Humanoid

This environment is part of the Mujoco environments.Please read that page first for general information.

Action Space	Box(-0.4, 0.4, (17,), float32)
Observation Shape	(376,)
Observation High	inf
Observation Low	-inf
Import	gymnasium.make("Humanoid-v4")

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 two links, and so the arms (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 y-coordinate of the abdomen	-0.4	0.4	hip_1 (front_left_leg)	hinge	torque (N m)
1	Torque applied on the hinge in the z-coordinate of the abdomen	-0.4	0.4	angle_1 (front_left_leg)	hinge	torque (N m)
2	Torque applied on the hinge in the x-coordinate of the abdomen	-0.4	0.4	hip_2 (front_right_leg)	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

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 y-coordinates of the torso. These may be included by passing exclude_current_positions_from_observation=False during construction. In that case, the observation space will have 378 dimensions where the first two dimensions represent the x- and y-coordinates of the torso. Regardless of whether exclude_current_positions_from_observation was set to true or false, the x- and y-coordinates will be returned in info with keys "x_position" and "y_position", respectively.

However, by default, the observation is a ndarray with shape (376,) where the elements correspond to the following:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	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)
19	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	anglular velocity (rad/s)
26	y-coordinate angular velocity of the torso (centre)	-Inf	Inf	root	free	anglular velocity (rad/s)
27	z-coordinate angular velocity of the torso (centre)	-Inf	Inf	root	free	anglular velocity (rad/s)
28	z-coordinate of angular velocity of the abdomen (in lower_waist)	-Inf	Inf	abdomen_z	hinge	anglular velocity (rad/s)
29	y-coordinate of angular velocity of the abdomen (in lower_waist)	-Inf	Inf	abdomen_y	hinge	anglular velocity (rad/s)
30	x-coordinate of angular velocity of the abdomen (in pelvis)	-Inf	Inf	abdomen_x	hinge	aanglular 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	anglular 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	anglular 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	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	x-coordinate 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	z-coordinate 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	y-coordinate 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	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	anglular 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	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	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	anglular 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	anglular velocity (rad/s)
44	angular velocitty of the angle between left upper arm and left_lower_arm	-Inf	Inf	left_elbow	hinge	anglular velocity (rad/s)

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 (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: Humanoid-v4 environment no longer has the following contact forces issue. If using previous Humanoid versions from v4, there have been reported issues that using a Mujoco-Py version > 2.0 results in the contact forces always being 0. As such we recommend to use a Mujoco-Py 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 x-direction). 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 as ctrl_cost_weight * sum(control²).

• 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 force²) to the interval specified by contact_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 z-position 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:

1. Truncation: The episode duration reaches a 1000 timesteps

2. 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('Humanoid-v4')

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('Humanoid-v4', 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 section on reward)
ctrl_cost_weight	float	0.1	Weight for ctrl_cost term (see section on reward)
contact_cost_weight	float	5e-7	Weight for contact_cost term (see section on reward)
healthy_reward	float	5.0	Constant reward given if the humanoid is “healthy” after timestep
terminate_when_unhealthy	bool	True	If true, issue a done signal if the z-coordinate of the torso is no longer in the healthy_z_range
healthy_z_range	tuple	(1.0, 2.0)	The humanoid is considered healthy if the z-coordinate of the torso is in this range
reset_noise_scale	float	1e-2	Scale of random perturbations of initial position and velocity (see section on Starting State)
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

Version History

• 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)

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