Humanoid¶
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 Tassa, Erez and Todorov in “Synthesis and stabilization of complex behaviors through online trajectory optimization”. The 3D bipedal robot is designed to simulate a human. It has a torso (abdomen) with a pair of legs and arms, and a pair of tendons connecting the hips to the knees. The legs each consist of three body parts (thigh, shin, foot), and the arms consist of two body parts (upper arm, forearm). The goal of the environment is to walk forward as fast as possible without falling over.
Action Space¶
The action space is a Box(0.4, 0.4, (17,), 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 hinge in the ycoordinate of the abdomen 
0.4 
0.4 
abdomen_y 
hinge 
torque (N m) 
1 
Torque applied on the hinge in the zcoordinate of the abdomen 
0.4 
0.4 
abdomen_z 
hinge 
torque (N m) 
2 
Torque applied on the hinge in the xcoordinate of the abdomen 
0.4 
0.4 
abdomen_x 
hinge 
torque (N m) 
3 
Torque applied on the rotor between torso/abdomen and the right hip (xcoordinate) 
0.4 
0.4 
right_hip_x (right_thigh) 
hinge 
torque (N m) 
4 
Torque applied on the rotor between torso/abdomen and the right hip (zcoordinate) 
0.4 
0.4 
right_hip_z (right_thigh) 
hinge 
torque (N m) 
5 
Torque applied on the rotor between torso/abdomen and the right hip (ycoordinate) 
0.4 
0.4 
right_hip_y (right_thigh) 
hinge 
torque (N m) 
6 
Torque applied on the rotor between the right hip/thigh and the right shin 
0.4 
0.4 
right_knee 
hinge 
torque (N m) 
7 
Torque applied on the rotor between torso/abdomen and the left hip (xcoordinate) 
0.4 
0.4 
left_hip_x (left_thigh) 
hinge 
torque (N m) 
8 
Torque applied on the rotor between torso/abdomen and the left hip (zcoordinate) 
0.4 
0.4 
left_hip_z (left_thigh) 
hinge 
torque (N m) 
9 
Torque applied on the rotor between torso/abdomen and the left hip (ycoordinate) 
0.4 
0.4 
left_hip_y (left_thigh) 
hinge 
torque (N m) 
10 
Torque applied on the rotor between the left hip/thigh and the left shin 
0.4 
0.4 
left_knee 
hinge 
torque (N m) 
11 
Torque applied on the rotor between the torso and right upper arm (coordinate 1) 
0.4 
0.4 
right_shoulder1 
hinge 
torque (N m) 
12 
Torque applied on the rotor between the torso and right upper arm (coordinate 2) 
0.4 
0.4 
right_shoulder2 
hinge 
torque (N m) 
13 
Torque applied on the rotor between the right upper arm and right lower arm 
0.4 
0.4 
right_elbow 
hinge 
torque (N m) 
14 
Torque applied on the rotor between the torso and left upper arm (coordinate 1) 
0.4 
0.4 
left_shoulder1 
hinge 
torque (N m) 
15 
Torque applied on the rotor between the torso and left upper arm (coordinate 2) 
0.4 
0.4 
left_shoulder2 
hinge 
torque (N m) 
16 
Torque applied on the rotor between the left upper arm and left lower arm 
0.4 
0.4 
left_elbow 
hinge 
torque (N m) 
Observation Space¶
The observation space consists of the following parts (in order)
qpos (22 elements by default): The position values of the robot’s body parts.
qvel (23 elements): The velocities of these individual body parts (their derivatives).
cinert (130 elements): Mass and inertia of the rigid body parts relative to the center of mass, (this is an intermediate result of the transition). It has shape 13*10 (nbody * 10). (cinert  inertia matrix and body mass offset and body mass)
cvel (78 elements): Center of mass based velocity. It has shape 13 * 6 (nbody * 6). (com velocity  velocity x, y, z and angular velocity x, y, z)
qfrc_actuator (17 elements): Constraint force generated as the actuator force at each joint. This has shape
(17,)
(nv * 1).cfrc_ext (78 elements): This is the center of mass based external force on the body parts. It has shape 13 * 6 (nbody * 6) and thus adds another 78 elements to the observation space. (external forces  force x, y, z and torque x, y, z)
where nbody is the number of bodies in the robot, and nv is the number of degrees of freedom (= dim(qvel)).
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, (350,), 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, (348,), 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 
xorientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
2 
yorientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
3 
zorientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
4 
worientation of the torso (centre) 
Inf 
Inf 
root 
free 
angle (rad) 
5 
zangle of the abdomen (in lower_waist) 
Inf 
Inf 
abdomen_z 
hinge 
angle (rad) 
6 
yangle of the abdomen (in lower_waist) 
Inf 
Inf 
abdomen_y 
hinge 
angle (rad) 
7 
xangle of the abdomen (in pelvis) 
Inf 
Inf 
abdomen_x 
hinge 
angle (rad) 
8 
xcoordinate of angle between pelvis and right hip (in right_thigh) 
Inf 
Inf 
right_hip_x 
hinge 
angle (rad) 
9 
zcoordinate of angle between pelvis and right hip (in right_thigh) 
Inf 
Inf 
