cs.ROOct 15, 2026

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

Authors: Zidong Liu, Xu Chen

Organizations: Department of Mechanical Engineering, University of Washington, Seattle, WA, USA.

Read PDF
Ask AI
Cite

Copy citation

DOINot available for this paper

Abstract

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.

Figures & tables

Fig. 1: Illustration of execution-time state mismatch in the ii -th planning cycle. At planning time tiplant_{i}^{\mathrm{plan}} , MPPI optimizes using the measured state xirefx_{i}^{\mathrm{ref}} . During the delay window, the robot continues executing the previous control ui−1u_{i-1} . Consequently, when the newly planned control uiu_{i} actually becomes effective at tisendt_{i}^{\mathrm{send}} , the system state has already evolved to xiapply≠xirefx_{i}^{\mathrm{apply}}\neq x_{i}^{\mathrm{ref}} .
Fig. 2: Overview of the proposed CLIS-MPPI. CLIS-MPPI converts execution delay into an initial-state uncertainty distribution, samples both perturbed initial states and control sequences, and performs parallel forward simulation to obtain rollout trajectories and costs. The weighted rollout distribution is then used to construct a nominal trajectory and extract local feedback gains. Finally, the applied control is computed as a closed-loop combination of the MPPI feedforward term and a state-feedback correction.
Fig. 3: Experimental setup.
ParameterValue
Rollouts KK50
Horizon NN12
Control step dtdt0.1 s (10 Hz)
Joint velocity bound ∣q˙i∣|\dot{q}_{i}|≤0.2\leq 0.2 rad/s
Joint position bound ∣qi∣|q_{i}|≤2π\leq 2\pi rad
Temperature λ\lambda0.05
TABLE I: Real-world experiment parameters
Fig. 4: Real-world UR5e tabletop experiment. A black box serves as the obstacle and the cube on the table is the end-effector goal target.
MethodMPPICLIS-MPPI
Collision-freeNoYes
Mean Planning Time (ms)87.587.6
Task Completion Time (s)25.424.4
End-effector Path (m)0.4560.425
TABLE II: Real-world results on the UR5e tabletop setup.
Fig. 5: Joint position errors with respect to the forward-simulated reference joint positions for MPPI and CLIS-MPPI
Fig. 6: Joint velocity errors with respect to the forward-simulated reference joint velocities for MPPI and CLIS-MPPI
More in this topic

MPPI Control

Model Predictive Path Integral (MPPI) control uses sampled future action sequences to optimize feedback actions under nonlinear dynamics and uncertainty.

See all 40 papers

Explore similar work

CardsList
Jul 7, 2026

Clustering-Embedded Model Predictive Path Integral Control: Avoiding Averaging-Induced Failure and Enabling Efficient Cluster Selection for Dynamic Obstacles

With the widespread availability of parallel computing hardware, sampling-based motion planning methods such as Model Predictive Path Integral (MPPI) control have become increasingly powerful for complex nonlinear systems in non-smooth task spaces. However, the sampling and forward-simulation pipeline in MPPI suffers from averaging-induced failure in cluttered environments, where the importance-weighted update averages incompatible rollouts and leads to hesitation or even collision when an obstacle lies directly ahead. This paper proposes Clustering-Embedded MPPI (CE-MPPI), a framework that architecturally resolves the averaging-induced failures inherent in standard MPPI within non-convex environments. Rather than simply mitigating interference, CE-MPPI redefines the control law by integrating a high-fidelity pruning and clustering stage. By leveraging density-based spatial clustering of applications with noise (DBSCAN) alongside a novel geometric direction feature that is extracted from collision-derived reference points, the system isolates feasible trajectory modes from the noise of infeasible rollouts. This is paired with an intelligent selection logic that optimizes for minimum cost in static scenes while actively steering opposite to obstacle flux in dynamic environments. Experiments in 2-D JAX-accelerated simulations show that CE-MPPI alleviates obstacle-front hesitation and avoids persistent coupling with moving obstacles in dynamic scenes. In particular, real-world tests on a 6-DoF UR5e manipulator with CUDA-parallel rollouts in Isaac Gym achieve a 48% reduction in time-to-goal and a 12% shorter end-effector path.

