Adroit Pen

Description

This environment was introduced in “Learning Complex Dexterous Manipulation with Deep Reinforcement Learning and Demonstrations” by Aravind Rajeswaran, Vikash Kumar, Abhishek Gupta, Giulia Vezzani, John Schulman, Emanuel Todorov, and Sergey Levine.

The environment is based on the Adroit manipulation platform, a 28 degree of freedom system which consists of a 24 degrees of freedom ShadowHand and a 4 degree of freedom arm. The task to be completed consists on repositioning the blue pen to match the orientation of the green target. The base of the hand is fixed. The target is also randomized to cover all configurations. The task will be considered successful when the orientations match within tolerance

Action Space

The action space is a Box(-1.0, 1.0, (24,), float32). The control actions are absolute angular positions of the Adroit hand joints. The input of the control actions is set to a range between -1 and 1 by scaling the real actuator angle ranges in radians. The elements of the action array are the following:

Num	Action	Control Min	Control Max	Angle Min	Angle Max	Name (in corresponding XML file)	Joint	Unit
0	Angular position of the horizontal wrist joint (radial/ulnar deviation)	-1	1	-0.524 (rad)	0.175 (rad)	A_WRJ1	hinge	angle (rad)
1	Angular position of the horizontal wrist joint (flexion/extension)	-1	1	-0.79 (rad)	0.61 (rad)	A_WRJ0	hinge	angle (rad)
2	Horizontal angular position of the MCP joint of the forefinger (adduction/abduction)	-1	1	-0.44 (rad)	0.44(rad)	A_FFJ3	hinge	angle (rad)
3	Vertical angular position of the MCP joint of the forefinger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_FFJ2	hinge	angle (rad)
4	Angular position of the PIP joint of the forefinger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_FFJ1	hinge	angle (rad)
5	Angular position of the DIP joint of the forefinger	-1	1	0 (rad)	1.6 (rad)	A_FFJ0	hinge	angle (rad)
6	Horizontal angular position of the MCP joint of the middle finger (adduction/abduction)	-1	1	-0.44 (rad)	0.44(rad)	A_MFJ3	hinge	angle (rad)
7	Vertical angular position of the MCP joint of the middle finger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_MFJ2	hinge	angle (rad)
8	Angular position of the PIP joint of the middle finger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_MFJ1	hinge	angle (rad)
9	Angular position of the DIP joint of the middle finger	-1	1	0 (rad)	1.6 (rad)	A_MFJ0	hinge	angle (rad)
10	Horizontal angular position of the MCP joint of the ring finger (adduction/abduction)	-1	1	-0.44 (rad)	0.44(rad)	A_RFJ3	hinge	angle (rad)
11	Vertical angular position of the MCP joint of the ring finger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_RFJ2	hinge	angle (rad)
12	Angular position of the PIP joint of the ring finger	-1	1	0 (rad)	1.6 (rad)	A_RFJ1	hinge	angle (rad)
13	Angular position of the DIP joint of the ring finger	-1	1	0 (rad)	1.6 (rad)	A_RFJ0	hinge	angle (rad)
14	Angular position of the CMC joint of the little finger	-1	1	0 (rad)	0.7(rad)	A_LFJ4	hinge	angle (rad)
15	Horizontal angular position of the MCP joint of the little finger (adduction/abduction)	-1	1	-0.44 (rad)	0.44(rad)	A_LFJ3	hinge	angle (rad)
16	Vertical angular position of the MCP joint of the little finger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_LFJ2	hinge	angle (rad)
17	Angular position of the PIP joint of the little finger (flexion/extension)	-1	1	0 (rad)	1.6 (rad)	A_LFJ1	hinge	angle (rad)
18	Angular position of the DIP joint of the little finger	-1	1	0 (rad)	1.6 (rad)	A_LFJ0	hinge	angle (rad)
19	Horizontal angular position of the CMC joint of the thumb finger	-1	1	-1.047 (rad)	1.047 (rad)	A_THJ4	hinge	angle (rad)
20	Vertical Angular position of the CMC joint of the thumb finger	-1	1	0 (rad)	1.3 (rad)	A_THJ3	hinge	angle (rad)
21	Horizontal angular position of the MCP joint of the thumb finger (adduction/abduction)	-1	1	-0.26 (rad)	0.26(rad)	A_THJ2	hinge	angle (rad)
22	Vertical angular position of the MCP joint of the thumb finger (flexion/extension)	-1	1	-0.52 (rad)	0.52 (rad)	A_THJ1	hinge	angle (rad)
23	Angular position of the IP joint of the thumb finger (flexion/extension)	-1	1	-1.571 (rad)	0 (rad)	A_THJ0	hinge	angle (rad)

Observation Space

The observation space is of the type Box(-inf, inf, (45,), float64). It contains information about the angular position of the finger joints, the pose of the palm of the hand, as well as the pose of the real pen and target goal.

