Half Cheetah#
This environment is part of the Mujoco environments which contains general information about the environment.
Action Space 

Observation Space 

import 

Description#
This environment is based on the work by P. Wawrzyński in “A CatLike Robot RealTime Learning to Run”. The HalfCheetah is a 2dimensional 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 xcoordinate 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 xcoordinate of the cheetah’s center of mass.
Regardless of whether exclude_current_positions_from_observation
was set to true or false, the xcoordinate
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 
zcoordinate 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 xaxis 
Inf 
Inf 
bfoot 
hinge 
angle (rad) 
5 
velocity of the tip along the yaxis 
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 
xcoordinate of the front tip 
Inf 
Inf 
rootx 
slide 
velocity (m/s) 
9 
ycoordinate 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 xaxis 
Inf 
Inf 
bfoot 
hinge 
angular velocity (rad/s) 
14 
velocity of the tip along the yaxis 
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
* (xcoordinate before action  xcoordinate 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(action^{2}) wherectrl_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('HalfCheetahv2')
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('HalfCheetahv4', ctrl_cost_weight=0.1, ....)
Parameter 
Type 
Default 
Description 


str 

Path to a MuJoCo model 

float 

Weight for forward_reward term (see section on reward) 

float 

Weight for ctrl_cost weight (see section on reward) 

float 

Scale of random perturbations of initial position and velocity (see section on Starting State) 

bool 

Whether or not to omit the xcoordinate from observations. Excluding the position can serve as an inductive bias to induce positionagnostic 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 asxml_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 mujocopy >= 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)