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 one introduced by Schulman, Moritz, Levine, Jordan, and Abbeel in “HighDimensional 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¶
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 ycoordinates 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 ycoordinates of the torso.
Regardless of whether exclude_current_positions_from_observation
is set to True
or False
, the x and ycoordinates 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 
zcoordinate of the torso (centre) 
Inf 
Inf 
root 
free 
position (m) 
1 
worientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
2 
xorientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
3 
yorientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
4 
zorientation 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 
xcoordinate velocity of the torso 
Inf 
Inf 
root 
free 
velocity (m/s) 
14 
ycoordinate velocity of the torso 
Inf 
Inf 
root 
free 
velocity (m/s) 
15 
zcoordinate velocity of the torso 
Inf 
Inf 
root 
free 
velocity (m/s) 
16 
xcoordinate angular velocity of the torso 
Inf 
Inf 
root 
free 
angular velocity (rad/s) 
17 
ycoordinate angular velocity of the torso 
Inf 
Inf 
root 
free 
angular velocity (rad/s) 
18 
zcoordinate 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 
xcoordinate of the torso (centre) 
Inf 
Inf 
root 
free 
position (m) 
excluded 
ycoordinate of the torso (centre) 
Inf 
Inf 
root 
free 
position (m) 
The body parts are:
body part 
id (for 
id (for 

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 Antv3 or earlier versions, problems have been reported when using a mujocopy
version > 2.0, resulting in contact forces always being 0.
Therefore, it is recommended to use a mujocopy
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
(\(x_{afteraction}  x_{beforeaction}\)), \(dt\) is the time between actions, which depends on theframe_skip
parameter (default is \(5\)), andframetime
, which is \(0.01\)  so the default is \(dt = 5 \times 0.01 = 0.05\), \(w_{forward}\) is theforward_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 bycontact_force_range
(seecfrc_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 xcoordinates are nonzero so that the ant can immediately stand up and face forward (xaxis).
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:
Any of the state space values is no longer finite.
The zcoordinate 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('Antv5', ctrl_cost_weight=0.5, ...)
Parameter 
Type 
Default 
Description 


str 

Path to a MuJoCo model 

float 

Weight for forward_reward term (see 

float 

Weight for ctrl_cost term (see 

float 

Weight for contact_cost term (see 

float 

Weight for healthy_reward term (see 

strint 

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

bool 

If 

tuple 

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

tuple 

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

float 

Scale of random perturbations of initial position and velocity (see 

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 (see 

bool 

Whether to include cfrc_ext elements in the observations (see 

bool 

If 
Version History¶
v5:
Minimum
mujoco
version is now 2.3.3.Added support for fully custom/third party
mujoco
models using thexml_file
argument (previously only a few changes could be made to the existing models).Added
default_camera_config
argument, a dictionary for setting themj_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 nonempty
info
withreset()
, previously an empty dictionary was returned, the new keys are the same state information asstep()
.Added
frame_skip
argument, used to configure thedt
(duration ofstep()
), 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. Theinfo["reward_survive"]
is updated with this change (related GitHub issue).The reward function now always includes
contact_cost
, before it was only included ifuse_contact_forces=True
(can be set to0
withcontact_cost_weight=0
).Excluded the
cfrc_ext
ofworldbody
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 to1
(effectively the same behavior as inv4
).Added the
include_cfrc_ext_in_observation
argument, previously inv4
the inclusion ofcfrc_ext
observations was controlled byuse_contact_forces
which defaulted toFalse
, whileinclude_cfrc_ext_in_observation
defaults toTrue
.Removed the
use_contact_forces
argument (note: its functionality has been replaced byinclude_cfrc_ext_in_observation
andcontact_cost_weight
) (related GitHub issue).Fixed
info["reward_ctrl"]
sometimes containingcontact_cost
instead ofctrl_cost
.Fixed
info["x_position"]
&info["y_position"]
&info["distance_from_origin"]
givingxpos
instead ofqpos
observations (xpos
observations are behind 1mj_step()
more here) (related GitHub issue #1 & GitHub issue #2).Removed
info["forward_reward"]
as it is equivalent toinfo["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 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