Walker2D

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

Action Space	Box(-1.0, 1.0, (6,), float32)
Observation Space	Box(-inf, inf, (17,), float64)
import	gymnasium.make("Walker2d-v5")

Description

This environment builds on the hopper environment by adding another set of legs that allow the robot to walk forward instead of hop. Like other MuJoCo environments, this environment aims to increase the number of independent state and control variables compared to classical control environments. The walker is a two-dimensional bipedal robot consisting of seven main body parts - a single torso at the top (with the two legs splitting after the torso), two thighs in the middle below the torso, two legs below the thighs, and two feet attached to the legs on which the entire body rests. The goal is to walk in the forward (right) direction by applying torque to the six hinges connecting the seven body parts.

Action Space

The action space is a Box(-1, 1, (6,), 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 thigh rotor	-1	1	thigh_joint	hinge	torque (N m)
1	Torque applied on the leg rotor	-1	1	leg_joint	hinge	torque (N m)
2	Torque applied on the foot rotor	-1	1	foot_joint	hinge	torque (N m)
3	Torque applied on the left thigh rotor	-1	1	thigh_left_joint	hinge	torque (N m)
4	Torque applied on the left leg rotor	-1	1	leg_left_joint	hinge	torque (N m)
5	Torque applied on the left foot rotor	-1	1	foot_left_joint	hinge	torque (N m)

Observation Space

The observation space consists of the following parts (in order):

• qpos (8 elements by default): Position values of the robot’s body parts.

• qvel (9 elements): The velocities of these individual body parts (their derivatives).

By default, the observation does not include the robot’s x-coordinate (rootx). This 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, (18,), float64), where the first observation element is the x-coordinate of the robot. Regardless of whether exclude_current_positions_from_observation is set to True or False, the x-coordinate are returned in info with the keys "x_position" and "y_position", respectively.

By default, however, the observation space is a Box(-Inf, Inf, (17,), float64) where the elements are as follows:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Type (Unit)
0	z-coordinate of the torso (height of Walker2d)	-Inf	Inf	rootz	slide	position (m)
1	angle of the torso	-Inf	Inf	rooty	hinge	angle (rad)
2	angle of the thigh joint	-Inf	Inf	thigh_joint	hinge	angle (rad)
3	angle of the leg joint	-Inf	Inf	leg_joint	hinge	angle (rad)
4	angle of the foot joint	-Inf	Inf	foot_joint	hinge	angle (rad)
5	angle of the left thigh joint	-Inf	Inf	thigh_left_joint	hinge	angle (rad)
6	angle of the left leg joint	-Inf	Inf	leg_left_joint	hinge	angle (rad)
7	angle of the left foot joint	-Inf	Inf	foot_left_joint	hinge	angle (rad)
8	velocity of the x-coordinate of the torso	-Inf	Inf	rootx	slide	velocity (m/s)
9	velocity of the z-coordinate (height) of the torso	-Inf	Inf	rootz	slide	velocity (m/s)
10	angular velocity of the angle of the torso	-Inf	Inf	rooty	hinge	angular velocity (rad/s)
11	angular velocity of the thigh hinge	-Inf	Inf	thigh_joint	hinge	angular velocity (rad/s)
12	angular velocity of the leg hinge	-Inf	Inf	leg_joint	hinge	angular velocity (rad/s)
13	angular velocity of the foot hinge	-Inf	Inf	foot_joint	hinge	angular velocity (rad/s)
14	angular velocity of the thigh hinge	-Inf	Inf	thigh_left_joint	hinge	angular velocity (rad/s)
15	angular velocity of the leg hinge	-Inf	Inf	leg_left_joint	hinge	angular velocity (rad/s)
16	angular velocity of the foot hinge	-Inf	Inf	foot_left_joint	hinge	angular velocity (rad/s)
excluded	x-coordinate of the torso	-Inf	Inf	rootx	slide	position (m)

Rewards

The total reward is: reward = healthy_reward bonus + forward_reward - ctrl_cost.

