class_docstr: ### Description
  
  This environment is based on the environment introduced by Schulman,
  Moritz, Levine, Jordan and Abbeel in ["High-Dimensional Continuous Control
  Using Generalized Advantage Estimation"](https://arxiv.org/abs/1506.02438).
  The ant is a 3D robot consisting of one torso (free rotational body) with
  four legs attached to it with each leg having two links. The goal is to
  coordinate the four legs to move in the forward (right) direction by applying
  torques on the eight hinges connecting the two links of each leg and the torso
  (nine parts and eight hinges).
  
  ### Action Space
  The action space is a `Box(-1, 1, (8,), float32)`. An action represents the torques applied at the hinge joints.
  
  | Num | Action                                                            | Control Min | Control Max | Name (in corresponding XML file) | Joint | Unit         |
  | --- | ----------------------------------------------------------------- | ----------- | ----------- | -------------------------------- | ----- | ------------ |
  | 0   | Torque applied on the rotor between the torso and front left hip  | -1          | 1           | hip_1 (front_left_leg)           | hinge | torque (N m) |
  | 1   | Torque applied on the rotor between the front left two links      | -1          | 1           | angle_1 (front_left_leg)         | hinge | torque (N m) |
  | 2   | Torque applied on the rotor between the torso and front right hip | -1          | 1           | hip_2 (front_right_leg)          | hinge | torque (N m) |
  | 3   | Torque applied on the rotor between the front right two links     | -1          | 1           | angle_2 (front_right_leg)        | hinge | torque (N m) |
  | 4   | Torque applied on the rotor between the torso and back left hip   | -1          | 1           | hip_3 (back_leg)                 | hinge | torque (N m) |
  | 5   | Torque applied on the rotor between the back left two links       | -1          | 1           | angle_3 (back_leg)               | hinge | torque (N m) |
  | 6   | Torque applied on the rotor between the torso and back right hip  | -1          | 1           | hip_4 (right_back_leg)           | hinge | torque (N m) |
  | 7   | Torque applied on the rotor between the back right two links      | -1          | 1           | angle_4 (right_back_leg)         | hinge | torque (N m) |
  
  ### Observation Space
  
  Observations consist of positional values of different body parts of the ant,
  followed by the velocities of those individual parts (their derivatives) with all
  the positions ordered before all the velocities.
  
  By default, observations do not include the x- and y-coordinates of the ant's torso. These may
  be included by passing `exclude_current_positions_from_observation=False` during construction.
  In that case, the observation space will have 113 dimensions where the first two dimensions
  represent the x- and y- coordinates of the ant's torso.
  Regardless of whether `exclude_current_positions_from_observation` was set to true or false, the x- and y-coordinates
  of the torso will be returned in `info` with keys `"x_position"` and `"y_position"`, respectively.
  
  However, by default, an observation is a `ndarray` with shape `(111,)`
  where the elements correspond to the following:
  
