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. The legs each consist of three body parts, and the arms 2 body parts (representing the knees and elbows respectively). The goal of the environment is to walk forward as fast as possible without falling over.
Action Space#
The action space is a Box(1, 1, (17,), 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 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#
Observations consist of positional values of different body parts of the Humanoid, 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 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, (378,), float64)
where the first two observations
represent the x and ycoordinates of the torso.
Regardless of whether exclude_current_positions_from_observation
was set to true or false, the x and ycoordinates
will be returned in info
with keys "x_position"
and "y_position"
, respectively.
However, by default, the observation is a Box(Inf, Inf, (376,), float64)
. 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 
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 
anglular velocity (rad/s) 
26 
ycoordinate angular velocity of the torso (centre) 
Inf 
Inf 
root 
free 
anglular velocity (rad/s) 
27 
zcoordinate angular velocity of the torso (centre) 
Inf 
Inf 
root 
free 
anglular velocity (rad/s) 
28 
zcoordinate of angular velocity of the abdomen (in lower_waist) 
Inf 
Inf 
abdomen_z 
hinge 
anglular velocity (rad/s) 
29 
ycoordinate of angular velocity of the abdomen (in lower_waist) 
Inf 
Inf 
abdomen_y 
hinge 
anglular velocity (rad/s) 
30 
xcoordinate of angular velocity of the abdomen (in pelvis) 
Inf 
Inf 
abdomen_x 
hinge 
aanglular 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 
anglular 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 
anglular 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 
anglular velocity (rad/s) 
34 
angular velocity of the angle between right hip and the right shin (in right_knee) 
Inf 
Inf 
right_knee 
hinge 
anglular 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 
anglular 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 
anglular 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 
anglular velocity (rad/s) 
38 
angular velocity of the angle between left hip and the left shin (in left_knee) 
Inf 
Inf 
left_knee 
hinge 
anglular 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 
anglular 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 
anglular velocity (rad/s) 
41 
angular velocity of the angle between right upper arm and right_lower_arm 
Inf 
Inf 
right_elbow 
hinge 
anglular 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 
anglular 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 
anglular velocity (rad/s) 
44 
angular velocity of the angle between left upper arm and left_lower_arm 
Inf 
Inf 
left_elbow 
hinge 
anglular 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) 
Additionally, after all the positional and velocity based values in the table, the observation contains (in order):
cinert: Mass and inertia of a single rigid body relative to the center of mass (this is an intermediate result of transition). It has shape 14*10 (nbody * 10) and hence adds to another 140 elements in the state space.
cvel: Center of mass based velocity. It has shape 14 * 6 (nbody * 6) and hence adds another 84 elements in the state space
qfrc_actuator: Constraint force generated as the actuator force. This has shape
(23,)
(nv * 1) and hence adds another 23 elements to the state space.cfrc_ext: This is the center of mass based external force on the body. It has shape 14 * 6 (nbody * 6) and hence adds to another 84 elements in the state space. where nbody stands for the number of bodies in the robot and nv stands for the number of degrees of freedom (= dim(qvel))
The body parts are:
id (for 
body part 

0 
worldBody (note: all values are constant 0) 
1 
torso 
2 
lwaist 
3 
pelvis 
4 
right_thigh 
5 
right_sin 
6 
right_foot 
7 
left_thigh 
8 
left_sin 
9 
left_foot 
10 
right_upper_arm 
11 
right_lower_arm 
12 
left_upper_arm 
13 
left_lower_arm 
The joints are:
id (for 
joint 

0 
root 
1 
root 
2 
root 
3 
root 
4 
root 
5 
root 
6 
abdomen_z 
7 
abdomen_y 
8 
abdomen_x 
9 
right_hip_x 
10 
right_hip_z 
11 
right_hip_y 
12 
right_knee 
13 
left_hip_x 
14 
left_hiz_z 
15 
left_hip_y 
16 
left_knee 
17 
right_shoulder1 
18 
right_shoulder2 
19 
right_elbow 
20 
left_shoulder1 
21 
left_shoulder2 
22 
left_elfbow 
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: Humanoidv4 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 Humanoid 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 humanoid is alive (see section Episode Termination for definition), it gets a reward of fixed value
healthy_reward
forward_reward: A reward of walking forward which is measured as
forward_reward_weight
* (average center of mass before action  average center of mass after action)/dt. dt is the time between actions and is dependent on the frame_skip parameter (default is 5), where the frametime is 0.003  making the default dt = 5 * 0.003 = 0.015. This reward would be positive if the humanoid walks forward (in positive xdirection). The calculation for the center of mass is defined in the.py
file for the Humanoid.ctrl_cost: A negative reward for penalising the humanoid if it has too large of a control force. If there are nu actuators/controls, then the control has shape
nu x 1
. It is measured asctrl_cost_weight
* sum(control^{2}).contact_cost: A negative reward for penalising the humanoid if the external contact force is too large. It is calculated by clipping
contact_cost_weight
* sum(external contact force^{2}) to the interval specified bycontact_cost_range
.
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, 1.4, 1.0, 0.0 … 0.0) with a uniform noise in the range
of [reset_noise_scale
, reset_noise_scale
] added to the positional and velocity values (values in the table)
for stochasticity. Note that the initial z coordinate is intentionally
selected to be high, thereby indicating a standing up humanoid. The initial
orientation is designed to make it face forward as well.
Episode End#
The humanoid is said to be unhealthy if the zposition of the torso is no longer contained in the
closed interval specified by the argument healthy_z_range
.
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 humanoid 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('Humanoidv4')
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('Humanoidv4', ctrl_cost_weight=0.1, ....)
Parameter 
Type 
Default 
Description 


str 

Path to a MuJoCo model 

float 

Weight for forward_reward term (see section on reward) 

float 

Weight for ctrl_cost term (see section on reward) 

float 

Weight for contact_cost term (see section on reward) 

float 

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

bool 

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

tuple 

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

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
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)