• healthy_reward: Every timestep that the Walker2d is alive, it receives a fixed reward of value healthy_reward (default is \(1\)),

• forward_reward: A reward for moving forward, this reward would be positive if the Swimmer moves forward (in the positive \(x\) direction / in the right direction). \(w_{forward} \times \frac{dx}{dt}\), where \(dx\) is the displacement of the (front) “tip” (\(x_{after-action} - x_{before-action}\)), \(dt\) is the time between actions, which depends on the frame_skip parameter (default is \(4\)), and frametime which is \(0.002\) - so the default is \(dt = 4 \times 0.002 = 0.008\), \(w_{forward}\) is the forward_reward_weight (default is \(1\)).

• ctrl_cost: A negative reward to penalize the Walker2d for taking actions that are too large. \(w_{control} \times \|action\|_2^2\), where \(w_{control}\) is ctrl_cost_weight (default is \(10^{-3}\)).

info contains the individual reward terms.

Starting State

The initial position state is \([0, 1.25, 0, 0, 0, 0, 0, 0, 0] + \mathcal{U}_{[-reset\_noise\_scale \times I_{9}, reset\_noise\_scale \times I_{9}]}\). The initial velocity state is \(\mathcal{U}_{[-reset\_noise\_scale \times I_{9}, reset\_noise\_scale \times I_{9}]}\).

where \(\mathcal{U}\) is the multivariate uniform continuous distribution.

Note that the z-coordinate is non-zero so that the Walker2d can stand up immediately.

Episode End

Termination

If terminate_when_unhealthy is True (which is the default), the environment terminates when the Walker2d is unhealthy. The Walker2d is unhealthy if any of the following happens:

1. Any of the state space values is no longer finite

2. The z-coordinate of the torso (the height) is not in the closed interval given by the healthy_z_range argument (default to \([0.8, 1.0]\)).

3. The absolute value of the angle (observation[1] if exclude_current_positions_from_observation=False, else observation[2]) is not in the closed interval specified by the healthy_angle_range argument (default is \([-1, 1]\)).

Truncation

The default duration of an episode is 1000 timesteps.

Arguments

Walker2d 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('Walker2d-v5', ctrl_cost_weight=1e-3, ...)

Parameter	Type	Default	Description
xml_file	str	"walker2d_v5.xml"	Path to a MuJoCo model
forward_reward_weight	float	1	Weight for forward_reward term (see Rewards section)
ctrl_cost_weight	float	1e-3	Weight for ctr_cost term (see Rewards section)
healthy_reward	float	1	Weight for healthy_reward reward (see Rewards section)
terminate_when_unhealthy	bool	True	If True, issue a terminated signal is unhealthy (see Episode End section)
healthy_z_range	tuple	(0.8, 2)	The z-coordinate of the torso of the walker must be in this range to be considered healthy (see Episode End section)
healthy_angle_range	tuple	(-1, 1)	The angle must be in this range to be considered healthy (see Episode End section)
reset_noise_scale	float	5e-3	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-coordinate from observations. Excluding the position can serve as an inductive bias to induce position-agnostic behavior in policies (see Observation Space 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.

  • In v2, v3 and v4 the models have different friction values for the two feet (left foot friction == 1.9 and right foot friction == 0.9). The Walker-v5 model is updated to have the same friction for both feet (set to 1.9). This causes the Walker2d’s the right foot to slide less on the surface and therefore require more force to move (related GitHub issue).

  • Fixed bug: healthy_reward was given on every step (even if the Walker2D is unhealthy), now it is only given if the Walker2d is healthy. The info “reward_survive” is updated with this change (related GitHub issue).

  • Restored the xml_file argument (was removed in v4).

  • Added individual reward terms in info (info["reward_forward"], info["reward_ctrl"], info["reward_survive"]).

  • Added info["z_distance_from_origin"] which is equal to the vertical distance of the “torso” body from its initial position.

• 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