   | constraint force - 1                                              | -Inf | Inf |                                  |       | Force (N)                |
  | 9   | constraint force - 2                                              | -Inf | Inf |                                  |       | Force (N)                |
  | 10  | constraint force - 3                                              | -Inf | Inf |                                  |       | Force (N)                |
  
  
  There is physical contact between the robots and their environment - and Mujoco
  attempts at getting realisitic physics simulations for the possible physical contact
  dynamics by aiming for physical accuracy and computational efficiency.
  
  There is one constraint force for contacts for each degree of freedom (3).
  The approach and handling of constraints by Mujoco is unique to the simulator
  and is based on their research. Once can find more information in their
  [*documentation*](https://mujoco.readthedocs.io/en/latest/computation.html)
  or in their paper
  ["Analytically-invertible dynamics with contacts and constraints: Theory and implementation in MuJoCo"](https://homes.cs.washington.edu/~todorov/papers/TodorovICRA14.pdf).
  
  
  ### Rewards
  
  The reward consists of two parts:
  - *alive_bonus*: The goal is to make the second inverted pendulum stand upright
  (within a certain angle limit) as long as possible - as such a reward of +10 is awarded
   for each timestep that the second pole is upright.
  - *distance_penalty*: This reward is a measure of how far the *tip* of the second pendulum
  (the only free end) moves, and it is calculated as
  *0.01 * x<sup>2</sup> + (y - 2)<sup>2</sup>*, where *x* is the x-coordinate of the tip
  and *y* is the y-coordinate of the tip of the second pole.
  - *velocity_penalty*: A negative reward for penalising the agent if it moves too
  fast *0.001 *  v<sub>1</sub><sup>2</sup> + 0.005 * v<sub>2</sub> <sup>2</sup>*
  
  The total reward returned is ***reward*** *=* *alive_bonus - distance_penalty - velocity_penalty*
  
  ### Starting State
  All observations start in state
  (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) with a uniform noise in the range
  of [-0.1, 0.1] added to the positional values (cart position and pole angles) and standard
  normal force with a standard deviation of 0.1 added to the velocity values for stochasticity.
  
  ### Episode End
  The episode ends when any of the following happens:
  
  1.Truncation:  The episode duration reaches 1000 timesteps.
  2.Termination: Any of the state space values is no longer finite.
  3.Termination: The y_coordinate of the tip of the second pole *is less than or equal* to 1. The maximum standing height of the system is 1.196 m when all the parts are perpendicularly vertical on top of each other).
  
  ### Arguments
  
  No additional arguments are currently supported.
  
  ```
  env = gym.make('InvertedDoublePendulum-v4')
  ```
  There is no v3 for InvertedPendulum, unlike the robot environments where a v3 and
  beyond take gym.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale etc.
  
  
  ### Version History
  
  * v4: all mujoco environments now use the mujoco bindings in mujoco>=2.1.3
  * v3: support for gym.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale etc. rgb rendering comes from tracking camera (so agent does not run away from screen)
  * v2: All continuous control environments now use mujoco_py >= 1.50
  * v1: max_time_steps raised to 1000 for robot based tasks (including inverted pendulum)
  * v0: Initial versions release (1.0.0)
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code: def reset_model(self):
      self.set_state(
          self.init_qpos
          + self.np_random.uniform(
              low=-0.1, high=0.1, size=self.model.nq
          ),
          self.init_qvel
          + self.np_random.standard_normal(self.model.nv) * 0.1,
      )
      return self._get_obs()
  
file_path: gym/gym/envs/mujoco/inverted_double_pendulum_v4.py
imports: import numpy
  from gym import utils
  from gym.envs.mujoco import MujocoEnv
  from gym.spaces import Box
label_desc: Use image node_id 4 for calling the InvertedDoublePendulumEnv obj's underlying member method code with example usage: obj.reset_model() and returns: self