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

Zidong Liu, Xu Chen

arXiv:2610.21239v1cs.RO

TL;DR

Planning delay can make MPPI apply a control optimized for an earlier state to a different execution-time state, degrading performance and risking collisions. CLIS-MPPI samples plausible execution-time initial states and control sequences, then combines the MPPI feedforward update with rollout-based local feedback. Across five UR5e trials, MPPI collided in two runs while CLIS-MPPI was collision-free in all five; among collision-free runs, completion time fell from 25.4 s to 24.4 s and end-effector path length from 0.456 m to 0.425 m.

  • Problem

    Planning delay can make MPPI apply a control optimized for an earlier state to a different execution-time state, degrading performance and risking collisions.

    Source: §I · p. 1, B. Experimental Results · p. 6

  • Method

    CLIS-MPPI samples plausible execution-time initial states and control sequences, then combines the MPPI feedforward update with rollout-based local feedback.

    Source: §I · pp. 1–2

  • Results

    Across five UR5e trials, MPPI collided in two runs while CLIS-MPPI was collision-free in all five; among collision-free runs, completion time fell from 25.4 s to 24.4 s and end-effector path length from 0.456 m to 0.425 m.

    Source: B. Experimental Results · pp. 5–6

  • Takeaways & Limitations

    In delay-sensitive tasks, CLIS-MPPI improved safety and reduced overall joint-position RMSE from 0.100 rad to 0.017 rad and joint-velocity RMSE from 0.108 rad/s to 0.011 rad/s.

    Source: §IV · p. 7, B. Experimental Results · p. 7

Abstract

from arXiv · show

Sampling-based motion planning such as Model Predictive Path Integral (MPPI) control has become attractive for robotics due to its ability to handle nonlinear dynamics and non-smooth objectives without gradient information, while leveraging parallel rollout computation for real-time performance. However, in real-world robotic systems, the optimized control input is often applied after a non-negligible planning delay, causing a mismatch between the state used in forward simulation and the actual state at control execution, which can significantly degrade planning accuracy and may even lead to unsafe behavior such as collisions. This paper proposes Closed-Loop MPPI with Initial-State Sampling (CLIS-MPPI), which explicitly addresses execution-time state mismatch by modeling planning delay as a distribution over plausible execution-time initial states, performing rollout optimization from sampled initial states, and applying a rollout-based local feedback correction during control execution. The proposed method is validated through real-world experiments on a 6-DoF UR5e manipulator in a narrow-passage task involving obstacle avoidance and end-effector target reaching. Across 5 real-world runs of the same task, standard MPPI collided in 2 runs, whereas CLIS-MPPI remained collision-free in all 5 runs. Averaged over all collision-free runs for each method (3 for MPPI and 5 for CLIS-MPPI), CLIS-MPPI reduced the average task completion time from 25.4s to 24.4s and the average end-effector path length from 0.456 m to 0.425 m. It also reduced the overall joint-position and joint-velocity root mean square errors (RMSEs) from 0.100 rad and 0.108 rad/s to 0.017 rad and 0.011 rad/s, respectively. These results demonstrate improved safety, planning-execution consistency, and motion smoothness.

I. INTRODUCTION

MPPI enables online motion planning for nonlinear systems and complex objectives, but planning delay can make its optimized control stale before execution. CLIS-MPPI models that delay as initial-state uncertainty and adds rollout-based feedback correction.

I. INTRODUCTION

  • MPPI supports real-time robotic planning through stochastic rollouts, path-integral weighted updates, non-differentiable objectives, and GPU-parallel computation.The paper contrasts this online approach with gradient-based MPC and offline-training-dependent reinforcement learning.Source: §I · p. 1
  • Planning delay creates a mismatch because the robot continues executing the previous control while MPPI simulates from the measured planning state.The new control is therefore applied to a state that has evolved since optimization began.Source: §I · p. 1
  • In high-frequency or large-action settings, even small delays can cause substantial state deviation and collisions in narrow-space obstacle avoidance.The planned rollouts may be collision-free even when execution-time mismatch causes unsafe behavior.Source: §I · p. 1
  • CLIS-MPPI samples plausible execution-time initial states alongside control perturbations, then uses a rollout-derived local feedback correction with the MPPI feedforward update.This is intended to improve planning-execution consistency, motion smoothness, and safety in delay-sensitive tasks.Source: §I · pp. 1–2

A. Related Work

Prior MPPI work spans robotic platforms and safety or feedback enhancements, but the cited approaches do not explicitly address execution-time mismatch caused by planning delay. CLIS-MPPI targets that gap, while standard MPPI's receding-horizon optimization relies on an immediate-actuation assumption.

