Hopper

A planar one-legged hopper. Four actuators across the leg drive locomotion or stationary balance depending on the variant. The body and dynamics are shared across both Hop and Stand; only the reward function changes.

HopperHop

Property	Value
Canonical ID	mjx/hopper_hop-v0
Action space	Box(-1.0, 1.0, (4,), float32)
Observation space	Box(-inf, inf, (15,), float32)
Episode length	1000
Config	{"ctrl_dt": 0.02, "sim_dt": 0.005, "naconmax": 50_000, "njmax": 50}

Description

The hopper must produce sustained forward locomotion across flat ground while keeping its torso above a minimum standing height. A collapsed slide is fast but disqualifies the policy on the height constraint; a tall but stationary stance fails the locomotion constraint. Hopping is the only gait that satisfies both simultaneously, which is the whole challenge.

Rewards

Uses a dense reward that multiplies a standing-height tolerance with a forward-speed tolerance:

standing = tolerance(torso_height, (STAND_HEIGHT, 2))
hopping  = tolerance(
    forward_speed,
    bounds=(HOP_SPEED, inf),
    margin=HOP_SPEED / 2,
    value_at_margin=0.5,
    sigmoid="linear",
)
reward = standing * hopping

The two terms are multiplied so neither alone is enough:

• standing — 1.0 while torso height sits in (STAND_HEIGHT, 2), decaying smoothly outside that band.
• hopping — linear ramp from 0.5 (at half target speed) to 1.0 (at HOP_SPEED or above). Soft floor at 0.5 so the gradient survives even slow hopping.

Starting state

obs = [ 0.     -2.5709  0.2635 -0.4848  0.5367 -0.475   0.      0.
        0.      0.      0.      0.      0.      0.      0.    ]

(joint positions followed by joint velocities — leg initialised in a default rest configuration.)

Termination

Episode ends when step >= max_steps (default 1000). No early termination on falling.

Usage

import envrax
env = envrax.make("mjx/hopper_hop-v0")

Reference

Upstream: mujoco_playground/_src/dm_control_suite/hopper.py.

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HopperStand

Property	Value
Canonical ID	mjx/hopper_stand-v0
Action space	Box(-1.0, 1.0, (4,), float32)
Observation space	Box(-inf, inf, (15,), float32)
Episode length	1000
Config	{"ctrl_dt": 0.02, "sim_dt": 0.005, "naconmax": 50_000, "njmax": 50}

Description

The same one-legged hopper, but now stationary. The agent must balance the body upright above a minimum standing height with as little control effort as possible. Steady balance is preferred over jittery "standing" — a calm posture that holds the leg roughly still scores better than one that twitches constantly to stay upright.

Rewards

Uses a dense reward that multiplies a standing-height tolerance with a small-control penalty:

standing      = tolerance(torso_height, (STAND_HEIGHT, 2))
small_control = (4 + tolerance(action, margin=1, sigmoid="quadratic").mean()) / 5
reward = standing * small_control

The two terms encode separate soft constraints:

• standing — 1.0 while torso height sits in (STAND_HEIGHT, 2), decaying smoothly outside that band.
• small_control — quadratic action penalty rescaled into [0.8, 1.0], so it lightly modulates the primary standing term rather than dominating it.

Starting state

obs = [ 0.     -2.5709  0.2635 -0.4848  0.5367 -0.475   0.      0.
        0.      0.      0.      0.      0.      0.      0.    ]

Termination

Episode ends when step >= max_steps (default 1000). No early termination on falling.

Usage

import envrax
env = envrax.make("mjx/hopper_stand-v0")

Reference

Upstream: mujoco_playground/_src/dm_control_suite/hopper.py.