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

Observation Space 

import 

Description#
“Pusher” is a multijointed robot arm which is very similar to that of a human. The goal is to move a target cylinder (called object) to a goal position using the robot’s end effector (called fingertip). The robot consists of shoulder, elbow, forearm, and wrist joints.
Action Space#
The action space is a Box(2, 2, (7,), float32)
. An action (a, b)
represents the torques applied at the hinge joints.
Num 
Action 
Control Min 
Control Max 
Name (in corresponding XML file) 
Joint 
Unit 

0 
Rotation of the panning the shoulder 
2 
2 
r_shoulder_pan_joint 
hinge 
torque (N m) 
1 
Rotation of the shoulder lifting joint 
2 
2 
r_shoulder_lift_joint 
hinge 
torque (N m) 
2 
Rotation of the shoulder rolling joint 
2 
2 
r_upper_arm_roll_joint 
hinge 
torque (N m) 
3 
Rotation of hinge joint that flexed the elbow 
2 
2 
r_elbow_flex_joint 
hinge 
torque (N m) 
4 
Rotation of hinge that rolls the forearm 
2 
2 
r_forearm_roll_joint 
hinge 
torque (N m) 
5 
Rotation of flexing the wrist 
2 
2 
r_wrist_flex_joint 
hinge 
torque (N m) 
6 
Rotation of rolling the wrist 
2 
2 
r_wrist_roll_joint 
hinge 
torque (N m) 
Observation Space#
Observations consist of
Angle of rotational joints on the pusher
Angular velocities of rotational joints on the pusher
The coordinates of the fingertip of the pusher
The coordinates of the object to be moved
The coordinates of the goal position
The observation is a Box(Inf, Inf, (23,), float64)
where the elements correspond to the table below.
An analogy can be drawn to a human arm in order to help understand the state space, with the words flex and roll meaning the
same as human joints.
Num 
Observation 
Min 
Max 
Name (in corresponding XML file) 
Joint 
Unit 

0 
Rotation of the panning the shoulder 
Inf 
Inf 
r_shoulder_pan_joint 
hinge 
angle (rad) 
1 
Rotation of the shoulder lifting joint 
Inf 
Inf 
r_shoulder_lift_joint 
hinge 
angle (rad) 
2 
Rotation of the shoulder rolling joint 
Inf 
Inf 
r_upper_arm_roll_joint 
hinge 
angle (rad) 
3 
Rotation of hinge joint that flexed the elbow 
Inf 
Inf 
r_elbow_flex_joint 
hinge 
angle (rad) 
4 
Rotation of hinge that rolls the forearm 
Inf 
Inf 
r_forearm_roll_joint 
hinge 
angle (rad) 
5 
Rotation of flexing the wrist 
Inf 
Inf 
r_wrist_flex_joint 
hinge 
angle (rad) 
6 
Rotation of rolling the wrist 
Inf 
Inf 
r_wrist_roll_joint 
hinge 
angle (rad) 
7 
Rotational velocity of the panning the shoulder 
Inf 
Inf 
r_shoulder_pan_joint 
hinge 
angular velocity (rad/s) 
8 
Rotational velocity of the shoulder lifting joint 
Inf 
Inf 
r_shoulder_lift_joint 
hinge 
angular velocity (rad/s) 
9 
Rotational velocity of the shoulder rolling joint 
Inf 
Inf 
r_upper_arm_roll_joint 
hinge 
angular velocity (rad/s) 
10 
Rotational velocity of hinge joint that flexed the elbow 
Inf 
Inf 
r_elbow_flex_joint 
hinge 
angular velocity (rad/s) 
11 
Rotational velocity of hinge that rolls the forearm 
Inf 
Inf 
r_forearm_roll_joint 
hinge 
angular velocity (rad/s) 
12 
Rotational velocity of flexing the wrist 
Inf 
Inf 
r_wrist_flex_joint 
hinge 
angular velocity (rad/s) 
13 
Rotational velocity of rolling the wrist 
Inf 
Inf 
r_wrist_roll_joint 
hinge 
angular velocity (rad/s) 
14 
xcoordinate of the fingertip of the pusher 
Inf 
Inf 
tips_arm 
slide 
position (m) 
15 
ycoordinate of the fingertip of the pusher 
Inf 
Inf 
tips_arm 
slide 
position (m) 
16 
zcoordinate of the fingertip of the pusher 
Inf 
Inf 
tips_arm 
slide 
position (m) 
17 
xcoordinate of the object to be moved 
Inf 
Inf 
object (obj_slidex) 
slide 
position (m) 
18 
ycoordinate of the object to be moved 
Inf 
Inf 
object (obj_slidey) 
slide 
position (m) 
19 
zcoordinate of the object to be moved 
Inf 
Inf 
object 
cylinder 
position (m) 
20 
xcoordinate of the goal position of the object 
Inf 
Inf 
goal (goal_slidex) 
slide 
position (m) 
21 
ycoordinate of the goal position of the object 
Inf 
Inf 
goal (goal_slidey) 
slide 
position (m) 
22 
zcoordinate of the goal position of the object 
Inf 
Inf 
goal 
sphere 
position (m) 
Rewards#
The reward consists of two parts:
*reward_near *: This reward is a measure of how far the fingertip of the pusher (the unattached end) is from the object, with a more negative value assigned for when the pusher’s fingertip is further away from the target. It is calculated as the negative vector norm of (position of the fingertip  position of target), or norm(“fingertip”  “target”).
*reward_dist *: This reward is a measure of how far the object is from the target goal position, with a more negative value assigned for object is further away from the target. It is calculated as the negative vector norm of (position of the object  position of goal), or norm(“object”  “target”).
reward_control: A negative reward for penalising the pusher if it takes actions that are too large. It is measured as the negative squared Euclidean norm of the action, i.e. as  sum(action^{2}).
The total reward returned is reward = reward_dist + 0.1 * reward_ctrl + 0.5 * reward_near
Unlike other environments, Pusher does not allow you to specify weights for the individual reward terms.
However, info
does contain the keys reward_dist and reward_ctrl. Thus, if you’d like to weight the terms,
you should create a wrapper that computes the weighted reward from info
.
Starting State#
All pusher (not including object and goal) states start in (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). A uniform noise in the range [0.005, 0.005] is added to the velocity attributes only. The velocities of the object and goal are permanently set to 0. The object’s xposition is selected uniformly between [0.3, 0] while the yposition is selected uniformly between [0.2, 0.2], and this process is repeated until the vector norm between the object’s (x,y) position and origin is not greater than 0.17. The goal always have the same position of (0.45, 0.05, 0.323).
The default framerate is 5 with each frame lasting for 0.01, giving rise to a dt = 5 * 0.01 = 0.05
Episode End#
The episode ends when any of the following happens:
Truncation: The episode duration reaches a 100 timesteps.
Termination: Any of the state space values is no longer finite.
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)..
import gymnasium as gym
env = gym.make('Pusherv4')
There is no v3 for Pusher, unlike the robot environments where a v3 and
beyond take gymnasmium.make
kwargs such as xml_file
, ctrl_cost_weight
, reset_noise_scale
, etc.
import gymnasium as gym
env = gym.make('Pusherv2')
Version History#
v4: All MuJoCo environments now use the MuJoCo bindings in mujoco >= 2.1.3
v2: All continuous control environments now use mujocopy >= 1.50
v1: max_time_steps raised to 1000 for robot based tasks (not including reacher, which has a max_time_steps of 50). Added reward_threshold to environments.
v0: Initial versions release (1.0.0)