  | Num | Observation                                                  | Min    | Max    | Name (in corresponding XML file)       | Joint | Unit                     |
  |-----|--------------------------------------------------------------|--------|--------|----------------------------------------|-------|--------------------------|
  | 0   | z-coordinate of the torso (centre)                           | -Inf   | Inf    | torso                                  | free  | position (m)             |
  | 1   | x-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
  | 2   | y-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
  | 3   | z-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
  | 4   | w-orientation of the torso (centre)                          | -Inf   | Inf    | torso                                  | free  | angle (rad)              |
  | 5   | angle between torso and first link on front left             | -Inf   | Inf    | hip_1 (front_left_leg)                 | hinge | angle (rad)              |
  | 6   | angle between the two links on the front left                | -Inf   | Inf    | ankle_1 (front_left_leg)               | hinge | angle (rad)              |
  | 7   | angle between torso and first link on front right            | -Inf   | Inf    | hip_2 (front_right_leg)                | hinge | angle (rad)              |
  | 8   | angle between the two links on the front right               | -Inf   | Inf    | ankle_2 (front_right_leg)              | hinge | angle (rad)              |
  | 9   | angle between torso and first link on back left              | -Inf   | Inf    | hip_3 (back_leg)                       | hinge | angle (rad)              |
  | 10  | angle between the two links on the back left                 | -Inf   | Inf    | ankle_3 (back_leg)                     | hinge | angle (rad)              |
  | 11  | angle between torso and first link on back right             | -Inf   | Inf    | hip_4 (right_back_leg)                 | hinge | angle (rad)              |
  | 12  | angle between the two links on the back right                | -Inf   | Inf    | ankle_4 (right_back_leg)               | hinge | angle (rad)              |
  | 13  | x-coordinate velocity of the torso                           | -Inf   | Inf    | torso                                  | free  | velocity (m/s)           |
  | 14  | y-coordinate velocity of the torso                           | -Inf   | Inf    | torso                                  | free  | velocity (m/s)           |
  | 15  | z-coordinate velocity of the torso                           | -Inf   | Inf    | torso                                  | free  | velocity (m/s)           |
  | 16  | x-coordinate angular velocity of the torso                   | -Inf   | Inf    | torso                                  | free  | angular velocity (rad/s) |
  | 17  | y-coordinate angular velocity of the torso                   | -Inf   | Inf    | torso                                  | free  | angular velocity (rad/s) |
  | 18  | z-coordinate angular velocity of the torso                   | -Inf   | Inf    | torso                                  | free  | angular velocity (rad/s) |
  | 19  | angular velocity of angle between torso and front left link  | -Inf   | Inf    | hip_1 (front_left_leg)                 | hinge | angle (rad)              |
  | 20  | angular velocity of the angle between front left links       | -Inf   | Inf    | ankle_1 (front_left_leg)               | hinge | angle (rad)              |
  | 21  | angular velocity of angle between torso and front right link | -Inf   | Inf    | hip_2 (front_right_leg)                | hinge | angle (rad)              |
  | 22  | angular velocity of the angle between front right links      | -Inf   | Inf    | ankle_2 (front_right_leg)              | hinge | angle (rad)              |
  | 23  | angular velocity of angle between torso and back left link   | -Inf   | Inf    | hip_3 (back_leg)                       | hinge | angle (rad)              |
  | 24  | angular velocity of the angle between back left links        | -Inf   | Inf    | ankle_3 (back_leg)                     | hinge | angle (rad)              |
  | 25  | angular velocity of angle between torso and back right link  | -Inf   | Inf    | hip_4 (right_back_leg)                 | hinge | angle (rad)              |
  | 26  |angular velocity of the angle between back right links        | -Inf   | Inf    | ankle_4 (right_back_leg)               | hinge | angle (rad)              |
  
  
  The remaining 14*6 = 84 elements of the observation are contact forces
  (external forces - force x, y, z and torque x, y, z) applied to the
  center of mass of each of the links. The 14 links are: the ground link,
  the torso link, and 3 links for each leg (1 + 1 + 12) with the 6 external forces.
  
  The (x,y,z) coordinates are translational DOFs while the orientations are rotational
  DOFs expressed as quaternions. One can read more about free joints on the [Mujoco Documentation](https://mujoco.readthedocs.io/en/latest/XMLreference.html).
  
  
  **Note:** Ant-v4 environment no longer has the following contact forces issue.
  If using previous Humanoid versions from v4, there have been reported issues that using a Mujoco-Py version > 2.0 results
  in the contact forces always being 0. As such we recommend to use a Mujoco-Py version < 2.0
  when using the Ant environment if you would like to report results with contact forces (if
  contact forces are not used in your experiments, you can use version > 2.0).
  