Num	Observation	Min	Max	Joint Name (in corresponding XML file)	Site/Body Name (in corresponding XML file)	Joint Type	Unit
0	Angular position of the horizontal wrist joint	-Inf	Inf	WRJ1	-	hinge	angle (rad)
1	Angular position of the vertical wrist joint	-Inf	Inf	WRJ0	-	hinge	angle (rad)
2	Horizontal angular position of the MCP joint of the forefinger	-Inf	Inf	FFJ3	-	hinge	angle (rad)
3	Vertical angular position of the MCP joint of the forefinge	-Inf	Inf	FFJ2	-	hinge	angle (rad)
4	Angular position of the PIP joint of the forefinger	-Inf	Inf	FFJ1	-	hinge	angle (rad)
5	Angular position of the DIP joint of the forefinger	-Inf	Inf	FFJ0	-	hinge	angle (rad)
6	Horizontal angular position of the MCP joint of the middle finger	-Inf	Inf	MFJ3	-	hinge	angle (rad)
7	Vertical angular position of the MCP joint of the middle finger	-Inf	Inf	MFJ2	-	hinge	angle (rad)
8	Angular position of the PIP joint of the middle finger	-Inf	Inf	MFJ1	-	hinge	angle (rad)
9	Angular position of the DIP joint of the middle finger	-Inf	Inf	MFJ0	-	hinge	angle (rad)
10	Horizontal angular position of the MCP joint of the ring finger	-Inf	Inf	RFJ3	-	hinge	angle (rad)
11	Vertical angular position of the MCP joint of the ring finger	-Inf	Inf	RFJ2	-	hinge	angle (rad)
12	Angular position of the PIP joint of the ring finger	-Inf	Inf	RFJ1	-	hinge	angle (rad)
13	Angular position of the DIP joint of the ring finger	-Inf	Inf	RFJ0	-	hinge	angle (rad)
14	Angular position of the CMC joint of the little finger	-Inf	Inf	LFJ4	-	hinge	angle (rad)
15	Horizontal angular position of the MCP joint of the little finger	-Inf	Inf	LFJ3	-	hinge	angle (rad)
16	Vertical angular position of the MCP joint of the little finger	-Inf	Inf	LFJ2	-	hinge	angle (rad)
17	Angular position of the PIP joint of the little finger	-Inf	Inf	LFJ1	-	hinge	angle (rad)
18	Angular position of the DIP joint of the little finger	-Inf	Inf	LFJ0	-	hinge	angle (rad)
19	Horizontal angular position of the CMC joint of the thumb finger	-Inf	Inf	THJ4	-	hinge	angle (rad)
20	Vertical Angular position of the CMC joint of the thumb finger	-Inf	Inf	THJ3	-	hinge	angle (rad)
21	Horizontal angular position of the MCP joint of the thumb finger	-Inf	Inf	THJ2	-	hinge	angle (rad)
22	Vertical angular position of the MCP joint of the thumb finger	-Inf	Inf	THJ1	-	hinge	angle (rad)
23	Angular position of the IP joint of the thumb finger	-Inf	Inf	THJ0	-	hinge	angle (rad)
24	Position of the pen’s center of mass in the x direction	-Inf	Inf	-	Object	-	position (m)
25	Position of the pen’s center of mass in the y direction	-Inf	Inf	-	Object	-	position (m)
26	Position of the pen’s center of mass in the z direction	-Inf	Inf	-	Object	-	position (m)
27	Linear velocity of the pen in the x direction	-Inf	Inf	OBJTx	-	free	velocity (m/s)
28	Linear velocity of the pen in the y direction	-Inf	Inf	OBJTy	-	free	velocity (m/s)
29	Linear velocity of the pen in the z direction	-Inf	Inf	OBJTz	-	free	velocity (m/s)
30	Angular velocity of the pen around x axis	-Inf	Inf	OBJRx	-	free	angular velocity (rad/s)
31	Angular velocity of the pen around y axis	-Inf	Inf	OBJRy	-	free	angular velocity (rad/s)
32	Angular velocity of the pen around z axis	-Inf	Inf	OBJRz	-	free	angular velocity (rad/s)
33	Relative rotation of the pen’s center of mass with respect to the x axis	-Inf	Inf	-	object_top,object_bottom	-	angle (rad)
34	Relative rotation of the pen’s center of mass with respect to the y axis	-Inf	Inf	-	object_top,object_bottom	-	angle (rad)
35	Relative rotation of the pen’s center of mass with respect to the z axis	-Inf	Inf	-	object_top,object_bottom	-	angle (rad)
36	Relative rotation of the target’s center of mass with respect to the x axis	-Inf	Inf	-	target_top,target_bottom	-	angle (rad)
37	Relative rotation of the target’s center of mass with respect to the y axis	-Inf	Inf	-	target_top,target_bottom	-	angle (rad)
38	Relative rotation of the target’s center of mass with respect to the z axis	-Inf	Inf	-	target_top,target_bottom	-	angle (rad)
39	x linear distance from pen to target goal	-Inf	Inf	-	-	-	position (m)
40	y linear distance from pen to target goal	-Inf	Inf	-	-	-	position (m)
41	z linear distance from pen to target goal	-Inf	Inf	-	-	-	position (m)
42	Rotational distance from pen to target goal with respect to the x axis	-Inf	Inf	-	-	-	angle (rad)
43	Rotational distance from pen to target goal with respect to the x axis	-Inf	Inf	-	-	-	angle (rad)
44	Rotational distance from pen to target goal with respect to the x axis	-Inf	Inf	-	-	-	angle (rad)

