Ant#
This environment is part of the Mujoco environments which contains general information about the environment.
Action Space 

Observation Space 

import 

Description#
This environment is based on the environment introduced by Schulman, Moritz, Levine, Jordan and Abbeel in “HighDimensional Continuous Control Using Generalized Advantage Estimation”. The ant is a 3D robot consisting of one torso (free rotational body) with four legs attached to it with each leg having two body parts. 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 body parts of each leg and the torso (nine body 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 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#
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 ycoordinates 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 be a Box(Inf, Inf, (29,), float64)
where the first two observations
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 ycoordinates
of the torso will be returned in info
with keys "x_position"
and "y_position"
, respectively.
However, by default, observation Space is a Box(Inf, Inf, (27,), float64)
where the elements correspond to the following:
Num 
Observation 
Min 
Max 
Name (in corresponding XML file) 
Joint 
Unit 

0 
zcoordinate of the torso (centre) 
Inf 
Inf 
torso 
free 
position (m) 
1 
xorientation of the torso (centre) 
Inf 
Inf 
torso 
free 
angle (rad) 
2 
yorientation of the torso (centre) 
Inf 
Inf 
torso 
free 
angle (rad) 
3 
zorientation of the torso (centre) 
Inf 
Inf 
torso 
free 
angle (rad) 
4 
worientation 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 
xcoordinate velocity of the torso 
Inf 
Inf 
torso 
free 
velocity (m/s) 
14 
ycoordinate velocity of the torso 
Inf 
Inf 
torso 
free 
velocity (m/s) 
15 
zcoordinate velocity of the torso 
Inf 
Inf 
torso 
free 
velocity (m/s) 
16 
xcoordinate angular velocity of the torso 
Inf 
Inf 
torso 
free 
angular velocity (rad/s) 
17 
ycoordinate angular velocity of the torso 
Inf 
Inf 
torso 
free 
angular velocity (rad/s) 
18 
zcoordinate 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) 
excluded 
xcoordinate of the torso (centre) 
Inf 
Inf 
torso 
free 
position (m) 
excluded 
ycoordinate of the torso (centre) 
Inf 
Inf 
torso 
free 
position (m) 
If version < v4
or use_contact_forces
is True
then the observation space is extended by 14*6 = 84 elements, which are contact forces
(external forces  force x, y, z and torque x, y, z) applied to the
center of mass of each of the body parts. The 14 body parts are:
id (for 
body parts 

0 
worldbody (note: forces are always full of zeros) 
1 
torso 
2 
front_left_leg 
3 
aux_1 (front left leg) 
4 
ankle_1 (front left leg) 
5 
front_right_leg 
6 
aux_2 (front right leg) 
7 
ankle_2 (front right leg) 
8 
back_leg (back left leg) 
9 
aux_3 (back left leg) 
10 
ankle_3 (back left leg) 
11 
right_back_leg 
12 
aux_4 (back right leg) 
13 
ankle_4 (back right leg) 
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.
Note: Antv4 environment no longer has the following contact forces issue. If using previous Humanoid versions from v4, there have been reported issues that using a MujocoPy version > 2.0 results in the contact forces always being 0. As such we recommend to use a MujocoPy 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 (xcoordinate before action  xcoordinate 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^{2}) wherectr_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 tocontact_force_range
)^{2}).
The total reward returned is reward = healthy_reward + forward_reward  ctrl_cost.
But if use_contact_forces=True
or version < v4
The total reward returned is reward = healthy_reward + forward_reward  ctrl_cost  contact_cost.
In either case 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:
Any of the state space values is no longer finite
The zcoordinate 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:
Truncation: The episode duration reaches a 1000 timesteps
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.
import gymnasium as gym
env = gym.make('Antv2')
v3 and v4 take gymnasium.make
kwargs such as xml_file
, ctrl_cost_weight
, reset_noise_scale
, etc.
import gymnasium as gym
env = gym.make('Antv4', ctrl_cost_weight=0.1, ...)
Parameter 
Type 
Default 
Description 


str 

Path to a MuJoCo model 

float 

Weight for ctrl_cost term (see section on reward) 

bool 

If true, it extends the observation space by adding contact forces (see 

float 

Weight for contact_cost term (see section on reward) 

float 

Constant reward given if the ant is “healthy” after timestep 

bool 

If true, issue a done signal if the zcoordinate of the torso is no longer in the 

tuple 

The ant is considered healthy if the zcoordinate of the torso is in this range 

tuple 

Contact forces are clipped to this range in the computation of contact_cost 

float 

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

bool 

Whether or not to omit the x and ycoordinates from observations. Excluding the position can serve as an inductive bias to induce positionagnostic behavior in policies 
Version History#
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 asxml_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 mujocopy >= 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)