Inverted Pendulum

This environment is part of the Mujoco environments which contains general information about the environment.

Action Space	Box(-3.0, 3.0, (1,), float32)
Observation Space	Box(-inf, inf, (4,), float64)
import	gymnasium.make("InvertedPendulum-v5")

Description

This environment is the Cartpole environment, based on the work of 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 consists of a cart that can be moved linearly, with a pole attached to one end and having another end free. The cart can be pushed left or right, and the goal is to balance the pole on top of the cart by applying forces to 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	Type (Unit)
0	Force applied on the cart	-3	3	slider	slide	Force (N)

Observation Space

The observation space consists of the following parts (in order):

• qpos (2 element): Position values of the robot’s cart and pole.

• qvel (2 elements): The velocities of cart and pole (their derivatives).

The observation space is a Box(-Inf, Inf, (4,), float64) where the elements are as follows:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Type (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	angular velocity (rad/s)

Rewards

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

The pole is considered upright if: \(|angle| < 0.2\).

and info also contains the reward.

Starting State

The initial position state is \(\mathcal{U}_{[-reset\_noise\_scale imes I_{2}, reset\_noise\_scale imes I_{2}]}\). The initial velocity state is \(\mathcal{U}_{[-reset\_noise\_scale imes I_{2}, reset\_noise\_scale imes I_{2}]}\).

where \(\mathcal{U}\) is the multivariate uniform continuous distribution.

Episode End

Termination

The environment terminates when the Inverted Pendulum is unhealthy. The Inverted Pendulum is unhealthy if any of the following happens:

1. Any of the state space values is no longer finite.

2. The absolute value of the vertical angle between the pole and the cart is greater than 0.2 radians.

Truncation

The default duration of an episode is 1000 timesteps.

Arguments

InvertedPendulum provides a range of parameters to modify the observation space, reward function, initial state, and termination condition. These parameters can be applied during gymnasium.make in the following way:

import gymnasium as gym
env = gym.make('InvertedPendulum-v5', reset_noise_scale=0.1)

Parameter	Type	Default	Description
xml_file	str	"inverted_pendulum.xml"	Path to a MuJoCo model
reset_noise_scale	float	0.01	Scale of random perturbations of initial position and velocity (see Starting State section)

Version History

• v5:

  • Minimum mujoco version is now 2.3.3.

  • Added support for fully custom/third party mujoco models using the xml_file argument (previously only a few changes could be made to the existing models).

  • Added default_camera_config argument, a dictionary for setting the mj_camera properties, mainly useful for custom environments.

  • Added env.observation_structure, a dictionary for specifying the observation space compose (e.g. qpos, qvel), useful for building tooling and wrappers for the MuJoCo environments.

  • Added frame_skip argument, used to configure the dt (duration of step()), default varies by environment check environment documentation pages.

  • Fixed bug: healthy_reward was given on every step (even if the Pendulum is unhealthy), now it is only given if the Pendulum is healthy (not terminated) (related GitHub issue).

  • Added xml_file argument.

  • Added reset_noise_scale argument to set the range of initial states.

  • Added info["reward_survive"] which contains the reward.

• v4: All MuJoCo environments now use the MuJoCo bindings in mujoco >= 2.1.3.

• v3: This environment does not have a v3 release.

• v2: All continuous control environments now use mujoco-py >= 1.5.

• v1: max_time_steps raised to 1000 for robot based tasks (including inverted pendulum).

• v0: Initial versions release.