Inverted Pendulum

This environment is part of the Mujoco environments.Please read that page first for general information.

Action Space	Box(-3.0, 3.0, (1,), float32)
Observation Shape	(4,)
Observation High	inf
Observation Low	-inf
Import	gymnasium.make("InvertedPendulum-v4")

Description

This environment is the cartpole environment based on the work done by Barto, Sutton, and Anderson in “Neuronlike adaptive elements that can solve difficult learning control problems”, just like in the classic environments but now powered by the Mujoco physics simulator - allowing for more complex experiments (such as varying the effects of gravity). This environment involves a cart that can moved linearly, with a pole fixed on it at one end and having another end free. The cart can be pushed left or right, and the goal is to balance the pole on the top of the cart by applying forces on the cart.

Action Space

The agent take a 1-element vector for actions.

The action space is a continuous (action) in [-3, 3], where action represents the numerical force applied to the cart (with magnitude representing the amount of force and sign representing the direction)

Num	Action	Control Min	Control Max	Name (in corresponding XML file)	Joint	Unit
0	Force applied on the cart	-3	3	slider	slide	Force (N)

Observation Space

The state space consists of positional values of different body parts of the pendulum system, 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 (4,) where the elements correspond to the following:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Unit
0	position of the cart along the linear surface	-Inf	Inf	slider	slide	position (m)
1	vertical angle of the pole on the cart	-Inf	Inf	hinge	hinge	angle (rad)
2	linear velocity of the cart	-Inf	Inf	slider	slide	velocity (m/s)
3	angular velocity of the pole on the cart	-Inf	Inf	hinge	hinge	anglular velocity (rad/s)

Rewards

The goal is to make the inverted pendulum stand upright (within a certain angle limit) as long as possible - as such a reward of +1 is awarded for each timestep that the pole is upright.

Starting State

All observations start in state (0.0, 0.0, 0.0, 0.0) with a uniform noise in the range of [-0.01, 0.01] added to the values for stochasticity.

Episode End

The episode ends when any of the following happens:

1. Truncation: The episode duration reaches 1000 timesteps.

2. Termination: Any of the state space values is no longer finite.

3. Termination: The absolute value of the vertical angle between the pole and the cart is greater than 0.2 radian.

Arguments

No additional arguments are currently supported.

import gymnasium as gym
env = gym.make('InvertedPendulum-v4')

There is no v3 for InvertedPendulum, unlike the robot environments where a v3 and beyond take gymnasium.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale, etc.

import gymnasium as gym
env = gym.make('InvertedPendulum-v2')

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 (including inverted pendulum)

• v0: Initial versions release (1.0.0)