Mountain Car Continuous¶

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


Action Space	`Box(-1.0, 1.0, (1,), float32)`
Observation Space	`Box([-1.2 -0.07], [0.6 0.07], (2,), float32)`
import	`gymnasium.make("MountainCarContinuous-v0")`

Description¶

The Mountain Car MDP is a deterministic MDP that consists of a car placed stochastically at the bottom of a sinusoidal valley, with the only possible actions being the accelerations that can be applied to the car in either direction. The goal of the MDP is to strategically accelerate the car to reach the goal state on top of the right hill. There are two versions of the mountain car domain in gymnasium: one with discrete actions and one with continuous. This version is the one with continuous actions.

This MDP first appeared in Andrew Moore’s PhD Thesis (1990)

@TECHREPORT{Moore90efficientmemory-based,
    author = {Andrew William Moore},
    title = {Efficient Memory-based Learning for Robot Control},
    institution = {University of Cambridge},
    year = {1990}
}

Observation Space¶

The observation is a ndarray with shape (2,) where the elements correspond to the following:

Num	Observation	Min	Max	Unit
0	position of the car along the x-axis	-Inf	Inf	position (m)
1	velocity of the car	-Inf	Inf	position (m)

Action Space¶

The action is a ndarray with shape (1,), representing the directional force applied on the car. The action is clipped in the range [-1,1] and multiplied by a power of 0.0015.

Transition Dynamics:¶

Given an action, the mountain car follows the following transition dynamics:

velocity_t+1 = velocity_t+1 + force * self.power - 0.0025 * cos(3 * position_t)

position_t+1 = position_t + velocity_t+1

where force is the action clipped to the range [-1,1] and power is a constant 0.0015. The collisions at either end are inelastic with the velocity set to 0 upon collision with the wall. The position is clipped to the range [-1.2, 0.6] and velocity is clipped to the range [-0.07, 0.07].

Reward¶

A negative reward of -0.1 * action² is received at each timestep to penalise for taking actions of large magnitude. If the mountain car reaches the goal then a positive reward of +100 is added to the negative reward for that timestep.

Starting State¶

The position of the car is assigned a uniform random value in [-0.6 , -0.4]. The starting velocity of the car is always assigned to 0.

Episode End¶

The episode ends if either of the following happens:

Termination: The position of the car is greater than or equal to 0.45 (the goal position on top of the right hill)
Truncation: The length of the episode is 999.

Arguments¶

Continuous Mountain Car has two parameters for gymnasium.make with render_mode and goal_velocity. On reset, the options parameter allows the user to change the bounds used to determine the new random state.

>>> import gymnasium as gym
>>> env = gym.make("MountainCarContinuous-v0", render_mode="rgb_array", goal_velocity=0.1)  # default goal_velocity=0
>>> env
<TimeLimit<OrderEnforcing<PassiveEnvChecker<Continuous_MountainCarEnv<MountainCarContinuous-v0>>>>>
>>> env.reset(seed=123, options={"low": -0.7, "high": -0.5})  # default low=-0.6, high=-0.4
(array([-0.5635296,  0.       ], dtype=float32), {})

Version History¶

v0: Initial versions release