right_hip_z 
hinge 
angle (rad) 
10 
ycoordinate of angle between pelvis and right hip (in right_thigh) 
Inf 
Inf 
right_hip_y 
hinge 
angle (rad) 
11 
angle between right hip and the right shin (in right_knee) 
Inf 
Inf 
right_knee 
hinge 
angle (rad) 
12 
xcoordinate of angle between pelvis and left hip (in left_thigh) 
Inf 
Inf 
left_hip_x 
hinge 
angle (rad) 
13 
zcoordinate of angle between pelvis and left hip (in left_thigh) 
Inf 
Inf 
left_hip_z 
hinge 
angle (rad) 
14 
ycoordinate of angle between pelvis and left hip (in left_thigh) 
Inf 
Inf 
left_hip_y 
hinge 
angle (rad) 
15 
angle between left hip and the left shin (in left_knee) 
Inf 
Inf 
left_knee 
hinge 
angle (rad) 
16 
coordinate1 (multiaxis) angle between torso and right arm (in right_upper_arm) 
Inf 
Inf 
right_shoulder1 
hinge 
angle (rad) 
17 
coordinate2 (multiaxis) angle between torso and right arm (in right_upper_arm) 
Inf 
Inf 
right_shoulder2 
hinge 
angle (rad) 
18 
angle between right upper arm and right_lower_arm 
Inf 
Inf 
right_elbow 
hinge 
angle (rad) 
19 
coordinate1 (multiaxis) angle between torso and left arm (in left_upper_arm) 
Inf 
Inf 
left_shoulder1 
hinge 
angle (rad) 
20 
coordinate2 (multiaxis) angle between torso and left arm (in left_upper_arm) 
Inf 
Inf 
left_shoulder2 
hinge 
angle (rad) 
21 
angle between left upper arm and left_lower_arm 
Inf 
Inf 
left_elbow 
hinge 
angle (rad) 
22 
xcoordinate velocity of the torso (centre) 
Inf 
Inf 
root 
free 
velocity (m/s) 
23 
ycoordinate velocity of the torso (centre) 
Inf 
Inf 
root 
free 
velocity (m/s) 
24 
zcoordinate velocity of the torso (centre) 
Inf 
Inf 
root 
free 
velocity (m/s) 
25 
xcoordinate angular velocity of the torso (centre) 
Inf 
Inf 
root 
free 
angular velocity (rad/s) 
26 
ycoordinate angular velocity of the torso (centre) 
Inf 
Inf 
root 
free 
angular velocity (rad/s) 
27 
zcoordinate angular velocity of the torso (centre) 
Inf 
Inf 
root 
free 
angular velocity (rad/s) 
28 
zcoordinate of angular velocity of the abdomen (in lower_waist) 
Inf 
Inf 
abdomen_z 
hinge 
angular velocity (rad/s) 
29 
ycoordinate of angular velocity of the abdomen (in lower_waist) 
Inf 
Inf 
abdomen_y 
hinge 
angular velocity (rad/s) 
30 
xcoordinate of angular velocity of the abdomen (in pelvis) 
Inf 
Inf 
abdomen_x 
hinge 
angular velocity (rad/s) 
31 
xcoordinate of the angular velocity of the angle between pelvis and right hip (in right_thigh) 
Inf 
Inf 
right_hip_x 
hinge 
angular velocity (rad/s) 
32 
zcoordinate of the angular velocity of the angle between pelvis and right hip (in right_thigh) 
Inf 
Inf 
right_hip_z 
hinge 
angular velocity (rad/s) 
33 
ycoordinate of the angular velocity of the angle between pelvis and right hip (in right_thigh) 
Inf 
Inf 
right_hip_y 
hinge 
angular velocity (rad/s) 
34 
angular velocity of the angle between right hip and the right shin (in right_knee) 
Inf 
Inf 
right_knee 
hinge 
angular velocity (rad/s) 
35 
xcoordinate of the angular velocity of the angle between pelvis and left hip (in left_thigh) 
Inf 
Inf 
left_hip_x 
hinge 
angular velocity (rad/s) 
36 
zcoordinate of the angular velocity of the angle between pelvis and left hip (in left_thigh) 
Inf 
Inf 
left_hip_z 
hinge 
angular velocity (rad/s) 
37 
ycoordinate of the angular velocity of the angle between pelvis and left hip (in left_thigh) 
Inf 
Inf 
left_hip_y 
hinge 
angular velocity (rad/s) 
38 
angular velocity of the angle between left hip and the left shin (in left_knee) 
Inf 
Inf 
left_knee 
hinge 
angular velocity (rad/s) 
39 
coordinate1 (multiaxis) of the angular velocity of the angle between torso and right arm (in right_upper_arm) 
Inf 
Inf 
right_shoulder1 
hinge 
angular velocity (rad/s) 
40 
coordinate2 (multiaxis) of the angular velocity of the angle between torso and right arm (in right_upper_arm) 
Inf 
Inf 
right_shoulder2 
hinge 
angular velocity (rad/s) 
41 
angular velocity of the angle between right upper arm and right_lower_arm 
Inf 
Inf 
right_elbow 
hinge 
angular velocity (rad/s) 
42 
coordinate1 (multiaxis) of the angular velocity of the angle between torso and left arm (in left_upper_arm) 
Inf 
Inf 
left_shoulder1 
hinge 
angular velocity (rad/s) 
43 
coordinate2 (multiaxis) of the angular velocity of the angle between torso and left arm (in left_upper_arm) 
Inf 
Inf 
left_shoulder2 
hinge 
angular velocity (rad/s) 
44 
angular velocity of the angle between left upper arm and left_lower_arm 
Inf 
Inf 
left_elbow 
hinge 
angular velocity (rad/s) 
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 
lwaist 
2 
1 
pelvis 
3 
2 
right_thigh 
4 
3 
right_sin 
5 
4 
right_foot 
6 
5 
left_thigh 
7 
6 
left_sin 
8 
7 
left_foot 
9 
8 
right_upper_arm 
10 
9 
right_lower_arm 
11 
10 
left_upper_arm 
12 
11 
left_lower_arm 
13 
12 
The joints are:
joint 
id (for 
id (for 

