Hopper

This environment is part of the Mujoco environments. Please read that page first for general information.

Action Space	Box(-1.0, 1.0, (3,), float32)
Observation Shape	(11,)
Observation High	[inf inf inf inf inf inf inf inf inf inf inf]
Observation Low	[-inf -inf -inf -inf -inf -inf -inf -inf -inf -inf -inf]
Import	gym.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 agent take a 3-element vector for actions. The action space is a continuous (action, action, action) all in [-1, 1] , where action represents the numerical 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)
3	Torque applied on the foot rotor	-1	1	foot_joint	hinge	torque (N m)

Observation Space

The state space consists 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.

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	x-coordinate of the top	-Inf	Inf	rootx	slide	position (m)
1	z-coordinate of the top (height of hopper)	-Inf	Inf	rootz	slide	position (m)
2	angle of the top	-Inf	Inf	rooty	hinge	angle (rad)
3	angle of the thigh joint	-Inf	Inf	thigh_joint	hinge	angle (rad)
4	angle of the leg joint	-Inf	Inf	leg_joint	hinge	angle (rad)
5	angle of the foot joint	-Inf	Inf	foot_joint	hinge	angle (rad)
6	velocity of the x-coordinate of the top	-Inf	Inf	rootx	slide	velocity (m/s)
7	velocity of the z-coordinate (height) of the top	-Inf	Inf	rootz	slide	velocity (m/s)
8	angular velocity of the angle of the top	-Inf	Inf	rooty	hinge	angular velocity (rad/s)
9	angular velocity of the thigh hinge	-Inf	Inf	thigh_joint	hinge	angular velocity (rad/s)
10	angular velocity of the leg hinge	-Inf	Inf	leg_joint	hinge	angular velocity (rad/s)
11	angular velocity of the foot hinge	-Inf	Inf	foot_joint	hinge	angular velocity (rad/s)

Note: In practice (and Gym implementation), the first positional element is omitted from the state space since the reward function is calculated based on that value. This value is hidden from the algorithm, which in turn has to develop an abstract understanding of it from the observed rewards. Therefore, observation space has shape (11,) instead of (12,) and looks like:

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:

• alive bonus: Every timestep that the hopper is alive, it gets a reward of 1,

• reward_forward: A reward of hopping forward which is measured as (x-coordinate before action - x-coordinate after action)/dt. dt is the time between actions and is dependent on the frame_skip parameter (default is 4), where the dt for one frame is 0.002 - making the default dt = 40.002 = 0.008*. This reward would be positive if the hopper hops forward (right) desired.

• reward_control: A negative reward for penalising the hopper if it takes actions that are too large. It is measured as -coefficient x sum(action²) where coefficient is a parameter set for the control and has a default value of 0.001

The total reward returned is reward = alive bonus + reward_forward + reward_control

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 [-0.005, 0.005] added to the values for stochasticity.

Episode Termination

The episode terminates when any of the following happens:

1. The episode duration reaches a 1000 timesteps

2. Any of the state space values is no longer finite

3. The absolute value of any of the state variable indexed (angle and beyond) is greater than 100

4. The height of the hopper becomes greater than 0.7 metres (hopper has hopped too high).

5. The absolute value of the angle (index 2) is less than 0.2 radians (hopper has fallen down).

Arguments

No additional arguments are currently supported (in v2 and lower), but modifications can be made to the XML file in the assets folder (or by changing the path to a modified XML file in another folder).

env = gym.make('Hopper-v2')

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

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

Version History

• v4: all mujoco environments now use the mujoco bindings in mujoco>=2.1.3

• v3: support for gym.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)