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 agent take a 3element vector for actions.
The action space is a continuous (action, action, action)
all in [1, 1]
, where action
represents the numerical 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#
The state space consists 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.
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 
xcoordinate of the top 
Inf 
Inf 
rootx 
slide 
position (m) 
1 
zcoordinate of the top (height of hopper) 
Inf 
Inf 
rootz 
slide 
position (m) 
2 
angle of the top 
Inf 
Inf 
rooty 
hinge 
angle (rad) 
3 
angle of the thigh joint 
Inf 
Inf 
thigh_joint 
hinge 
angle (rad) 
4 
angle of the leg joint 
Inf 
Inf 
leg_joint 
hinge 
angle (rad) 
5 
angle of the foot joint 
Inf 
Inf 
foot_joint 
hinge 
angle (rad) 
6 
velocity of the xcoordinate of the top 
Inf 
Inf 
rootx 
slide 
velocity (m/s) 
7 
velocity of the zcoordinate (height) of the top 
Inf 
Inf 
rootz 
slide 
velocity (m/s) 
8 
angular velocity of the angle of the top 
Inf 
Inf 
rooty 
hinge 
angular velocity (rad/s) 
9 
angular velocity of the thigh hinge 
Inf 
Inf 
thigh_joint 
hinge 
angular velocity (rad/s) 
10 
angular velocity of the leg hinge 
Inf 
Inf 
leg_joint 
hinge 
angular velocity (rad/s) 
11 
angular velocity of the foot hinge 
Inf 
Inf 
foot_joint 
hinge 
angular velocity (rad/s) 
Note:
In practice (and Gym implementation), the first positional element is
omitted from the state space since the reward function is calculated based
on that value. This value is hidden from the algorithm, which in turn has
to develop an abstract understanding of it from the observed rewards.
Therefore, observation space has shape (11,)
instead of (12,)
and looks like:
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:
alive bonus: Every timestep that the hopper is alive, it gets a reward of 1,
reward_forward: A reward of hopping forward which is measured as (xcoordinate before action  xcoordinate after action)/dt. dt is the time between actions and is dependent on the frame_skip parameter (default is 4), where the dt for one frame is 0.002  making the default dt = 40.002 = 0.008*. This reward would be positive if the hopper hops forward (right) desired.
reward_control: A negative reward for penalising the hopper if it takes actions that are too large. It is measured as coefficient x sum(action^{2}) where coefficient is a parameter set for the control and has a default value of 0.001
The total reward returned is reward = alive bonus + reward_forward + reward_control
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 [0.005, 0.005] added to the values for stochasticity.
Episode Termination#
The episode terminates when any of the following happens:
The episode duration reaches a 1000 timesteps
Any of the state space values is no longer finite
The absolute value of any of the state variable indexed (angle and beyond) is greater than 100
The height of the hopper becomes greater than 0.7 metres (hopper has hopped too high).
The absolute value of the angle (index 2) is less than 0.2 radians (hopper has fallen down).
Arguments#
No additional arguments are currently supported (in v2 and lower), but modifications can be made to the XML file in the assets folder (or by changing the path to a modified XML file in another folder).
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, ....)
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)