root (note: all values are constant 0) 
0 
excluded 
root (note: all values are constant 0) 
1 
excluded 
root (note: all values are constant 0) 
2 
excluded 
root (note: all values are constant 0) 
3 
excluded 
root (note: all values are constant 0) 
4 
excluded 
root (note: all values are constant 0) 
5 
excluded 
abdomen_z 
6 
0 
abdomen_y 
7 
1 
abdomen_x 
8 
2 
right_hip_x 
9 
3 
right_hip_z 
10 
4 
right_hip_y 
11 
5 
right_knee 
12 
6 
left_hip_x 
13 
7 
left_hiz_z 
14 
8 
left_hip_y 
15 
9 
left_knee 
16 
10 
right_shoulder1 
17 
11 
right_shoulder2 
18 
12 
right_elbow 
19 
13 
left_shoulder1 
20 
14 
left_shoulder2 
21 
15 
left_elfbow 
22 
16 
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 Humanoidv3 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 Humanoid 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 Humanoid is alive (see definition in section “Episode End”), it gets a reward of fixed value
healthy_reward
(default is \(5\)).forward_reward: A reward for moving forward, this reward would be positive if the Humanoid moves forward (in the positive \(x\) direction / in the right direction). \(w_{forward} \times \frac{dx}{dt}\), where \(dx\) is the displacement of the center of mass (\(x_{afteraction}  x_{beforeaction}\)), \(dt\) is the time between actions, which depends on the
frame_skip
parameter (default is \(5\)), andframetime
which is \(0.001\)  so the default is \(dt = 5 \times 0.003 = 0.015\), \(w_{forward}\) is theforward_reward_weight
(default is \(1.25\)).ctrl_cost: A negative reward to penalize the Humanoid for taking actions that are too large. \(w_{control} \times \action\_2^2\), where \(w_{control}\) is
ctrl_cost_weight
(default is \(0.1\)).contact_cost: A negative reward to penalize the Humanoid if the external contact forces are too large. \(w_{contact} \times clamp(contact\_cost\_range, \F_{contact}\_2^2)\), where \(w_{contact}\) is
contact_cost_weight
(default is \(5\times10^{7}\)), \(F_{contact}\) are the external contact forces (seecfrc_ext
section on observation).
info
contains the individual reward terms.
Note: There is a bug in the Humanoidv4
environment that causes contact_cost to always be 0.
Starting State¶
The initial position state is \([0.0, 0.0, 1.4, 1.0, 0.0, ... 0.0] + \mathcal{U}_{[reset\_noise\_scale \times I_{24}, reset\_noise\_scale \times I_{24}]}\). The initial velocity state is \(\mathcal{U}_{[reset\_noise\_scale \times I_{23}, reset\_noise\_scale \times I_{23}]}\).
where \(\mathcal{U}\) is the multivariate uniform continuous distribution.
Note that the z and xcoordinates are nonzero so that the humanoid can immediately stand up and face forward (xaxis).
Episode End¶
Termination¶
If terminate_when_unhealthy is True
(the default), the environment terminates when the Humanoid is unhealthy.
The Humanoid is said to be unhealthy if any of the following happens:
The zcoordinate of the torso (the height) is not in the closed interval given by the
healthy_z_range
argument (default is \([1.0, 2.0]\)).
Truncation¶
The default duration of an episode is 1000 timesteps.
Arguments¶
Humanoid 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('Humanoidv5', ctrl_cost_weight=0.1, ....)
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 