  ### Rewards
  The reward consists of three parts:
  - *healthy_reward*: Every timestep that the ant is healthy (see definition in section "Episode Termination"), it gets a reward of fixed value `healthy_reward`
  - *forward_reward*: A reward of moving forward which is measured as
  *(x-coordinate before action - x-coordinate after action)/dt*. *dt* is the time
  between actions and is dependent on the `frame_skip` parameter (default is 5),
  where the frametime is 0.01 - making the default *dt = 5 * 0.01 = 0.05*.
  This reward would be positive if the ant moves forward (in positive x direction).
  - *ctrl_cost*: A negative reward for penalising the ant if it takes actions
  that are too large. It is measured as *`ctrl_cost_weight` * sum(action<sup>2</sup>)*
  where *`ctr_cost_weight`* is a parameter set for the control and has a default value of 0.5.
  - *contact_cost*: A negative reward for penalising the ant if the external contact
  force is too large. It is calculated *`contact_cost_weight` * sum(clip(external contact
  force to `contact_force_range`)<sup>2</sup>)*.
  
  The total reward returned is ***reward*** *=* *healthy_reward + forward_reward - ctrl_cost - contact_cost* and `info` will also contain the individual reward terms.
  
  ### Starting State
  All observations start in state
  (0.0, 0.0,  0.75, 1.0, 0.0  ... 0.0) with a uniform noise in the range
  of [-`reset_noise_scale`, `reset_noise_scale`] added to the positional values and standard normal noise
  with mean 0 and standard deviation `reset_noise_scale` added to the velocity values for
  stochasticity. Note that the initial z coordinate is intentionally selected
  to be slightly high, thereby indicating a standing up ant. The initial orientation
  is designed to make it face forward as well.
  
  ### Episode End
  The ant is said to be unhealthy if any of the following happens:
  
  1. Any of the state space values is no longer finite
  2. The z-coordinate of the torso is **not** in the closed interval given by `healthy_z_range` (defaults to [0.2, 1.0])
  
  If `terminate_when_unhealthy=True` is passed during construction (which is the default),
  the episode ends when any of the following happens:
  
  1. Truncation: The episode duration reaches a 1000 timesteps
  2. Termination: The ant is unhealthy
  
  If `terminate_when_unhealthy=False` is passed, the episode is ended only when 1000 timesteps are exceeded.
  
  ### Arguments
  
  No additional arguments are currently supported in v2 and lower.
  
  ```
  env = gym.make('Ant-v2')
  ```
  
  v3 and v4 take gym.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale etc.
  
  ```
  env = gym.make('Ant-v4', ctrl_cost_weight=0.1, ...)
  ```
  
  | Parameter               | Type       | Default      |Description                    |
  |-------------------------|------------|--------------|-------------------------------|
  | `xml_file`              | **str**    | `"ant.xml"`  | Path to a MuJoCo model |
  | `ctrl_cost_weight`      | **float**  | `0.5`        | Weight for *ctrl_cost* term (see section on reward) |
  | `contact_cost_weight`   | **float**  | `5e-4`       | Weight for *contact_cost* term (see section on reward) |
  | `healthy_reward`        | **float**  | `1`          | Constant reward given if the ant is "healthy" after timestep |
  | `terminate_when_unhealthy` | **bool**| `True`       | If true, issue a done signal if the z-coordinate of the torso is no longer in the `healthy_z_range` |
  | `healthy_z_range`       | **tuple**  | `(0.2, 1)`   | The ant is considered healthy if the z-coordinate of the torso is in this range |
  | `contact_force_range`   | **tuple**  | `(-1, 1)`    | Contact forces are clipped to this range in the computation of *contact_cost* |
  | `reset_noise_scale`     | **float**  | `0.1`        | Scale of random perturbations of initial position and velocity (see section on Starting State) |
  | `exclude_current_positions_from_observation`| **bool** | `True`| Whether or not to omit the x- and y-coordinates from observations. Excluding the position can serve as an inductive bias to induce position-agnostic behavior in policies |
  
  ### 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. Added reward_threshold to environments.
  * v0: Initial versions release (1.0.0)
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code: def control_cost(self, action):
      control_cost = self._ctrl_cost_weight * np.sum(np.square(action))
      return control_cost
  
file_path: gym/gym/envs/mujoco/ant_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 3 for calling the AntEnv obj's underlying member method code with example usage: obj.control_cost(action) and returns: control_cost