CLIS-MPPI: Closed-Loop Model Predictive Path Integral Control With Initial-State Sampling Under Execution Delay

Zidong Liu, Xu Chen†

Department of Mechanical Engineering, University of Washington

† Corresponding author

Accepted to 65th IEEE Conference on Decision and Control (CDC 2026)

Supported by
UW+Amazon Science Hub
arXiv Demo BibTeX

Bringing planning and execution closer together.
Delay-aware sampling. Rollout-based feedback. Closed-loop control.

Five stages of the real-world UR5e narrow-passage experiment, with matching Isaac Gym views: initial pose, approaching, two obstacle-bypassing stages, and target reaching.
A UR5e manipulator moves through a narrow passage to bring its end effector to a target cube while avoiding surrounding obstacles.
5 / 5collision-free hardware runs
5.9×lower joint-position RMSE
9.7×lower joint-velocity RMSE
87.6 msmean planning time

Hardware findings for the reported task; RMSE reductions are relative to standard MPPI.

What this work adds

Main Contributions

01

Delay-aware initial states

Represent execution-time state mismatch as a distribution of plausible initial states, and jointly sample initial-state and control perturbations for MPPI rollouts.

02

Feedback from rollouts

Extract a nominal trajectory and local feedback gains from the weighted rollout distribution, then combine the MPPI feedforward update with online state-feedback correction.

03

Real-world validation

Evaluate the combined formulation on a UR5e narrow-passage task, demonstrating improved collision avoidance and closer agreement between predicted and executed motion.

The challenge

The robot keeps moving while the planner computes.

By the time a new command takes effect, the state used to plan it can already be out of date. In a narrow passage, even a small deviation matters.

Planning and execution timeline showing the robot continuing to execute the previous control during planning delay, creating a mismatch between the measured planning state and the actual application state.
Execution delay separates the measured planning state from the state at which the new control becomes effective.

The approach

Method Overview

Account for uncertainty at the start of planning. Correct the remaining mismatch at execution.

CLIS-MPPI framework: initial-state and control sampling, GPU-parallel forward simulation, weighted nominal-trajectory and feedback-gain extraction, and a closed-loop MPPI update sent to the robot.
CLIS-MPPI converts execution delay into initial-state uncertainty and extracts a local feedback policy from the resulting rollouts.

  1. Sample initial states and controls

    Draw perturbed initial states around the measured state using delay-induced covariance, together with perturbed control sequences.

  2. Simulate and weight rollouts

    Run forward simulations in parallel, evaluate trajectory costs, and form an importance-weighted nominal state-control trajectory.

  3. Extract local feedback

    Compute regularized local feedback gains from weighted state-control covariance statistics of the rollouts.

  4. Apply closed-loop control

    Combine the feedforward command with a correction based on the current measured state at control execution.

Execution-time control law

utcmd = uff,t + Kt (xt − xt)

The feedforward term provides predictive guidance; local feedback corrects execution-time state deviations.

From simulation to hardware

Real-World Experiments

A tabletop obstacle and a vertical wall leave a narrow collision-free passage for the UR5e to reach a target cube.

ROS connects the physical UR5e to CUDA-accelerated forward simulation in Isaac Gym; robot states feed the simulator and CLIS-MPPI returns optimized joint-velocity commands.
ROS provides the state and command interface between the physical UR5e and CUDA-accelerated rollouts in Isaac Gym.
Platform
6-DoF UR5e
Control rate
10 Hz
Rollouts
50
Horizon
12 steps
Compute
GeForce GTX 1650

Representative Execution

Five stages of the UR5e experiment, with hardware views above and matching Isaac Gym simulation views below: initial pose, approaching, obstacle bypassing, and target reaching.
A black box in front of the UR5e and a nearby vertical wall form a narrow passage above the tabletop. A cube on the table marks the end-effector goal; the arm must pass through the gap without contacting the box, wall, or table. Columns (a)–(e) show the initial pose, approach, obstacle bypassing, and target reaching. The top row shows the physical experiment, and the bottom row shows the corresponding Isaac Gym scene.

Experimental findings

Safer Execution. Better Planning–Execution Consistency.

Comparison with standard MPPI on the same real-world narrow-passage task.

MetricMPPICLIS-MPPI Ours
Collision-free runs3 / 55 / 5
Mean planning time87.5 ms87.6 ms
Task completion time125.4 s24.4 s
End-effector path length10.456 m0.425 m
Joint-position RMSE20.100 rad0.017 rad
Joint-velocity RMSE20.108 rad/s0.011 rad/s

1 Completion time and path length are averaged over each method’s collision-free runs: 3 for MPPI and 5 for CLIS-MPPI.

2 RMSE measures deviation from the forward-simulated reference state. The paper reports the error curves from the trial with median end-effector path length among the 3 valid collision-free trials.

Joint Position Errors

Joint position errors with respect to the forward-simulated reference joint positions for all six joints, comparing MPPI in blue and CLIS-MPPI in orange.
Joint position errors with respect to the forward-simulated reference joint positions for MPPI and CLIS-MPPI.

Joint Velocity Errors

Joint velocity errors with respect to the forward-simulated reference joint velocities for all six joints, comparing MPPI in blue and CLIS-MPPI in orange.
Joint velocity errors with respect to the forward-simulated reference joint velocities for MPPI and CLIS-MPPI.

Read the full work

Paper

CLIS-MPPI: Closed-Loop Model Predictive Path Integral Control With Initial-State Sampling Under Execution Delay

Zidong Liu and Xu Chen · CDC 2026

Read paper
First page of the CLIS-MPPI paper with title, authors, abstract and execution-delay diagram.

Cite this work

BibTeX

.bib
@inproceedings{liu2026clismppi,
  title     = {{CLIS-MPPI}: Closed-Loop Model Predictive Path Integral
               Control With Initial-State Sampling Under Execution Delay},
  author    = {Liu, Zidong and Chen, Xu},
  booktitle = {65th IEEE Conference on Decision and Control (CDC)},
  year      = {2026},
  eprint    = {2610.21239},
  archivePrefix = {arXiv},
  primaryClass = {cs.RO},
  url       = {https://arxiv.org/abs/2610.21239}
}