Ant

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

Action Space	Box(-1.0, 1.0, (8,), float32)
Observation Space	Box(-inf, inf, (27,), float64)
import	gymnasium.make("Ant-v4")

Description

This environment is based on the environment introduced by Schulman, Moritz, Levine, Jordan and Abbeel in “High-Dimensional Continuous Control Using Generalized Advantage Estimation”. The ant is a 3D robot consisting of one torso (free rotational body) with four legs attached to it with each leg having two links. The goal is to coordinate the four legs to move in the forward (right) direction by applying torques on the eight hinges connecting the two links of each leg and the torso (nine parts and eight hinges).

Action Space

The action space is a Box(-1, 1, (8,), 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 rotor between the torso and back right hip	-1	1	hip_4 (right_back_leg)	hinge	torque (N m)
1	Torque applied on the rotor between the back right two links	-1	1	angle_4 (right_back_leg)	hinge	torque (N m)
2	Torque applied on the rotor between the torso and front left hip	-1	1	hip_1 (front_left_leg)	hinge	torque (N m)
3	Torque applied on the rotor between the front left two links	-1	1	angle_1 (front_left_leg)	hinge	torque (N m)
4	Torque applied on the rotor between the torso and front right hip	-1	1	hip_2 (front_right_leg)	hinge	torque (N m)
5	Torque applied on the rotor between the front right two links	-1	1	angle_2 (front_right_leg)	hinge	torque (N m)
6	Torque applied on the rotor between the torso and back left hip	-1	1	hip_3 (back_leg)	hinge	torque (N m)
7	Torque applied on the rotor between the back left two links	-1	1	angle_3 (back_leg)	hinge	torque (N m)

Observation Space

Observations consist of positional values of different body parts of the ant, 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 ant’s torso. These may be included by passing exclude_current_positions_from_observation=False during construction. In that case, the observation space will have 29 dimensions where the first two dimensions represent the x- and y- coordinates of the ant’s torso. Regardless of whether exclude_current_positions_from_observation was set to true or false, the x- and y-coordinates of the torso will be returned in info with keys "x_position" and "y_position", respectively.

However, by default, an observation is a ndarray with shape (27,) 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	torso	free	position (m)
1	x-orientation of the torso (centre)	-Inf	Inf	torso	free	angle (rad)
2	y-orientation of the torso (centre)	-Inf	Inf	torso	free	angle (rad)
3	z-orientation of the torso (centre)	-Inf	Inf	torso	free	angle (rad)
4	w-orientation of the torso (centre)	-Inf	Inf	torso	free	angle (rad)
5	angle between torso and first link on front left	-Inf	Inf	hip_1 (front_left_leg)	hinge	angle (rad)
6	angle between the two links on the front left	-Inf	Inf	ankle_1 (front_left_leg)	hinge	angle (rad)
7	angle between torso and first link on front right	-Inf	Inf	hip_2 (front_right_leg)	hinge	angle (rad)
8	angle between the two links on the front right	-Inf	Inf	ankle_2 (front_right_leg)	hinge	angle (rad)
9	angle between torso and first link on back left	-Inf	Inf	hip_3 (back_leg)	hinge	angle (rad)
10	angle between the two links on the back left	-Inf	Inf	ankle_3 (back_leg)	hinge	angle (rad)
11	angle between torso and first link on back right	-Inf	Inf	hip_4 (right_back_leg)	hinge	angle (rad)
12	angle between the two links on the back right	-Inf	Inf	ankle_4 (right_back_leg)	hinge	angle (rad)
13	x-coordinate velocity of the torso	-Inf	Inf	torso	free	velocity (m/s)
14	y-coordinate velocity of the torso	-Inf	Inf	torso	free	velocity (m/s)
15	z-coordinate velocity of the torso	-Inf	Inf	torso	free	velocity (m/s)
16	x-coordinate angular velocity of the torso	-Inf	Inf	torso	free	angular velocity (rad/s)
17	y-coordinate angular velocity of the torso	-Inf	Inf	torso	free	angular velocity (rad/s)
18	z-coordinate angular velocity of the torso	-Inf	Inf	torso	free	angular velocity (rad/s)
19	angular velocity of angle between torso and front left link	-Inf	Inf	hip_1 (front_left_leg)	hinge	angle (rad)
20	angular velocity of the angle between front left links	-Inf	Inf	ankle_1 (front_left_leg)	hinge	angle (rad)
21	angular velocity of angle between torso and front right link	-Inf	Inf	hip_2 (front_right_leg)	hinge	angle (rad)
22	angular velocity of the angle between front right links	-Inf	Inf	ankle_2 (front_right_leg)	hinge	angle (rad)
23	angular velocity of angle between torso and back left link	-Inf	Inf	hip_3 (back_leg)	hinge	angle (rad)
24	angular velocity of the angle between back left links	-Inf	Inf	ankle_3 (back_leg)	hinge	angle (rad)
25	angular velocity of angle between torso and back right link	-Inf	Inf	hip_4 (right_back_leg)	hinge	angle (rad)
26	angular velocity of the angle between back right links	-Inf	Inf	ankle_4 (right_back_leg)	hinge	angle (rad)

