AntCost gymnasium environment
An actuated 8-jointed ant. This environment corresponds to the Ant-v4 environment included in the gymnasium package. It is different in the fact that:
The objective was changed to a velocity-tracking task. To do this, the reward is replaced with a cost. This cost is the squared difference between the Ant’s forward velocity and a reference value (error).
Three optional variables were added to the observation space; The reference velocity, the reference error (i.e. the difference between the ant’s forward velocity and the reference) and the ant’s forward velocity. These variables can be enabled using the
exclude_reference_from_observation,exclude_reference_error_from_observationandexclude_velocity_from_observationenvironment arguments.
The rest of the environment is the same as the original Ant environment. Below, the modified cost is described. For more information about the environment (e.g. observation space, action space, episode termination, etc.), please refer to the gymnasium library.
Observation space
The original observation space of the Ant-v4 environment contains all eight motors’ angles, velocities and torques. In this modified version, the observation space has been extended to add three additional observations:
\(r\): The velocity reference signal that needs to be tracked.
\(r_{error}\): The difference between the current and reference velocities.
\(v_{x}\): The Ant’s forward velocity.
These observations optional and can be excluded from the observation space by setting the exclude_reference_from_observation, exclude_reference_error_from_observation and exclude_x_velocity_from_observation environment arguments to True.
Cost function
The cost function of this environment is designed in such a way that it tries to minimize the error between the Ant’s forward velocity and a reference value. The cost function is defined as:
Where:
\(w_{forward\_velocity}\) - is the weight of the forward velocity error.
\(x_{velocity}\) - is the Hopper’s forward velocity.
\(x_{reference\_x\_velocity}\) is the reference forward velocity.
\(w_{ctrl}\) is the weight of the control cost (optional).
\(c_{ctrl}\) is the control cost (optional).
\(p_{health}\) is a penalty for being unhealthy (i.e. if the ant falls over).
The control and health penalty are optional and can be disabled using the include_ctrl_cost and include_health_penalty environment arguments.
Environment step return
In addition to the observations, the cost and a termination and truncation boolean, the environment also returns an info dictionary:
[observation, cost, termination, truncation, info_dict]
Compared to the original Ant-v4 environment, the following keys were added to this info dictionary:
reference: The reference velocity.
state_of_interest: The state that should track the reference (SOI).
reference_error: The error between SOI and the reference.
How to use
This environment is part of the Stable Gym package. It is therefore registered as the stable_gym:AntCost-v1 gymnasium environment when you import the Stable Gym package. If you want to use the environment in stand-alone mode, you can register it yourself.
Warning
This environment is new and has not been thoroughly tested. As a result it may contain bugs and the cost function might be updated in the future.