Clamps the contact_cost term (see 

float 

Weight for healthy_reward term (see 

bool 

If 

tuple 

The humanoid is considered healthy if the zcoordinate of the torso is in this range (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 cinert elements in the observations (see 

bool 

Whether to include cvel elements in the observations (see 

bool 

Whether to include qfrc_actuator elements in the observations (see 

bool 

Whether to include cfrc_ext elements in the observations (see 
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 Humanoid was unhealthy), now it is only given when the Humanoid is healthy. Theinfo["reward_survive"]
is updated with this change (related GitHub issue).Restored
contact_cost
and the correspondingcontact_cost_weight
andcontact_cost_range
arguments, with the same defaults as inHumanoidv3
(was removed inv4
) (related GitHub issue).Excluded the
cinert
&cvel
&cfrc_ext
ofworldbody
androot
/freejoint
qfrc_actuator
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).Restored the
xml_file
argument (was removed inv4
).Added
include_cinert_in_observation
,include_cvel_in_observation
,include_qfrc_actuator_in_observation
,include_cfrc_ext_in_observation
arguments to allow for the exclusion of observation elements from the observation space.Fixed
info["x_position"]
&info["y_position"]
&info["distance_from_origin"]
returningxpos
instead ofqpos
based observations (xpos
observations are behind 1mj_step()
more here) (related GitHub issue #1 & GitHub issue #2).Added
info["tendon_length"]
andinfo["tendon_velocity"]
containing observations of the Humanoid’s 2 tendons connecting the hips to the knees.Renamed
info["reward_alive"]
toinfo["reward_survive"]
to be consistent with the other environments.Renamed
info["reward_linvel"]
toinfo["reward_forward"]
to be consistent with the other environments.Renamed
info["reward_quadctrl"]
toinfo["reward_ctrl"]
to be consistent with the other environments.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
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)Note: the environment robot model was slightly changed at
gym==0.21.0
and training results are not comparable withgym<0.21
andgym>=0.21
(related GitHub PR)
v2: All continuous control environments now use mujocopy >= 1.50
Note: the environment robot model was slightly changed at
gym==0.21.0
and training results are not comparable withgym<0.21
andgym>=0.21
(related GitHub PR)
v1: max_time_steps raised to 1000 for robot based tasks. Added reward_threshold to environments.
v0: Initial versions release