Hopper¶

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


Action Space	`Box(-1.0, 1.0, (3,), float32)`
Observation Space	`Box(-inf, inf, (11,), float64)`
import	`gymnasium.make("Hopper-v5")`

Description¶

This environment is based on the work of Erez, Tassa, and Todorov in “Infinite Horizon Model Predictive Control for Nonlinear Periodic Tasks”. The environment aims to increase the number of independent state and control variables compared to classical control environments. The hopper is a two-dimensional one-legged figure consisting of four main body parts - the torso at the top, the thigh in the middle, the leg at the bottom, and a single foot on which the entire body rests. The goal is to make hops that move in the forward (right) direction by applying torque to the three hinges that connect the four body parts.

Action Space¶

The action space is a Box(-1, 1, (3,), float32). An action represents the torques applied at the hinge joints.

Num	Action	Control Min	Control Max	Name (in corresponding XML file)	Joint	Type (Unit)
0	Torque applied on the thigh rotor	-1	1	thigh_joint	hinge	torque (N m)
1	Torque applied on the leg rotor	-1	1	leg_joint	hinge	torque (N m)
2	Torque applied on the foot rotor	-1	1	foot_joint	hinge	torque (N m)

Observation Space¶

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

qpos (5 elements by default): Position values of the robot’s body parts.
qvel (6 elements): The velocities of these individual body parts (their derivatives).

By default, the observation does not include the robot’s x-coordinate (rootx). This can be included by passing exclude_current_positions_from_observation=False during construction. In this case, the observation space will be a Box(-Inf, Inf, (12,), float64), where the first observation element is the x-coordinate of the robot. Regardless of whether exclude_current_positions_from_observation is set to True or False, the x- and y-coordinates are returned in info with the keys "x_position" and "y_position", respectively.

By default, however, the observation space is a Box(-Inf, Inf, (11,), float64) where the elements are as follows:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Type (Unit)
0	z-coordinate of the torso (height of hopper)	-Inf	Inf	rootz	slide	position (m)
1	angle of the torso	-Inf	Inf	rooty	hinge	angle (rad)
2	angle of the thigh joint	-Inf	Inf	thigh_joint	hinge	angle (rad)
3	angle of the leg joint	-Inf	Inf	leg_joint	hinge	angle (rad)
4	angle of the foot joint	-Inf	Inf	foot_joint	hinge	angle (rad)
5	velocity of the x-coordinate of the torso	-Inf	Inf	rootx	slide	velocity (m/s)
6	velocity of the z-coordinate (height) of the torso	-Inf	Inf	rootz	slide	velocity (m/s)
7	angular velocity of the angle of the torso	-Inf	Inf	rooty	hinge	angular velocity (rad/s)
8	angular velocity of the thigh hinge	-Inf	Inf	thigh_joint	hinge	angular velocity (rad/s)
9	angular velocity of the leg hinge	-Inf	Inf	leg_joint	hinge	angular velocity (rad/s)
10	angular velocity of the foot hinge	-Inf	Inf	foot_joint	hinge	angular velocity (rad/s)
excluded	x-coordinate of the torso	-Inf	Inf	rootx	slide	position (m)

Rewards¶

The total reward is: reward = healthy_reward + forward_reward - ctrl_cost.

healthy_reward: Every timestep that the Hopper is healthy (see definition in section “Episode End”), it gets a reward of fixed value healthy_reward (default is \(1\)).
forward_reward: A reward for moving forward, this reward would be positive if the Hopper moves forward (in the positive \(x\) direction / in the right direction). \(w_{forward} \times \frac{dx}{dt}\), where \(dx\) is the displacement of the “torso” (\(x_{after-action} - x_{before-action}\)), \(dt\) is the time between actions, which depends on the frame_skip parameter (default is \(4\)), and frametime which is \(0.002\) - so the default is \(dt = 4 \times 0.002 = 0.008\), \(w_{forward}\) is the forward_reward_weight (default is \(1\)).
ctrl_cost: A negative reward to penalize the Hopper for taking actions that are too large. \(w_{control} \times \|action\|_2^2\), where \(w_{control}\) is ctrl_cost_weight (default is \(10^{-3}\)).

info contains the individual reward terms.

