Ant#

../../../_images/ant.gif

This environment is part of the Mujoco environments which contains general information about the environment.

Action Space

Box(-1.0, 1.0, (8,), float32)

Observation Space

Box(-inf, inf, (105,), float64)

import

gymnasium.make("Ant-v5")

Description#

This environment is based on the one introduced by Schulman, Moritz, Levine, Jordan, and Abbeel in “High-Dimensional Continuous Control Using Generalized Advantage Estimation”. The ant is a 3D quadruped robot consisting of a torso (free rotational body) with four legs attached to it, where each leg has two body parts. The goal is to coordinate the four legs to move in the forward (right) direction by applying torque to the eight hinges connecting the two body parts of each leg and the torso (nine body parts and eight hinges).

Note: Although the robot is called “Ant”, it is actually 75cm tall and weighs 910.88g, with the torso being 327.25g and each leg being 145.91g.

Action Space#

../../../_images/ant.png

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

Type (Unit)

0

Torque applied on the rotor between the torso and back right hip

-1

1

hip_4 (right_back_leg)

hinge

torque (N m)

1

Torque applied on the rotor between the back right two links

-1

1

angle_4 (right_back_leg)

hinge

torque (N m)

2

Torque applied on the rotor between the torso and front left hip

-1

1

hip_1 (front_left_leg)

hinge

torque (N m)

3

Torque applied on the rotor between the front left two links

-1

1

angle_1 (front_left_leg)

hinge

torque (N m)

4

Torque applied on the rotor between the torso and front right hip

-1

1

hip_2 (front_right_leg)

hinge

torque (N m)

5

Torque applied on the rotor between the front right two links

-1

1

angle_2 (front_right_leg)

hinge

torque (N m)

6

Torque applied on the rotor between the torso and back left hip

-1

1

hip_3 (back_leg)

hinge

torque (N m)

7

Torque applied on the rotor between the back left two links

-1

1

angle_3 (back_leg)

hinge

torque (N m)

Observation Space#

The observation space consists of the following parts (in order):

  • qpos (13 elements by default): Position values of the robot’s body parts.

  • qvel (14 elements): The velocities of these individual body parts (their derivatives).

  • cfrc_ext (78 elements): This is the center of mass based external forces on the body parts. It has shape 13 * 6 (nbody * 6) and hence adds another 78 elements to the state space. (external forces - force x, y, z and torque x, y, z)

By default, the observation does not include the x- and y-coordinates of the torso. These can be included by passing exclude_current_positions_from_observation=False during construction. In this case, the observation space will be a Box(-Inf, Inf, (107,), float64), where the first two observations are the x- and y-coordinates of the torso. Regardless of whether exclude_current_positions_from_observation is set to True or False, the x- and y-coordinates are returned in info with the keys "x_position" and "y_position", respectively.

By default, however, the observation space is a Box(-Inf, Inf, (105,), float64), where the position and velocity elements are as follows:

Num

Observation

Min

Max

Name (in corresponding XML file)

Joint

Type (Unit)

0

z-coordinate of the torso (centre)

-Inf

Inf

root

free

position (m)

1

x-orientation of the torso (centre)

-Inf

Inf

root

free

angle (rad)

2

y-orientation of the torso (centre)

-Inf

Inf

root

free

angle (rad)

3

z-orientation of the torso (centre)

-Inf

Inf

root

free

angle (rad)

4

w-orientation of the torso (centre)

-Inf

Inf

root

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

root

free

velocity (m/s)

14

y-coordinate velocity of the torso

-Inf

Inf

root

free

velocity (m/s)

15

z-coordinate velocity of the torso

-Inf

Inf

root

free

velocity (m/s)

16

x-coordinate angular velocity of the torso

-Inf

Inf

root

free

angular velocity (rad/s)

17

y-coordinate angular velocity of the torso

-Inf

Inf

root

free

angular velocity (rad/s)

