Humanoid

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

Action Space	Box(-0.4, 0.4, (17,), float32)
Observation Space	Box(-inf, inf, (348,), float64)
import	gymnasium.make("Humanoid-v5")

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 y-coordinate of the abdomen	-0.4	0.4	abdomen_y	hinge	torque (N m)
1	Torque applied on the hinge in the z-coordinate of the abdomen	-0.4	0.4	abdomen_z	hinge	torque (N m)
2	Torque applied on the hinge in the x-coordinate 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 (x-coordinate)	-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 (z-coordinate)	-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 (y-coordinate)	-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 (x-coordinate)	-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 (z-coordinate)	-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 (y-coordinate)	-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 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, (350,), 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, (348,), 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	z-angle of the abdomen (in lower_waist)	-Inf	Inf	abdomen_z	hinge	angle (rad)
6	y-angle of the abdomen (in lower_waist)	-Inf	Inf	abdomen_y	hinge	angle (rad)
7	x-angle of the abdomen (in pelvis)	-Inf	Inf	abdomen_x	hinge	angle (rad)
8	x-coordinate of angle between pelvis and right hip (in right_thigh)	-Inf	Inf	right_hip_x	hinge	angle (rad)
9	z-coordinate of angle between pelvis and right hip (in right_thigh)	-Inf	Inf	right_hip_z	hinge	angle (rad)
10	y-coordinate 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	x-coordinate of angle between pelvis and left hip (in left_thigh)	-Inf	Inf	left_hip_x	hinge	angle (rad)
13	z-coordinate of angle between pelvis and left hip (in left_thigh)	-Inf	Inf	left_hip_z	hinge	angle (rad)
14	y-coordinate 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	coordinate-1 (multi-axis) angle between torso and right arm (in right_upper_arm)	-Inf	Inf	right_shoulder1	hinge	angle (rad)
17	coordinate-2 (multi-axis) 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	coordinate-1 (multi-axis) angle between torso and left arm (in left_upper_arm)	-Inf	Inf	left_shoulder1	hinge	angle (rad)
20	coordinate-2 (multi-axis) 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	x-coordinate velocity of the torso (centre)	-Inf	Inf	root	free	velocity (m/s)
23	y-coordinate velocity of the torso (centre)	-Inf	Inf	root	free	velocity (m/s)
24	z-coordinate velocity of the torso (centre)	-Inf	Inf	root	free	velocity (m/s)
25	x-coordinate angular velocity of the torso (centre)	-Inf	Inf	root	free	angular velocity (rad/s)
26	y-coordinate angular velocity of the torso (centre)	-Inf	Inf	root	free	angular velocity (rad/s)
27	z-coordinate angular velocity of the torso (centre)	-Inf	Inf	root	free	angular velocity (rad/s)
28	z-coordinate of angular velocity of the abdomen (in lower_waist)	-Inf	Inf	abdomen_z	hinge	angular velocity (rad/s)
29	y-coordinate of angular velocity of the abdomen (in lower_waist)	-Inf	Inf	abdomen_y	hinge	angular velocity (rad/s)
30	x-coordinate of angular velocity of the abdomen (in pelvis)	-Inf	Inf	abdomen_x	hinge	angular velocity (rad/s)
31	x-coordinate 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	z-coordinate 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	y-coordinate 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	x-coordinate 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	z-coordinate 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	y-coordinate 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	coordinate-1 (multi-axis) 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	coordinate-2 (multi-axis) 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	coordinate-1 (multi-axis) 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	coordinate-2 (multi-axis) 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	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
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 v2, v3, v4)	id (for v5)
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 Humanoid-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 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 (\(x_{after-action} - x_{before-action}\)), \(dt\) is the time between actions, which depends on the frame_skip parameter (default is \(5\)), and frametime which is \(0.001\) - so the default is \(dt = 5 \times 0.003 = 0.015\), \(w_{forward}\) is the forward_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 (see cfrc_ext section on observation).

info contains the individual reward terms.

Note: There is a bug in the Humanoid-v4 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 x-coordinates are non-zero so that the humanoid 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 Humanoid is unhealthy. The Humanoid is said to be unhealthy if any of the following happens:

1. The z-coordinate 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('Humanoid-v5', ctrl_cost_weight=0.1, ....)

Parameter	Type	Default	Description
xml_file	str	"humanoid.xml"	Path to a MuJoCo model
forward_reward_weight	float	1.25	Weight for forward_reward term (see Rewards section)
ctrl_cost_weight	float	0.1	Weight for ctrl_cost term (see Rewards section)
contact_cost_weight	float	5e-7	Weight for contact_cost term (see Rewards section)
contact_cost_range	float	(-np.inf, 10.0)	Clamps the contact_cost term (see Rewards section)
healthy_reward	float	5.0	Weight for healthy_reward term (see Rewards section)
terminate_when_unhealthy	bool	True	If True, issue a terminated signal is unhealthy (see Episode End section)
healthy_z_range	tuple	(1.0, 2.0)	The humanoid is considered healthy if the z-coordinate of the torso is in this range (see Episode End section)
reset_noise_scale	float	1e-2	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_cinert_in_observation	bool	True	Whether to include cinert elements in the observations (see Observation State section)
include_cvel_in_observation	bool	True	Whether to include cvel elements in the observations (see Observation State section)
include_qfrc_actuator_in_observation	bool	True	Whether to include qfrc_actuator elements in the observations (see Observation State section)
include_cfrc_ext_in_observation	bool	True	Whether to include cfrc_ext elements in the observations (see Observation State 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 Humanoid was unhealthy), now it is only given when the Humanoid is healthy. The info["reward_survive"] is updated with this change (related GitHub issue).

  • Restored contact_cost and the corresponding contact_cost_weight and contact_cost_range arguments, with the same defaults as in Humanoid-v3 (was removed in v4) (related GitHub issue).

  • Excluded the cinert & cvel & cfrc_ext of worldbody and root/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 in v4).

  • 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"] returning xpos instead of qpos based observations (xpos observations are behind 1 mj_step() more here) (related GitHub issue #1 & GitHub issue #2).

  • Added info["tendon_length"] and info["tendon_velocity"] containing observations of the Humanoid’s 2 tendons connecting the hips to the knees.

  • Renamed info["reward_alive"] to info["reward_survive"] to be consistent with the other environments.

  • Renamed info["reward_linvel"] to info["reward_forward"] to be consistent with the other environments.

  • Renamed info["reward_quadctrl"] to info["reward_ctrl"] to be consistent with the other environments.

  • 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

• 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)

  • Note: the environment robot model was slightly changed at gym==0.21.0 and training results are not comparable with gym<0.21 and gym>=0.21 (related GitHub PR)

• v2: All continuous control environments now use mujoco-py >= 1.50

  • Note: the environment robot model was slightly changed at gym==0.21.0 and training results are not comparable with gym<0.21 and gym>=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