Starting State¶

The initial position state is \([0, 1.25, 0, 0, 0, 0] + \mathcal{U}_{[-reset\_noise\_scale \times I_{6}, reset\_noise\_scale \times I_{6}]}\). The initial velocity state is \(\mathcal{U}_{[-reset\_noise\_scale \times I_{6}, reset\_noise\_scale \times I_{6}]}\).

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

Note that the z-coordinate is non-zero so that the hopper can stand up immediately.

Episode End¶

Termination¶

If terminate_when_unhealthy is True (the default), the environment terminates when the Hopper is unhealthy. The Hopper is unhealthy if any of the following happens:

An element of observation[1:] (if exclude_current_positions_from_observation=True, otherwise observation[2:]) is no longer contained in the closed interval specified by the healthy_state_range argument (default is \([-100, 100]\)).
The height of the hopper (observation[0] if exclude_current_positions_from_observation=True, otherwise observation[1]) is no longer contained in the closed interval specified by the healthy_z_range argument (default is \([0.7, +\infty]\)) (usually meaning that it has fallen).
The angle of the torso (observation[1] if exclude_current_positions_from_observation=True, otherwise observation[2]) is no longer contained in the closed interval specified by the healthy_angle_range argument (default is \([-0.2, 0.2]\)).

Truncation¶

The default duration of an episode is 1000 timesteps.

Arguments¶

Hopper 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('Hopper-v5', ctrl_cost_weight=1e-3, ....)

Parameter	Type	Default	Description
`xml_file`	str	`"hopper.xml"`	Path to a MuJoCo model
`forward_reward_weight`	float	`1`	Weight for forward_reward term (see `Rewards` section)
`ctrl_cost_weight`	float	`1e-3`	Weight for ctrl_cost reward (see `Rewards` section)
`healthy_reward`	float	`1`	Weight for healthy_reward reward (see `Rewards` section)
`terminate_when_unhealthy`	bool	`True`	If `True`, issue a `terminated` signal is unhealthy (see `Episode End` section)
`healthy_state_range`	tuple	`(-100, 100)`	The elements of `observation[1:]` (if `exclude_current_positions_from_observation=True`, else `observation[2:]`) must be in this range for the hopper to be considered healthy (see `Episode End` section)
`healthy_z_range`	tuple	`(0.7, float("inf"))`	The z-coordinate must be in this range for the hopper to be considered healthy (see `Episode End` section)
`healthy_angle_range`	tuple	`(-0.2, 0.2)`	The angle given by `observation[1]` (if `exclude_current_positions_from_observation=True`, else `observation[2]`) must be in this range for the hopper to be considered healthy (see `Episode End` section)
`reset_noise_scale`	float	`5e-3`	Scale of random perturbations of initial position and velocity (see `Starting State` section)
`exclude_current_positions_from_observation`	bool	`True`	Whether or not to omit the x-coordinate from observations. Excluding the position can serve as an inductive bias to induce position-agnostic behavior in policies(see `Observation Space` 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.
- Return a non-empty info with reset(), previously an empty dictionary was returned, the new keys are the same state information as step().
- 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 Hopper was unhealthy), now it is only given when the Hopper is healthy. The info["reward_survive"] is updated with this change (related GitHub issue).
- Restored the xml_file argument (was removed in v4).
- Added individual reward terms in info (info["reward_forward"], info["reward_ctrl"], info["reward_survive"]).
- Added info["z_distance_from_origin"] which is equal to the vertical distance of the “torso” body from its initial position.
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. Added reward_threshold to environments.
v0: Initial versions release.