18

z-coordinate angular velocity of the torso

-Inf

Inf

root

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)

excluded

x-coordinate of the torso (centre)

-Inf

Inf

root

free

position (m)

excluded

y-coordinate of the torso (centre)

-Inf

Inf

root

free

position (m)

The body parts are:

body part

id (for v2, v3, v4)

id (for v5)

worldbody (note: all values are constant 0)

0

excluded

torso

1

0

front_left_leg

2

1

aux_1 (front left leg)

3

2

ankle_1 (front left leg)

4

3

front_right_leg

5

4

aux_2 (front right leg)

6

5

ankle_2 (front right leg)

7

6

back_leg (back left leg)

8

7

aux_3 (back left leg)

9

8

ankle_3 (back left leg)

10

9

right_back_leg

11

10

aux_4 (back right leg)

12

11

ankle_4 (back right leg)

13

12

The (x,y,z) coordinates are translational DOFs, while the orientations are rotational DOFs expressed as quaternions. One can read more about free joints in the MuJoCo documentation.

Note: When using Ant-v3 or earlier versions, problems have been reported when using a mujoco-py version > 2.0, resulting in contact forces always being 0. Therefore, it is recommended to use a mujoco-py version < 2.0 when using the Ant environment if you want to report results with contact forces (if contact forces are not used in your experiments, you can use version > 2.0).

Rewards#

The total reward is reward = healthy_reward + forward_reward - ctrl_cost - contact_cost.

  • healthy_reward: Every timestep that the Ant is healthy (see definition in section “Episode End”), it gets a reward of fixed value healthy_reward (default is \(1\)).

  • forward_reward: A reward for moving forward, this reward would be positive if the Ant moves forward (in the positive \(x\) direction / in the right direction). \(w_{forward} \times \frac{dx}{dt}\), where \(dx\) is the displacement of the main_body (\(x_{after-action} - x_{before-action}\)), \(dt\) is the time between actions, which depends on the frame_skip parameter (default is \(5\)), and frametime, which is \(0.01\) - so the default is \(dt = 5 \times 0.01 = 0.05\), \(w_{forward}\) is the forward_reward_weight (default is \(1\)).

  • ctrl_cost: A negative reward to penalize the Ant for taking actions that are too large. \(w_{control} \times \|action\|_2^2\), where \(w_{control}\) is ctrl_cost_weight (default is \(0.5\)).

  • contact_cost: A negative reward to penalize the Ant if the external contact forces are too large. \(w_{contact} \times \|F_{contact}\|_2^2\), where \(w_{contact}\) is contact_cost_weight (default is \(5\times10^{-4}\)), \(F_{contact}\) are the external contact forces clipped by contact_force_range (see cfrc_ext section on Observation Space).

info contains the individual reward terms.

But if use_contact_forces=False on v4 The total reward returned is reward = healthy_reward + forward_reward - ctrl_cost.

Starting State#

The initial position state is \([0.0, 0.0, 0.75, 1.0, 0.0, ... 0.0] + \mathcal{U}_{[-reset\_noise\_scale \times I_{15}, reset\_noise\_scale \times I_{15}]}\). The initial velocity state is \(\mathcal{N}(0_{14}, reset\_noise\_scale^2 \times I_{14})\).

where \(\mathcal{N}\) is the multivariate normal distribution and \(\mathcal{U}\) is the multivariate uniform continuous distribution.

Note that the z- and x-coordinates are non-zero so that the ant can immediately stand up and face forward (x-axis).

Episode End#

Termination#

If terminate_when_unhealthy is True (the default), the environment terminates when the Ant is unhealthy. the Ant is 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 (the height) is not in the closed interval given by the healthy_z_range argument (default is \([0.2, 1.0]\)).

Truncation#

The default duration of an episode is 1000 timesteps.