Zidong Liu, Kaixin Chang, Xu Chen

Department of Mechanical Engineering, University of Washington, Seattle, WA, USA.

MPPI ControlDynamic Obstacle AvoidanceRobot Motion Planning
AskPDF
Aug 4, 2026

Projection-Retraction MPPI: Exact Constraint-Manifold Control for Manipulators

Model Predictive Path Integral (MPPI) control is widely used in manipulation for its gradient-free, parallel handling of non-convex costs. Manipulation tasks, however, often impose constraints that hold throughout the motion: a closed kinematic chain that two grasping arms keep exactly, or joint limits and obstacle clearances that are never crossed. MPPI handles such constraints only through the cost, as soft penalties that hold approximately and fail under a strong task cost. To address this, we propose Projection-Retraction MPPI (PR-MPPI), which enforces the constraints inside the sampled dynamics. At every rollout step, the sampled velocity is projected to satisfy both constraint types: the equality restricts it to a subspace, and each inequality to a half-space within that subspace, so inequality handling never breaks the equality. This projection, however, satisfies the constraints only to first order, and a finite step leaves a small drift off the equality. Therefore, we retract the returned command back onto the constraint to numerical tolerance and independent of task weighting. We validate PR-MPPI on 14-DoF dual-arm systems. In simulation, the returned commands satisfy the closed-chain equality to numerical tolerance through a joint-limit stress test and randomized obstacle avoidance. On real hardware, the arms of a Unitree H1-2 humanoid reactively avoid a moving obstacle. Code and experiment videos are available at https://rcilab.github.io/prmppi.

Seulchan Lee, Leesai Park, Minhyeong Kang +1

School of Mechanical Engineering, Kyung Hee University, Yongin-si 17104, Republic of Korea · Institutes of Convergence Technology, Suwon-si 16229, Republic of Korea

Robotic ControlConstrained Motion PlanningBimanual Robotic ManipulationRobotic ManipulationMPPI Control
AskPDF
May 24, 2026

Manifold-Constrained MPPI: Real-Time Sampling-Based Control for Nonlinear Equality-Constrained Robotic Systems

Sampling-based model predictive control methods, such as Model Predictive Path Integral (MPPI), offer derivative-free optimization and robustness in complex robotic systems. However, standard MPPI relies on cost-based soft penalties that cannot guarantee hard-constraint satisfaction, severely limiting its applicability to highly constrained tasks such as closed-chain manipulation. To address this, we propose Manifold-Constrained MPPI (MC-MPPI), a real-time sampling-based control framework that regulates nonlinear equality constraints while preserving the computational advantages of MPPI. The key idea is to decouple the constrained optimal control problem into latent-space planning and execution-level correction. At the planning stage, a Variational Autoencoder (VAE) learns a low-dimensional latent representation of the constraint manifold, enabling MPPI to efficiently generate near-feasible candidate trajectories without per-sample modification. Since this reference enables accurate linearization of the equality constraints, an execution-level Quadratic Programming (QP) controller resolves the residual manifold mismatch in a single solve rather than through iterative projection. Experiments on a 14-DoF closed-chain dual-arm system in both simulation and real-world settings demonstrate 100 Hz planning and 500 Hz execution, equality-residual regulation in static and dynamic environments, and a 95% success rate over 40 randomized hardware trials. Supplementary videos and implementation details are available at https://rcilab.github.io/mcmppi.

Seulchan Lee, Sanghyun Kim

School of Mechanical Engineering, Kyung Hee University, Yongin, South Korea

Robotic ControlConstrained Motion PlanningConstrained OptimizationMPPI Control
AskPDF