If version < v4 or use_contact_forces is True then the observation space is extended by 14*6 = 84 elements, which are contact forces (external forces - force x, y, z and torque x, y, z) applied to the center of mass of each of the objects. The 14 object are:

in v4 or earlier:

id	object
0	worldObject (note: forces are always full of zeros)
1	torso
2	front_left_leg
3	aux_1 (front left leg)
4	ankle_1 (front left leg)
5	front_right_leg
6	aux_2 (front right leg)
7	ankle_2 (front right leg)
8	back_leg (back left leg)
9	aux_3 (back left leg)
10	ankle_3 (back left leg)
11	right_back_leg
12	aux_4 (back right leg)
13	ankle_4 (back right leg)

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: Ant-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 Ant 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 ant is healthy (see definition in section “Episode Termination”), it gets a reward of fixed value healthy_reward

• forward_reward: A reward of moving forward which is measured as (x-coordinate before action - x-coordinate after action)/dt. dt is the time between actions and is dependent on the frame_skip parameter (default is 5), where the frametime is 0.01 - making the default dt = 5 * 0.01 = 0.05. This reward would be positive if the ant moves forward (in positive x direction).

• ctrl_cost: A negative reward for penalising the ant if it takes actions that are too large. It is measured as ctrl_cost_weight * sum(action²) where ctr_cost_weight is a parameter set for the control and has a default value of 0.5.

• contact_cost: A negative reward for penalising the ant if the external contact force is too large. It is calculated contact_cost_weight * sum(clip(external contact force to contact_force_range)²).

The total reward returned is reward = healthy_reward + forward_reward - ctrl_cost.

But if use_contact_forces=True or version < v4 The total reward returned is reward = healthy_reward + forward_reward - ctrl_cost - contact_cost.

In either case info will also contain the individual reward terms.

Starting State

All observations start in state (0.0, 0.0, 0.75, 1.0, 0.0 … 0.0) with a uniform noise in the range of [-reset_noise_scale, reset_noise_scale] added to the positional values and standard normal noise with mean 0 and standard deviation reset_noise_scale added to the velocity values for stochasticity. Note that the initial z coordinate is intentionally selected to be slightly high, thereby indicating a standing up ant. The initial orientation is designed to make it face forward as well.

Episode End

The ant is said to be 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 is not in the closed interval given by healthy_z_range (defaults to [0.2, 1.0])

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 ant 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('Ant-v2')

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('Ant-v4', ctrl_cost_weight=0.1, ...)

Parameter	Type	Default	Description
xml_file	str	"ant.xml"	Path to a MuJoCo model
ctrl_cost_weight	float	0.5	Weight for ctrl_cost term (see section on reward)
use_contact_forces	bool	False	If true, it extends the observation space by adding contact forces (see Observation Space section) and includes contact_cost to the reward function (see Rewards section)
contact_cost_weight	float	5e-4	Weight for contact_cost term (see section on reward)
healthy_reward	float	1	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 torso is no longer in the healthy_z_range
healthy_z_range	tuple	(0.2, 1)	The ant is considered healthy if the z-coordinate of the torso is in this range
contact_force_range	tuple	(-1, 1)	Contact forces are clipped to this range in the computation of contact_cost
reset_noise_scale	float	0.1	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, also removed contact forces from the default observation space (new variable use_contact_forces=True can restore them)

• 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)