Motrixlab/docs/source/en/user_guide/demo/dm_hopper.md

Single-Leg Hopping Robot

Hopper is a classic single-leg hopping control task in dm-control, simulating a 2D single-leg hopping robot.

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Task Description

The 2D robot consists of four body segments: torso, pelvis, thigh, calf, and foot. Actions are generated through four articulated joints, including: waist, hip, knee, and ankle. Each joint is driven by a motor with different gear ratios, enabling behaviors such as standing, balancing, and hopping forward.

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Action Space

Item	Details
Type	Box(-1.0, 1.0, (3,), float32)
Dimension	3

Joint mapping:

Index	Action Description	Min	Max	XML Name
0	Torque applied on the thigh rotor	-1	1	thigh_joint
1	Torque applied on the leg rotor	-1	1	leg_joint
2	Torque applied on the foot rotor	-1	1	foot_joint

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Observation Space

Item	Details
Type	Box(-inf, inf, (13,), float64)
Dimension	13

Component	Description	Dim	Notes
qpos	Joint angles and torso height	5	torso x-position excluded by default
qvel	Joint and torso velocities	6	Velocity as derivative of position
contact sensors	Toe and heel ground sensors	2	Normalized by log1p

The observation vector consists of joint positions (qpos), velocities (qvel), and contact force sensors. The full dimension is 13, including two contact sensors:

Index	Observation	XML Name	Joint Type	Physical Meaning
0	torso z-position	rootz	slide	torso height
1	torso angle	rooty	hinge	body pitch angle
2	thigh joint angle	thigh_joint	hinge	thigh rotation
3	leg joint angle	leg_joint	hinge	calf rotation
4	foot joint angle	foot_joint	hinge	foot rotation
5	torso x-velocity	rootx	slide	forward velocity
6	torso z-velocity	rootz	slide	vertical velocity
7	torso angular velocity	rooty	hinge	torso angular velocity
8	thigh joint angular velocity	thigh_joint	hinge	thigh angular velocity
9	leg joint angular velocity	leg_joint	hinge	calf angular velocity
10	foot joint angular velocity	foot_joint	hinge	foot angular velocity
11	toe touch sensor	touch_toe	sensor	toe ground contact force
12	heel touch sensor	touch_heel	sensor	heel ground contact force

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Reward Function Design

The Hopper reward consists of the following terms:

Stand Task

# Stand reward: maintain stable height

Hop Task

# Stand reward: maintain stable height
# Hopping reward: achieve target forward velocity
# Leg movement reward: encourage moderate leg motion
# Knee extension reward: encourage proper knee extension
# Foot contact reward: encourage proper ground reaction forces
# Total reward = stand_reward + hop_reward + leg_motion_reward + knee_reward + contact_reward

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Initial State

• Randomize joint angles within allowed ranges during reset

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Episode Termination Conditions

• Observation values contain invalid numerical values (NaN)

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Usage Guide

1. Environment Preview

uv run scripts/view.py --env dm-hopper-stand
uv run scripts/view.py --env dm-hopper-hop

2. Start Training

uv run scripts/train.py --env dm-hopper-stand
uv run scripts/train.py --env dm-hopper-hop

3. View Training Progress

uv run tensorboard --logdir runs/dm-hopper-stand

4. Test Training Results

uv run scripts/play.py --env dm-hopper-stand
uv run scripts/play.py --env dm-hopper-hop

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Expected Training Results

1. Maintain stable standing behavior
2. Achieve a target hopping speed of 2.0