Model Predictive Control

Also known as MPC

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Overview

Model Predictive Control (MPC) predicts how a system will evolve, optimizes a sequence of actions over a finite horizon, applies the first action, and replans as measurements arrive. Work spans linear and nonlinear optimization, sampling-based methods such as MPPI, and learned dynamics from Gaussian processes, Koopman models, and neural world models; these methods are used in robotics, autonomous vehicles, energy systems, and process control. Robust and stochastic MPC, control barrier functions, reachability, and distributed optimization address uncertainty, safety, and coordination, while GPU and embedded solvers aim to meet real-time limits. A central tension is that longer, richer predictions can improve planning but increase computation and sensitivity to model error, so practical controllers must balance performance, safety guarantees, and reliable execution.

Latest papers

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305 papers40 papers in the last four weeks, down 7% on the four weeks before. 0.2% of all new papers.

Apr 3, 2026

Hierarchical Planning with Latent World Models

World models are a promising path to zero-shot embodied control through planning. However, existing world model planners struggle on long-horizon, multi-stage tasks: prediction errors compound and naive search is exponential in the planning horizon. Hierarchy mitigates both by decomposing tasks into shorter, tractable subproblems; yet prior hierarchical approaches either amortize control into task-specific policies (hierarchical RL) or assume low-dimensional states and known dynamics (classical hierarchical MPC). We present Hierarchical Planning with Latent World Models (HWM), an architecture and planning paradigm for hierarchical model predictive control directly on visual world models trained solely via next-latent prediction. HWM learns world models at multiple temporal scales within a shared latent space, so predictions from the long horizon model serve as subgoals for the short horizon model via latent matching, without task-specific rewards or hierarchical policies. To keep long-horizon search tractable, HWM learns an action encoder that compresses primitive action chunks into latent macro-actions. On real-world Franka manipulation, HWM solves pick-and-place from a single goal image at 70% success vs. 0% for single-level planning. Across simulated push manipulation and maze navigation, HWM consistently improves performance on long-horizon tasks while requiring up to 3x less planning compute.

Wancong Zhang, Basile Terver, Artem Zholus +7

FAIR at Meta · New York University · Mila - Québec AI Institute +1

Hierarchical PlanningHierarchical Robot ControlHierarchical World ModelsLong-Horizon Robotic ManipulationModel Predictive ControlLatent World Models
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Apr 2, 2026

Neural Network-Assisted Model Predictive Control for Implicit Balancing

In Europe, balance responsible parties can deliberately take out-of-balance positions to support transmission system operators (TSOs) in maintaining grid stability and earn profit, a practice called implicit balancing. Model predictive control (MPC) is widely adopted as an effective approach for implicit balancing. The balancing market model accuracy in MPC is critical to decision quality. Previous studies modeled this market using either (i) a convex market clearing approximation, ignoring proactive manual actions by TSOs and the market sub-quarter-hour dynamics, or (ii) machine learning methods, which cannot be directly integrated into MPC. To address these shortcomings, we propose a data-driven balancing market model integrated into MPC using an input convex neural network to ensure convexity while capturing uncertainties. To keep the core network computationally efficient, we incorporate attention-based input gating mechanisms to remove irrelevant data. Evaluating on Belgian data shows that the proposed model both improves MPC decisions and reduces computational time.

Seyed Soroush Karimi Madahi, Kenneth Bruninx, Bert Claessens +1

IDLab, Ghent University – imec, Ghent, Belgium · Faculty of Technology, Policy & Management, Delft University of Technology, Delft, The Netherlands · Beebop.ai, Belgium

Model Predictive ControlData-Driven ControlNeural Surrogate Modeling
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Apr 2, 2026

Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine

This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine. A physics-based component-level model is developed to generate training data and validate the controllers. A meta-heuristic extended dynamic mode decomposition is adapted, with a cost function designed to accurately capture both spool-speed dynamics and the engine pressure ratio (EPR), enabling the construction of a single Koopman model that can be reused across multiple control strategies. Using the identified time-varying Koopman model, an adaptive Koopman-based model predictive controller (AKMPC) with a disturbance observer is developed and compared with a Koopman-based feedback linearization controller (K-FBLC) and its integrator-augmented version (K-FBLC-I). The Koopman representation further enables nonlinear GTE output limiters, such as rotor-acceleration and turbine-inlet-temperature limits, to be expressed as linear constraints in the AKMPC. The controllers are evaluated for two control configurations of spool speeds and EPR, under both sea-level and varying flight conditions. The results demonstrate that the proposed identification approach enables accurate predictions of both spool speeds and EPR, allowing the Koopman model to be reused flexibly across different control formulations. While all strategies achieve comparable performance in sea-level conditions, the AKMPC demonstrates improved performance under varying flight conditions due to its ability to capture nonlinear dynamics, handle constraints, and compensate for model mismatch. Moreover, the EPR control strategy improves the thrust response. The study highlights the applicability of Koopman-based control and the advantages of the AKMPC framework for robust turbofan engine control.

David Grasev

Department of Aviation Technology, University of Defence, Brno, Czech Republic.