Rewards

The environment can be initialized in either a dense or sparse reward variant.

In the dense reward setting, the environment returns a dense reward function that consists of the following parts:

• target_distance: increasing negative reward the further away the pen is from its target. This is computed as the 3 dimensional Euclidean distance between both body frames. This penalty is scaled by a factor of 0.1 in the final reward.

• orientation_similarity: add the dot product between the target’s and real pen orientation.

• close_to_target: bonus reward for the pen being close to the target orientation. If the dot product between both ortientations is greater than 0.9 and the Euclidean distance less than 0.075 add a 10 reward, if the same distance holds and the orientation dot product is greater than 0.95 add 50.

• dropping_pen: If the pen drops from the hand (pen’s height less than 0.075) add a negative reward of 5.

The sparse reward variant of the environment can be initialized by calling gym.make('AdroitHandPenSparse-v1'). In this variant, the environment returns a reward of 10 for environment success and -0.1 otherwise.

Starting State

The real pen is reset to the palm of the Adroit arm. The target orientation of the pen is then randomly selected from a uniform distribution with range [-1,1] radians. Only roll and pitch are randomly selected. The initial position of the target is (x,y,z)=(0,-0.2,0.25).

The joint values of the environment are deterministically initialized to a zero.

For reproducibility, the starting state of the environment can also be set when calling env.reset() by passing the options dictionary argument (https://gymnasium.farama.org/api/env/#gymnasium.Env.reset) with the initial_state_dict key. The initial_state_dict key must be a dictionary with the following items:

• qpos: np.ndarray with shape (30,), MuJoCo simulation joint positions

• qvel: np.ndarray with shape (30,), MuJoCo simulation joint velocities

• desired_orien: np.ndarray with shape (4,), quaternion values of the target pen orientation

The state of the simulation can also be set at any step with the env.set_env_state(initial_state_dict) method.

Episode End

The episode will be truncated when the duration reaches a total of max_episode_steps which by default is set to 200 timesteps. The episode will be terminated when the Euclidean distancd to the target is less than 0.075, and the dot product of the pen’s and target orientatin is greater than 0.95.

Arguments

To increase/decrease the maximum number of timesteps before the episode is truncated the max_episode_steps argument can be set at initialization. The default value is 50. For example, to increase the total number of timesteps to 400 make the environment as follows:

import gymnasium as gym

env = gym.make('AdroitHandPen-v1', max_episode_steps=400)

Version History

• v1: refactor version of the D4RL environment, also create dependency on newest mujoco python bindings maintained by the MuJoCo team in Deepmind.

• v0: legacy versions in the D4RL.