Arguments#

Ant provides a range of parameters to modify the observation space, reward function, initial state, and termination condition. These parameters can be applied during gymnasium.make in the following way:

import gymnasium as gym
env = gym.make('Ant-v5', ctrl_cost_weight=0.5, ...)

Parameter

Type

Default

Description

xml_file

str

"ant.xml"

Path to a MuJoCo model

forward_reward_weight

float

1

Weight for forward_reward term (see Rewards section)

ctrl_cost_weight

float

0.5

Weight for ctrl_cost term (see Rewards section)

contact_cost_weight

float

5e-4

Weight for contact_cost term (see Rewards section)

healthy_reward

float

1

Weight for healthy_reward term (see Rewards section)

main_body

str|int

1(“torso”)

Name or ID of the body, whose displacement is used to calculate the dx/forward_reward (useful for custom MuJoCo models) (see Rewards section)

terminate_when_unhealthy

bool

True

If True, issue a terminated signal is unhealthy (see Episode End section)

healthy_z_range

tuple

(0.2, 1)

The ant is considered healthy if the z-coordinate of the torso is in this range (see Episode End section)

contact_force_range

tuple

(-1, 1)

Contact forces are clipped to this range in the computation of contact_cost (see Rewards section)

reset_noise_scale

float

0.1

Scale of random perturbations of initial position and velocity (see Starting State section)

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 (see Observation State section)

include_cfrc_ext_in_observation

bool

True

Whether to include cfrc_ext elements in the observations (see Observation State section)

use_contact_forces (v4 only)

bool

False

If True, it extends the observation space by adding contact forces (see Observation Space section) and includes contact_cost to the reward function (see Rewards section)

Version History#

  • v5:

    • Minimum mujoco version is now 2.3.3.

    • Added support for fully custom/third party mujoco models using the xml_file argument (previously only a few changes could be made to the existing models).

    • Added default_camera_config argument, a dictionary for setting the mj_camera properties, mainly useful for custom environments.

    • Added env.observation_structure, a dictionary for specifying the observation space compose (e.g. qpos, qvel), useful for building tooling and wrappers for the MuJoCo environments.

    • Return a non-empty info with reset(), previously an empty dictionary was returned, the new keys are the same state information as step().

    • Added frame_skip argument, used to configure the dt (duration of step()), default varies by environment check environment documentation pages.

    • Fixed bug: healthy_reward was given on every step (even if the Ant is unhealthy), now it is only given when the Ant is healthy. The info["reward_survive"] is updated with this change (related GitHub issue).

    • The reward function now always includes contact_cost, before it was only included if use_contact_forces=True (can be set to 0 with contact_cost_weight=0).

    • Excluded the cfrc_ext of worldbody from the observation space, as it was always 0 and thus provided no useful information to the agent, resulting in slightly faster training (related GitHub issue).

    • Added the main_body argument, which specifies the body used to compute the forward reward (mainly useful for custom MuJoCo models).

    • Added the forward_reward_weight argument, which defaults to 1 (effectively the same behavior as in v4).

    • Added the include_cfrc_ext_in_observation argument, previously in v4 the inclusion of cfrc_ext observations was controlled by use_contact_forces which defaulted to False, while include_cfrc_ext_in_observation defaults to True.

    • Removed the use_contact_forces argument (note: its functionality has been replaced by include_cfrc_ext_in_observation and contact_cost_weight) (related GitHub issue).

    • Fixed info["reward_ctrl"] sometimes containing contact_cost instead of ctrl_cost.

    • Fixed info["x_position"] & info["y_position"] & info["distance_from_origin"] giving xpos instead of qpos observations (xpos observations are behind 1 mj_step() more here) (related GitHub issue #1 & GitHub issue #2).

    • Removed info["forward_reward"] as it is equivalent to info["reward_forward"].

  • v4: All MuJoCo environments now use the MuJoCo bindings in mujoco >= 2.1.3, also removed contact forces from the default observation space (new variable use_contact_forces=True can restore them).

  • v3: Support for gymnasium.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