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-v4")

Description

This environment builds on the hopper environment based on the work done by Erez, Tassa, and Todorov in “Infinite Horizon Model Predictive Control for Nonlinear Periodic Tasks” by adding another set of legs making it possible for the robot to walker forward instead of hop. Like other Mujoco environments, this environment aims to increase the number of independent state and control variables as compared to the classic control environments. The walker is a two-dimensional two-legged figure that consist of four 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 in the bottom below the thighs, and two feet attached to the legs on which the entire body rests. The goal is to make coordinate both sets of feet, legs, and thighs to move in the forward (right) direction by applying torques on the six hinges connecting the six 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	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

Observations consist of positional values of different body parts of the walker, 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-coordinate of the top. It may be included by passing exclude_current_positions_from_observation=False during construction. In that case, the observation space will have 18 dimensions where the first dimension represent the x-coordinates of the top of the walker. Regardless of whether exclude_current_positions_from_observation was set to true or false, the x-coordinate of the top will be returned in info with key "x_position".

By default, observation is a ndarray with shape (17,) where the elements correspond to the following:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Unit
0	z-coordinate of the top (height of hopper)	-Inf	Inf	rootz (torso)	slide	position (m)
1	angle of the top	-Inf	Inf	rooty (torso)	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 top	-Inf	Inf	rootx	slide	velocity (m/s)
9	velocity of the z-coordinate (height) of the top	-Inf	Inf	rootz	slide	velocity (m/s)
10	angular velocity of the angle of the top	-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)

Rewards

The reward consists of three parts:

• healthy_reward: Every timestep that the walker is alive, it receives a fixed reward of value healthy_reward,

• forward_reward: A reward of walking forward which is measured as forward_reward_weight * (x-coordinate before action - x-coordinate after action)/dt. dt is the time between actions and is dependeent on the frame_skip parameter (default is 4), where the frametime is 0.002 - making the default dt = 4 * 0.002 = 0.008. This reward would be positive if the walker walks forward (right) desired.

• ctrl_cost: A cost for penalising the walker if it takes actions that are too large. It is measured as ctrl_cost_weight * sum(action²) where ctrl_cost_weight is a parameter set for the control and has a default value of 0.001

The total reward returned is reward = healthy_reward bonus + forward_reward - ctrl_cost and info will also contain the individual reward terms

Starting State

All observations start in state (0.0, 1.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) with a uniform noise in the range of [-reset_noise_scale, reset_noise_scale] added to the values for stochasticity.

Episode End

The walker is said to be unhealthy if any of the following happens:

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

2. The height of the walker is not in the closed interval specified by healthy_z_range

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 healthy_angle_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 walker 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('Walker2d-v4')

v3 and beyond take gymnasium.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale, etc.

import gymnasium as gym
env = gym.make('Walker2d-v4', ctrl_cost_weight=0.1, ....)

Parameter	Type	Default	Description
xml_file	str	"walker2d.xml"	Path to a MuJoCo model
forward_reward_weight	float	1.0	Weight for forward_reward term (see section on reward)
ctrl_cost_weight	float	1e-3	Weight for ctr_cost term (see section on reward)
healthy_reward	float	1.0	Constant reward given if the ant is “healthy” after timestep
terminate_when_unhealthy	bool	True	If true, issue a done signal if the z-coordinate of the walker is no longer healthy
healthy_z_range	tuple	(0.8, 2)	The z-coordinate of the top of the walker must be in this range to be considered healthy
healthy_angle_range	tuple	(-1, 1)	The angle must be in this range to be considered healthy
reset_noise_scale	float	5e-3	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-coordinate 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)