A. Related Work

  • Prior work applies MPPI to manipulators, aerial robots, and safety or feedback enhancements, but does not explicitly address the state mismatch caused by planning delay.The cited approaches include CBF-based safety methods and Feedback-MPPI's rollout-sensitivity feedback gains.Source: A. Related Work · p. 2

B. Contributions

  • CLIS-MPPI models planning delay as a distribution over plausible execution-time initial states and combines joint initial-state/control sampling with rollout-based feedback correction.In five UR5e narrow-passage trials, MPPI collided in two runs while CLIS-MPPI remained collision-free in all five; among collision-free trials, completion time fell from 25.4 s to 24.4 s and path length from 0.456 m to 0.425 m.Source: B. Contributions · p. 2

A. MPPI Preliminaries

  • Standard MPPI assumes immediate actuation and state agreement, then optimizes a horizon-N control sequence using stochastic rollouts and importance-weighted control updates.Only the first control is executed before the procedure repeats in receding-horizon fashion.Source: A. MPPI Preliminaries · pp. 2–3

B. Proposed CLIS-MPPI

CLIS-MPPI augments standard MPPI with delay-aware initial-state sampling and rollout-based local feedback for closed-loop execution.

B. Proposed CLIS-MPPI

  • CLIS-MPPI adds delay-induced initial-state uncertainty modeling, initial-state-sampled rollouts, and rollout-based local feedback extraction.The workflow is illustrated in Fig. 2, with corresponding pseudocode in Algorithm 1.Source: B. Proposed CLIS-MPPI · p. 3
  • The method samples execution-time initial states as well as control sequences during forward simulation.The resulting weighted rollout distribution supports closed-loop control with local feedback.Source: B. Proposed CLIS-MPPI · p. 3
  • The applied control combines MPPI's feedforward update with feedback extracted from the rollouts.This closes the execution loop rather than relying on the feedforward update alone.Source: B. Proposed CLIS-MPPI · p. 3

1) Delay-Induced Initial-State Uncertainty:

CLIS-MPPI represents the delay between planning and policy execution as uncertainty in the execution-time initial state. It uses delay-induced mismatch covariance to sample plausible initial states for rollout propagation.

1) Delay-Induced Initial-State Uncertainty:

  • The planner models the interval before a newly computed policy takes effect as execution-time state uncertainty, rather than assuming the planning state remains unchanged.The robot continues executing the previous command during this interval.Source: 1) Delay-Induced Initial-State… · p. 3
  • For streaming velocity commands, the dominant position mismatch is modeled using the average previously issued command during the delay window and the effective delay.The covariance approximation assumes approximate independence between the held command and delay.Source: 1) Delay-Induced Initial-State… · p. 3
  • The initial-state sampling covariance is set to the delay-induced execution-time mismatch covariance, so rollouts start from plausible delayed states.Source: 1) Delay-Induced Initial-State… · p. 4

2) Initial-State-Sampled MPPI:

CLIS-MPPI samples execution-time initial states alongside control perturbations, then propagates rollouts from those sampled states. It therefore optimizes over plausible execution-time conditions rather than one assumed planning state.

2) Initial-State-Sampled MPPI:

3) Rollout-Based Feedback Extraction and Closed-Loop Execution:

CLIS-MPPI extracts local feedback from weighted rollout deviations and combines it with the feedforward MPPI update for closed-loop execution. Delay statistics are estimated online to adapt the delay covariance.

