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-v4")`

Description#

This environment is based on the work done by 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 as compared to the classic control environments. The hopper is a two-dimensional one-legged figure that consist of four main body parts - the torso at the top, the thigh in the middle, the leg in 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 torques on the three hinges connecting the four body parts.

Action Space#

The action space is a Box(-1, 1, (3,), float32). An action represents the torques applied between links

Num	Action	Control Min	Control Max	Name (in corresponding XML file)	Joint	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#

Observations consist of positional values of different body parts of the hopper, followed by the velocities of those individual parts (their derivatives) with all the positions ordered before all the velocities.

By default, observations do not include the x-coordinate of the hopper. It may be included by passing exclude_current_positions_from_observation=False during construction. In that case, the observation space will have 12 dimensions where the first dimension represents the x-coordinate of the hopper. Regardless of whether exclude_current_positions_from_observation was set to true or false, the x-coordinate will be returned in info with key "x_position".

However, by default, the observation is a ndarray with shape (11,) where the elements correspond to the following:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Unit
0	z-coordinate of the top (height of hopper)	-Inf	Inf	rootz	slide	position (m)
1	angle of the top	-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 top	-Inf	Inf	rootx	slide	velocity (m/s)
6	velocity of the z-coordinate (height) of the top	-Inf	Inf	rootz	slide	velocity (m/s)
7	angular velocity of the angle of the top	-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)

Rewards#

The reward consists of three parts:

healthy_reward: Every timestep that the hopper is healthy (see definition in section “Episode Termination”), it gets a reward of fixed value healthy_reward.
forward_reward: A reward of hopping forward which is measured as forward_reward_weight * (x-coordinate before action - x-coordinate after action)/dt. dt is the time between actions and is dependent on the frame_skip parameter (fixed to 4), where the frametime is 0.002 - making the default dt = 4 * 0.002 = 0.008. This reward would be positive if the hopper hops forward (positive x direction).
ctrl_cost: A cost for penalising the hopper if it takes actions that are too large. It is measured as ctrl_cost_weight * sum(action²) where ctrl_cost_weight is a parameter set for the control and has a default value of 0.001

The total reward returned is reward = healthy_reward + forward_reward - ctrl_cost and info will also contain the individual reward terms

Starting State#

All observations start in state (0.0, 1.25, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) with a uniform noise in the range of [-reset_noise_scale, reset_noise_scale] added to the values for stochasticity.

Episode End#

The hopper is said to be unhealthy if any of the following happens:

An element of observation[1:] (if exclude_current_positions_from_observation=True, else observation[2:]) is no longer contained in the closed interval specified by the argument healthy_state_range
The height of the hopper (observation[0] if exclude_current_positions_from_observation=True, else observation[1]) is no longer contained in the closed interval specified by the argument healthy_z_range (usually meaning that it has fallen)
The angle (observation[1] if exclude_current_positions_from_observation=True, else observation[2]) is no longer contained in the closed interval specified by the argument healthy_angle_range

If terminate_when_unhealthy=True is passed during construction (which is the default), the episode ends when any of the following happens:

Truncation: The episode duration reaches a 1000 timesteps
Termination: The hopper is unhealthy

If terminate_when_unhealthy=False is passed, the episode is ended only when 1000 timesteps are exceeded.

Arguments#

No additional arguments are currently supported in v2 and lower.

import gymnasium as gym
env = gym.make('Hopper-v2')

v3 and v4 take gymnasium.make kwargs such as xml_file, ctrl_cost_weight, reset_noise_scale, etc.

import gymnasium as gym
env = gym.make('Hopper-v4', ctrl_cost_weight=0.1, ....)

Parameter	Type	Default	Description
`xml_file`	str	`"hopper.xml"`	Path to a MuJoCo model
`forward_reward_weight`	float	`1.0`	Weight for forward_reward term (see section on reward)
`ctrl_cost_weight`	float	`0.001`	Weight for ctrl_cost reward (see section on reward)
`healthy_reward`	float	`1`	Constant reward given if the ant is “healthy” after timestep
`terminate_when_unhealthy`	bool	`True`	If true, issue a done signal if the hopper is no longer healthy
`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
`healthy_z_range`	tuple	`(0.7, float("inf"))`	The z-coordinate must be in this range for the hopper to be considered healthy
`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
`reset_noise_scale`	float	`5e-3`	Scale of random perturbations of initial position and velocity (see section on Starting State)
`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

Version History#

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 (1.0.0)