Gymnasium/docs/classic_control/acrobot.md

Acrobot-v1

Title	Action Type	Action Shape	Action Values	Observation Type	Observation Shape	Observation Values	Average Total Reward	Import
Acrobot-v1	Discrete	(2,)	(0,1,2)	Box	(6,)	[(-1,1),(-1,1), (-1, 1), (-1, 1), (-12.567, 12.567), (-28.274, 28.274)]		from gym.envs.classic_control import acrobot

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Description

The Acrobot system includes two joints and two links, where the joint between the two links is actuated. Initially, the links are hanging downwards, and the goal is to swing the end of the lower link up to a given height by applying changes to torque on the actuated joint (middle).

Image: two blue pendulum links connected by two green joints. The joint in between the two pendulum links is acted upon by the agent via changes in torque. The goal is to swing the end of the outer-link to reach the target height (black horizontal line above system).

Action Space

The action is either applying +1, 0 or -1 torque on the joint between the two pendulum links.

Num	Action
0	apply -1 torque to the joint
1	apply 0 torque to the joint
2	apply 1 torque to the joint

Observation Space

The observation space gives information about the two rotational joint angles theta1 and theta2, as well as their angular velocities:

• theta1 is the angle of the inner link joint, where an angle of 0 indicates the first link is pointing directly downwards.
• theta2 is relative to the angle of the first link. An angle of 0 corresponds to having the same angle between the two links.

The angular velocities of theta1 and theta2 are bounded at ±4π, and ±9π respectively. The observation is a ndarray with shape (6,) where the elements correspond to the following:

Num	Observation	Min	Max
0	Cosine of theta1	-1	1
1	Sine of theta1	-1	1
2	Cosine of theta2	-1	1
3	Sine of theta2	-1	1
4	Angular velocity of theta1	~ -12.567 (-4 * pi)	~ 12.567 (4 * pi)
5	Angular velocity of theta2	~ -28.274 (-9 * pi)	~ 28.274 (9 * pi)

or [cos(theta1) sin(theta1) cos(theta2) sin(theta2) thetaDot1 thetaDot2]. As an example, a state of [1, 0, 1, 0, ..., ...] indicates that both links are pointing downwards.

Rewards

All steps that do not reach the goal (termination criteria) incur a reward of -1. Achieving the target height and terminating incurs a reward of 0. The reward threshold is -100.

Starting State

At start, each parameter in the underlying state (theta1, theta2, and the two angular velocities) is initialized uniformly at random between -0.1 and 0.1. This means both links are pointing roughly downwards.

Episode Termination

The episode terminates of one of the following occurs:

1. The target height is achieved. As constructed, this occurs when -cos(theta1) - cos(theta2 + theta1) > 1.0
2. Episode length is greater than 500 (200 for v0)

Arguments

There are no arguments supported in constructing the environment. As an example:

import gym
env_name = 'Acrobot-v1'
env = gym.make(env_name)

By default, the dynamics of the acrobot follow those described in Richard Sutton's book Reinforcement Learning: An Introduction. However, a book_or_nips setting can be modified on the environment to change the pendulum dynamics to those described in the original NeurIPS paper. See the following note and the implementation for details:

The dynamics equations were missing some terms in the NIPS paper which are present in the book. R. Sutton confirmed in personal correspondence that the experimental results shown in the paper and the book were generated with the equations shown in the book. However, there is the option to run the domain with the paper equations by setting book_or_nips = 'nips'

Continuing from the prior example:

# To change the dynamics as described above
env.env.book_or_nips = 'nips'

Version History

• v1: Maximum number of steps increased from 200 to 500. The observation space for v0 provided direct readings of theta1 and theta2 in radians, having a range of [-pi, pi]. The v1 observation space as described here provides the sin and cosin of each angle instead.
• v0: Initial versions release (1.0.0) (removed from openai/gym for v1)

References

• Sutton, R. S. (1996). Generalization in Reinforcement Learning: Successful Examples Using Sparse Coarse Coding. In D. Touretzky, M. C. Mozer, & M. Hasselmo (Eds.), Advances in Neural Information Processing Systems (Vol. 8). MIT Press. https://proceedings.neurips.cc/paper/1995/file/8f1d43620bc6bb580df6e80b0dc05c48-Paper.pdf
• Sutton, R. S., Barto, A. G. (2018 ). Reinforcement Learning: An Introduction. The MIT Press.