3) Rollout-Based Feedback Extraction and Closed-Loop Execution:

  • CLIS-MPPI fits a local linear state-feedback relation from weighted rollout deviations around the nominal trajectory.The deviations are centered before fitting the relation by weighted least squares.Source: 3) Rollout-Based Feedback Extraction… · p. 4
  • The applied control combines the MPPI feedforward update with feedback that compensates for delay-induced mismatch and local execution errors.The planner packages the feedforward sequence, reference state trajectory, and extracted local feedback gains.Source: 3) Rollout-Based Feedback Extraction… · pp. 4–5
  • Online delay samples estimate E[τ], Var(τ), and E[τ^2] to adapt Σ_delay; execution also uses saturation, rate limits, and an effective-sample-size threshold for robustness under weight collapse.Source: 3) Rollout-Based Feedback Extraction… · p. 5

III. EXPERIMENTS

Real-world experiments on a 6-DoF manipulator evaluated CLIS-MPPI on obstacle-avoidance and goal-reaching tasks, with the reported comparison favoring it over standard MPPI in narrow-space obstacle avoidance.

III. EXPERIMENTS

  • In the reported real-world narrow-space obstacle-avoidance experiments, CLIS-MPPI achieved collision-free execution, shorter total path length, and lower error relative to the reference state than standard MPPI.Source: §III · p. 5

A. Real-World Experimental Setup

Figure 3 is identified as the experimental setup.

1) Hardware and implementation:

Experiments use a 6-DoF UR5e with GPU-parallel rollout simulation.

  • The platform is a 6-DoF UR5e, with MPPI rollouts simulated in Isaac Gym using CUDA-based parallel computation.The onboard PC has an Intel Core i7-9750H CPU, NVIDIA GeForce GTX 1650 GPU, and 32 GB RAM.Source: 1) Hardware and implementation · p. 5

2) State and control interface:

In narrow-passage UR5e trials, CLIS-MPPI avoided collisions and improved completion time, path length, and reference-tracking errors over MPPI. The experiment uses joint-position and joint-velocity state feedback, with a stage cost for end-effector pose and collision penalties.

2) State and control interface:

  • The state vector contains 12 dimensions for six joint positions and six joint velocities, and the UR5e receives six-dimensional joint-velocity commands through ROS.The control rate is 10 Hz (dt = 0.1 s).Source: 2) State and control interface · p. 5

3) Cost function:

  • The stage cost accounts for end-effector pose mismatch and collision penalties, with collision or contact involving the table, shelf, or obstacle flagged by Icol(qt).For this UR5e task, the weights are (wp,wR,wc) = (10,3,1000).Source: 3) Cost function · p. 5

B. Experimental Results

  • In the real-world tabletop task, baseline MPPI collided in 2 of 5 repeated trials, while CLIS-MPPI, using delay-aware initial-state sampling and online state-feedback correction, completely avoided this issue in all real-world trials.The tabletop scene used a black box as an obstacle and a cube as the end-effector goal; the passage between the obstacle and wall was narrow.Source: B. Experimental Results · pp. 5–6
  • 24.4 s versus 25.4 s average completion time and 0.425 m versus 0.456 m average end-effector path length favored CLIS-MPPI among collision-free trials.Averages use 5 CLIS-MPPI trials and 3 MPPI trials.Source: Table II · p. 5, B. Experimental Results · p. 6
  • In the median-end-effector-path-length trial among three valid collision-free trials, CLIS-MPPI’s overall joint-position and joint-velocity RMSEs were 0.017 rad and 0.011 rad/s, versus MPPI’s 0.100 rad and 0.108 rad/s.Figs. 5 and 6 show errors relative to the reference joint positions and velocities, respectively.Source: Figure 5 · p. 6, Figure 6 · p. 6, B. Experimental Results · p. 7

IV. CONCLUSIONS

CLIS-MPPI models planning delay as initial-state uncertainty and adds online state-feedback correction to mitigate state mismatch. Real-world UR5e experiments show improved collision avoidance, state consistency, and motion smoothness compared with standard MPPI.

  • CLIS-MPPI models planning delay as initial-state uncertainty and combines MPPI with online state-feedback correction to mitigate execution-time state mismatch.Source: §IV · p. 7
  • Real-world experiments on a 6-DoF UR5e manipulator found improved collision avoidance and state consistency with CLIS-MPPI compared with standard MPPI.Source: §IV · p. 7
  • CLIS-MPPI also produced smoother and more stable robot motion during execution than standard MPPI in the reported experiments.Source: §IV · p. 7
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