Reacher

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

Action Space	Box(-1.0, 1.0, (2,), float32)
Observation Space	Box(-inf, inf, (10,), float64)
import	gymnasium.make("Reacher-v5")

Description

“Reacher” is a two-jointed robot arm. The goal is to move the robot’s end effector (called fingertip) close to a target that is spawned at a random position.

Action Space

The action space is a Box(-1, 1, (2,), float32). An action (a, b) 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 at the first hinge (connecting the link to the point of fixture)	-1	1	joint0	hinge	torque (N m)
1	Torque applied at the second hinge (connecting the two links)	-1	1	joint1	hinge	torque (N m)

Observation Space

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

• cos(qpos) (2 elements): The cosine of the angles of the two arms.

• sin(qpos) (2 elements): The sine of the angles of the two arms.

• qpos (2 elements): The coordinates of the target.

• qvel (2 elements): The angular velocities of the arms (their derivatives).

• xpos (2 elements): The vector between the target and the reacher’s.

The observation space is a Box(-Inf, Inf, (10,), float64) where the elements are as follows:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Type (Unit)
0	cosine of the angle of the first arm	-Inf	Inf	cos(joint0)	hinge	unitless
1	cosine of the angle of the second arm	-Inf	Inf	cos(joint1)	hinge	unitless
2	sine of the angle of the first arm	-Inf	Inf	sin(joint0)	hinge	unitless
3	sine of the angle of the second arm	-Inf	Inf	sin(joint1)	hinge	unitless
4	x-coordinate of the target	-Inf	Inf	target_x	slide	position (m)
5	y-coordinate of the target	-Inf	Inf	target_y	slide	position (m)
6	angular velocity of the first arm	-Inf	Inf	joint0	hinge	angular velocity (rad/s)
7	angular velocity of the second arm	-Inf	Inf	joint1	hinge	angular velocity (rad/s)
8	x-value of position_fingertip - position_target	-Inf	Inf	NA	slide	position (m)
9	y-value of position_fingertip - position_target	-Inf	Inf	NA	slide	position (m)
excluded	z-value of position_fingertip - position_target (constantly 0 since reacher is 2d)	-Inf	Inf	NA	slide	position (m)

Most Gymnasium environments just return the positions and velocities of the joints in the .xml file as the state of the environment. In reacher, however, the state is created by combining only certain elements of the position and velocity and performing some function transformations on them. The reacher.xml contains these 4 joints:

Num	Observation	Min	Max	Name (in corresponding XML file)	Joint	Unit
0	angle of the first arm	-Inf	Inf	joint0	hinge	angle (rad)
1	angle of the second arm	-Inf	Inf	joint1	hinge	angle (rad)
2	x-coordinate of the target	-Inf	Inf	target_x	slide	position (m)
3	y-coordinate of the target	-Inf	Inf	target_y	slide	position (m)

Rewards

The total reward is: reward = reward_distance + reward_control.

• reward_distance: This reward is a measure of how far the fingertip of the reacher (the unattached end) is from the target, with a more negative value assigned if the reacher’s fingertip is further away from the target. It is \(-w_{near} \|(P_{fingertip} - P_{target})\|_2\). where \(w_{near}\) is the reward_near_weight (default is \(1\)).

• reward_control: A negative reward to penalize the walker for taking actions that are too large. It is measured as the negative squared Euclidean norm of the action, i.e. as \(-w_{control} \|action\|_2^2\). where \(w_{control}\) is the reward_control_weight. (default is \(0.1\))

info contains the individual reward terms.

Starting State

The initial position state of the reacher arm is \(\mathcal{U}_{[-0.1 \times I_{2}, 0.1 \times I_{2}]}\). The position state of the goal is (permanently) \(\mathcal{S}(0.2)\). The initial velocity state of the Reacher arm is \(\mathcal{U}_{[-0.005 \times 1_{2}, 0.005 \times 1_{2}]}\). The velocity state of the object is (permanently) \(0_2\).

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

The default frame rate is \(2\), with each frame lasting \(0.01\), so dt = 5 * 0.01 = 0.02.

Episode End

Termination

The Reacher never terminates.

Truncation

The default duration of an episode is 50 timesteps.

Arguments

Reacher 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('Reacher-v5', xml_file=...)

Parameter	Type	Default	Description
xml_file	str	"reacher.xml"	Path to a MuJoCo model
reward_dist_weight	float	1	Weight for reward_dist term (see Rewards section)
reward_control_weight	float	0.1	Weight for reward_control term (see Rewards section)

Version History

• v5:

  • Minimum mujoco version is now 2.3.3.

  • Added default_camera_config argument, a dictionary for setting the mj_camera properties, mainly useful for custom environments.

  • Added frame_skip argument, used to configure the dt (duration of step()), default varies by environment check environment documentation pages.

  • Fixed bug: reward_distance was based on the state before the physics step, now it is based on the state after the physics step (related GitHub issue).

  • Removed "z - position_fingertip" from the observation space since it is always 0 and therefore provides no useful information to the agent, this should result is slightly faster training (related GitHub issue).

  • Added xml_file argument.

  • Added reward_dist_weight, reward_control_weight arguments to configure the reward function (defaults are effectively the same as in v4).

  • Fixed info["reward_ctrl"] not being multiplied by the reward weight.

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

• v3: This environment does not have a v3 release.

• v2: All continuous control environments now use mujoco-py >= 1.50

• v1: max_time_steps raised to 1000 for robot based tasks (not including reacher, which has a max_time_steps of 50). Added reward_threshold to environments.

• v0: Initial versions release