Hopper#
This environment is part of the Mujoco environments. Please read that page first for general information.
Action Space 
Box(1.0, 1.0, (3,), float32) 
Observation Shape 
(11,) 
Observation High 
[inf inf inf inf inf inf inf inf inf inf inf] 
Observation Low 
[inf inf inf inf inf inf inf inf inf inf inf] 
Import 

Description#
This environment is based on the work done by Erez, Tassa, and Todorov in “Infinite Horizon Model Predictive Control for Nonlinear Periodic Tasks”. The environment aims to increase the number of independent state and control variables as compared to the classic control environments. The hopper is a twodimensional onelegged figure that consist of four main body parts  the torso at the top, the thigh in the middle, the leg in the bottom, and a single foot on which the entire body rests. The goal is to make hops that move in the forward (right) direction by applying torques on the three hinges connecting the four body parts.
Action Space#
The action space is a Box(1, 1, (3,), 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 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) 
3 
Torque applied on the foot rotor 
1 
1 
foot_joint 
hinge 
torque (N m) 
Observation Space#
Observations consist of positional values of different body parts of the hopper, 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 hopper. It may
be included by passing exclude_current_positions_from_observation=False
during construction.
In that case, the observation space will have 12 dimensions where the first dimension
represents the xcoordinate of the hopper.
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 (11,)
where the elements
correspond to the following:
Num 
Observation 
Min 
Max 
Name (in corresponding XML file) 
Joint 
Unit 

0 
zcoordinate of the top (height of hopper) 
Inf 
Inf 
rootz 
slide 
position (m) 
1 
angle of the top 
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 
velocity of the xcoordinate of the top 
Inf 
Inf 
rootx 
slide 
velocity (m/s) 
6 
velocity of the zcoordinate (height) of the top 
Inf 
Inf 
rootz 
slide 
velocity (m/s) 
7 
angular velocity of the angle of the top 
Inf 
Inf 
rooty 
hinge 
angular velocity (rad/s) 
8 
angular velocity of the thigh hinge 
Inf 
Inf 
thigh_joint 
hinge 
angular velocity (rad/s) 
9 
angular velocity of the leg hinge 
Inf 
Inf 
leg_joint 
hinge 
angular velocity (rad/s) 
10 
angular velocity of the foot hinge 
Inf 
Inf 
foot_joint 
hinge 
angular velocity (rad/s) 
Rewards#
The reward consists of three parts:
healthy_reward: Every timestep that the hopper is healthy (see definition in section “Episode Termination”), it gets a reward of fixed value
healthy_reward
.forward_reward: A reward of hopping 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 4), where the frametime is 0.002  making the default dt = 4 * 0.002 = 0.008. This reward would be positive if the hopper hops forward (positive x direction).ctrl_cost: A cost for penalising the hopper 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 0.001
The total reward returned is reward = healthy_reward + 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) with a uniform noise
in the range of [reset_noise_scale
, reset_noise_scale
] added to the values for stochasticity.
Episode End#
The hopper is said to be unhealthy if any of the following happens:
An element of
observation[1:]
(ifexclude_current_positions_from_observation=True
, elseobservation[2:]
) is no longer contained in the closed interval specified by the argumenthealthy_state_range
The height of the hopper (
observation[0]
ifexclude_current_positions_from_observation=True
, elseobservation[1]
) is no longer contained in the closed interval specified by the argumenthealthy_z_range
(usually meaning that it has fallen)The angle (
observation[1]
ifexclude_current_positions_from_observation=True
, elseobservation[2]
) is no longer contained in the closed interval specified by the argumenthealthy_angle_range
If terminate_when_unhealthy=True
is passed during construction (which is the default),
the episode ends when any of the following happens:
Truncation: The episode duration reaches a 1000 timesteps
Termination: The hopper 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.
env = gym.make('Hopperv2')
v3 and v4 take gym.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale etc.
env = gym.make('Hopperv4', 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 reward (see section on reward) 

float 

Constant reward given if the ant is “healthy” after timestep 

bool 

If true, issue a done signal if the hopper is no longer healthy 

tuple 

The elements of 

tuple 

The zcoordinate must be in this range for the hopper to be considered healthy 

tuple 

The angle given by 

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 gym.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)