MDOCRSS 2026
Model-Based Diffusion Optimal Control for Multi-Robot Motion Planning
Generate feasible motion. Coordinate safely.
A modular robotics frameworkGenerative
Generative
dynamics
on manifold.
Connect generative models, manifold geometry, and robot learning. Turn structured proposals into motion that responds to constraints and contact.
SIMULATION + REAL ROBOTSAdaptive contactMGA · Simulation G1 · AR obstacles2GO · Real robot · 1× Feasible footholds2GO · Simulation · 1× Corridor navigation2GO · Simulation · 1× Compliant contactMGA · Real robot · 1× Contact-rich insertionMGA · Real robot · 1× Humanoid pushingMGA · Simulation · 1× Force regulationMGA · Simulation · 1× Contact unjammingMGA · Simulation · 1×
Planning.Control.Learning.
Shared tasks. Composable constraints. Interchangeable algorithms.The framework in motionOne stack.
One stack.
Many ways to move.
From coordinating robots to maintaining contact, explore original demonstrations from the research behind the framework.
SIMULATION
Multi-robot coordination
MDOC-CBS coordinates multiple robots in a constrained scene.
SIMULATION
7-DoF obstacle avoidance
An arm executes obstacle-avoidance motion in the D3IL environment.
SIMULATION
Quadruped stepping stones
Governed quadruped motion follows discrete footholds.
SIMULATION
Humanoid corridor
Body posture and clearance adapt through a constrained corridor.
SIMULATION
Compliant surface scanning
A rigid arm scans a surface with changing material compliance.
SIMULATION
Contact-rich insertion
Motion and impedance adapt during peg insertion.
REAL ROBOT
Humanoid hardware
Real Unitree G1 navigates motion-capture-registered AR virtual obstacles.
REAL ROBOT
Compliant scanning hardware
Original MGA hardware footage of contact with compliant material.
REAL ROBOT
Peg insertion hardware
Original MGA hardware footage of peg insertion.
SIMULATION
Humanoid pushing
Unitree H1 pushes a box forward from a fixed stance.
SIMULATION
Humanoid force regulation
Unitree H1 regulates contact force against a stationary box.
SIMULATION
Humanoid contact unjamming
Unitree H1 adjusts contact to free a box from a narrow passage.
2GO, humanoid pushing, and hardware clips preserve source timing. Playback details are listed with each result.
A connected research trajectoryWhat should guide
Explore MDOC
What should guide
generation?
Dynamics, constraints, geometry, and contact feedback. Each work opens the next question in making generated behavior useful for robots.
Can we generate dynamically feasible, collision-free motion without demonstration training, and use that planner to coordinate a team of robots?
A useful motion plan must obey the robot's dynamics and avoid collisions, even when many robots share the same space. MDOC brings these requirements inside model-based diffusion: candidate controls are corrected during rollout, and known dynamics turn them into executable state trajectories. The planner estimates its denoising direction from evaluated rollouts without learning from demonstrations. MDOC-CBS then uses the same low-level mechanism to resolve conflicts between robots.
Dynamics rolloutsCBF projectionMulti-robot coordination
Connected ideas, distinct problem settings. Each method has its own scope, evidence, and trade-offs.
Built to composeA framework for
A framework for
the next idea.
Swap the algorithm, keep the task.
Compare generative planners and control methods through shared environments, configurations, and evaluation protocols.
Learn priors. Refine with models.
Reuse policy checkpoints or learned trajectory distributions, then guide candidates with dynamics, geometry, and constraints.
Bring your own components.
Add planners, robot tasks, constraints, metrics, and visualizations through explicit interfaces and registries.
Define the task
Dynamics · Objectives · Geometry
Robot models, task costs, collision geometry, and physical constraints.
Generate & refine
Planners · Priors · Constraint solvers
Interchangeable algorithms, learned proposals, and geometry-aware updates.
Connect to execution
Controllers · Governors · Observers
Replanning, feedback, safety components, and inspectable results.
Start with one trajectoryYour task.
Your task.
Your planner.
Your Python.
Create a planar task and use 2GO directly. The CPU example needs no robot simulator or pretrained checkpoint.
Install the package and optimization extras first. Repository access is required while the release is being prepared.
import jax
import numpy as np
from genedynamics.envs import make_env, make_energy
from genedynamics.solvers import TwoGOSolver
from genedynamics.core.backends.runtime import (
RuntimeBackendManager,
)
RuntimeBackendManager.set_backend("jax", device="cpu")
env = make_env("single_integrator_box_2d")
planner = TwoGOSolver(
dynamics=env,
energy=make_energy("single_integrator_box_2d"),
backend=RuntimeBackendManager.get_backend(),
dt=env.dt, horizon=20, Nsample=128, Ndiffuse=16,
)
plan = planner.solve(
np.array([0.8, 0.8], dtype=np.float32),
horizon=20, rng_key=jax.random.PRNGKey(0),
)
next_state = env.transition(
np.array([0.8, 0.8], dtype=np.float32),
plan.actions[0],
)Plan → execute the first action → replan
Research behind the framework
A growing body of work.
Each method contributes a different piece of the planning and control stack. Read the ideas, inspect the evidence, and find the corresponding recipe.
MD-COASIROS 2026
Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling
Balance exploration, feasibility, and compute.
2GOPreprint
Model-Based Geometry-Aware Generative Optimization for Constrained Locomotion Planning
Let constraint geometry guide the search.
MGAPreprint
Manifold Generative Annealing for Contact Constraint-aware Impedance Control with Reinforcement Learning Prior
Refine interaction through its physical response.
Build on the ideas.
Start with a CPU example, then explore constraints, learning, and robot tasks.