Half Cheetah

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("HalfCheetah-v4")

Description

This environment is based on the work by P. Wawrzyński in “A Cat-Like Robot Real-Time Learning to Run”. The HalfCheetah is a 2-dimensional robot consisting of 9 links and 8 joints connecting them (including two paws). The goal is to apply a torque on the joints to make the cheetah run forward (right) as fast as possible, with a positive reward allocated based on the distance moved forward and a negative reward allocated for moving backward. The torso and head of the cheetah are fixed, and the torque can only be applied on the other 6 joints over the front and back thighs (connecting to the torso), shins (connecting to the thighs) and feet (connecting to the shins).

Action Space

The action space is a Box(-1, 1, (6,), float32). An action represents the torques applied between links.

Num	Action	Control Min	Control Max	Name (in corresponding XML file)	Joint	Unit
0	Torque applied on the back thigh rotor	-1	1	bthigh	hinge	torque (N m)
1	Torque applied on the back shin rotor	-1	1	bshin	hinge	torque (N m)
2	Torque applied on the back foot rotor	-1	1	bfoot	hinge	torque (N m)
3	Torque applied on the front thigh rotor	-1	1	fthigh	hinge	torque (N m)
4	Torque applied on the front shin rotor	-1	1	fshin	hinge	torque (N m)
5	Torque applied on the front foot rotor	-1	1	ffoot	hinge	torque (N m)

Observation Space

Observations consist of positional values of different body parts of the cheetah, 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 cheetah’s center of mass. 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 represents the x-coordinate of the cheetah’s center of mass. Regardless of whether exclude_current_positions_from_observation was set to true or false, the x-coordinate will be returned in info with key "x_position".

However, by default, the 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 front tip	-Inf	Inf	rootz	slide	position (m)
1	angle of the front tip	-Inf	Inf	rooty	hinge	angle (rad)
2	angle of the second rotor	-Inf	Inf	bthigh	hinge	angle (rad)
3	angle of the second rotor	-Inf	Inf	bshin	hinge	angle (rad)
4	velocity of the tip along the x-axis	-Inf	Inf	bfoot	hinge	angle (rad)
5	velocity of the tip along the y-axis	-Inf	Inf	fthigh	hinge	angle (rad)
6	angular velocity of front tip	-Inf	Inf	fshin	hinge	angle (rad)
7	angular velocity of second rotor	-Inf	Inf	ffoot	hinge	angle (rad)
8	x-coordinate of the front tip	-Inf	Inf	rootx	slide	velocity (m/s)
9	y-coordinate of the front tip	-Inf	Inf	rootz	slide	velocity (m/s)
10	angle of the front tip	-Inf	Inf	rooty	hinge	angular velocity (rad/s)
11	angle of the second rotor	-Inf	Inf	bthigh	hinge	angular velocity (rad/s)
12	angle of the second rotor	-Inf	Inf	bshin	hinge	angular velocity (rad/s)
13	velocity of the tip along the x-axis	-Inf	Inf	bfoot	hinge	angular velocity (rad/s)
14	velocity of the tip along the y-axis	-Inf	Inf	fthigh	hinge	angular velocity (rad/s)
15	angular velocity of front tip	-Inf	Inf	fshin	hinge	angular velocity (rad/s)
16	angular velocity of second rotor	-Inf	Inf	ffoot	hinge	angular velocity (rad/s)

Rewards

The reward consists of two parts:

• forward_reward: A reward of moving 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 dependent on the frame_skip parameter (fixed to 5), where the frametime is 0.01 - making the default dt = 5 * 0.01 = 0.05. This reward would be positive if the cheetah runs forward (right).

• ctrl_cost: A cost for penalising the cheetah 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 0.1

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

Starting State

All observations start in state (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, 0.0, 0.0,) with a noise added to the initial state for stochasticity. As seen before, the first 8 values in the state are positional and the last 9 values are velocity. A uniform noise in the range of [-reset_noise_scale, reset_noise_scale] is added to the positional values while a standard normal noise with a mean of 0 and standard deviation of reset_noise_scale is added to the initial velocity values of all zeros.

Episode End

The episode truncates when the episode length is greater than 1000.

Arguments

No additional arguments are currently supported in v2 and lower.

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

Parameter	Type	Default	Description
xml_file	str	"half_cheetah.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	0.1	Weight for ctrl_cost weight (see section on reward)
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-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)