Adaptive MPCExtended Dynamic Mode DecompositionFeedback ControlModel Predictive ControlNonlinear MPCNonlinear System Identification+2
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Apr 1, 2026

Soft MPCritic: Value-Based Reinforcement Learning for Non-Differentiable Predictive Control

Reinforcement learning (RL) and model predictive control (MPC) offer complementary strengths, yet existing MPC-RL frameworks commonly rely on gradient-based optimization and therefore cannot handle the non-differentiable dynamics and objectives common in RL. We propose Soft MPCritic, an MPC-RL framework that learns a soft value function and uses sampling-based planning both for online control and for generating value targets. Specifically, Soft MPCritic instantiates MPC with model predictive path integral control (MPPI) and learns a terminal Q-function through fitted value iteration. Because the value targets are computed by the same planner used for control, the learned value function is aligned with the planner and implicitly extends its effective horizon. To keep target generation tractable, we introduce an amortized warm-start strategy that reuses the open-loop action sequences planned during online control to initialize batched MPPI computations of value targets, reducing computational cost without sacrificing solution quality. For robustness to model error, Soft MPCritic plans over scenarios drawn from an ensemble of dynamics models trained for next-step prediction. On both classical and constrained control tasks, Soft MPCritic learns effective policies with non-differentiable objectives, particularly where finite-horizon MPPI alone falls short. Soft MPCritic thus offers a practical blueprint for synthesizing MPC policies directly from black-box objectives, without differentiable surrogates.

Thomas Banker, Nathan P. Lawrence, Ali Mesbah

Department of Chemical and Biomolecular Engineering, University of California, Berkeley, CA 94720, USA.

Model Predictive ControlModel-Based RLValue Function Estimation
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Apr 1, 2026

An Online Machine Learning Multi-resolution Optimization Framework for Energy System Design Limit of Performance Analysis

Designing reliable integrated energy systems for industrial processes requires optimization and verification models across multiple fidelities, from architecture-level sizing to high-fidelity dynamic operation. However, model mismatch across fidelities obscures the sources of performance loss and complicates the quantification of architecture-to-operation performance gaps. We propose an online, machine-learning-accelerated multi-resolution optimization framework that estimates an architecture-specific upper bound on achievable performance while minimizing expensive high-fidelity model evaluations. We demonstrate the approach on a pilot energy system supplying a 1 MW industrial heat load. First, we solve a multi-objective architecture optimization to select the system configuration and component capacities. We then develop an machine learning (ML)-accelerated multi-resolution, receding-horizon optimal control strategy that approaches the achievable-performance bound for the specified architecture, given the additional controls and dynamics not captured by the architectural optimization model. The ML-guided controller adaptively schedules the optimization resolution based on predictive uncertainty and warm-starts high-fidelity solves using elite low-fidelity solutions. Our results on the pilot case study show that the proposed multi-resolution strategy reduces the architecture-to-operation performance gap by up to 42% relative to a rule-based controller, while reducing required high-fidelity model evaluations by 34% relative to the same multi-fidelity approach without ML guidance, enabling faster and more reliable design verification. Together, these gains make high-fidelity verification tractable, providing a practical upper bound on achievable operational performance.

Oluwamayowa O. Amusat, Luka Grbcic, Remi Patureau +3

Scientific Data Division, Computing Sciences, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 · Applied Mathematics & Computational Research Division (AMCR), Computing Sciences, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 · Building & Industrial Energy Systems (BIES) Division, Energy Technologies Area, Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA 94720 +1

Multi-Fidelity OptimizationModel Predictive Control
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Apr 1, 2026

Stein Variational Uncertainty-Adaptive Model Predictive Control

We propose a Stein variational distributionally robust controller for nonlinear dynamical systems with latent parametric uncertainty. The method is an alternative to conservative worst-case ambiguity-set optimization with a deterministic particle-based approximation of a task-dependent uncertainty distribution, enabling the controller to concentrate on parameter sensitivities that most strongly affect closed-loop performance. Our method yields a controller that is robust to latent parameter uncertainty by coupling optimal control with Stein variational inference, and avoiding restrictive parametric assumptions on the uncertainty model while preserving computational parallelism. In contrast to classical DRO, which can sacrifice nominal performance through worst-case design, we find our approach achieves robustness by shaping the control law around relevant uncertainty that are most critical to the task objective. The proposed framework therefore reconciles robust control and variational inference in a single decision-theoretic formulation for broad classes of control systems with parameter uncertainty. We demonstrate our approach on representative control problems that empirically illustrate improved performance-robustness tradeoffs over nominal, ensemble, and classical distributionally robust baselines.

Hrishikesh Sathyanarayan, Ian Abraham

Department of Mechanical Engineering, Yale University, USA · Department of Electrical Engineering, University of Sydney, Australia

Model Predictive ControlNonlinear MPCDistributionally Robust Optimization
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Mar 31, 2026

Long-Horizon Geometry-Aware Navigation among Polytopes via MILP-MPC and Minkowski-Based CBFs

Autonomous navigation in complex, non-convex environments remains challenging when robot dynamics, control limits, and exact robot geometry must all be taken into account. In this paper, we propose a hierarchical planning and control framework that bridges long-horizon guidance and geometry-aware safety guarantees for a polytopic robot navigating among polytopic obstacles. At the high level, Mixed-Integer Linear Programming (MILP) is embedded within a Model Predictive Control (MPC) framework to generate a nominal trajectory around polytopic obstacles while modeling the robot as a point mass for computational tractability. At the low level, we employ a control barrier function (CBF) based on the exact signed distance in the Minkowski-difference space as a safety filter to explicitly enforce the geometric constraints of the robot shape, and further extend its formulation to a high-order CBF (HOCBF). We demonstrate the proposed framework in U-shaped and maze-like environments under single- and double-integrator dynamics. The results show that the proposed architecture mitigates the topology-induced local-minimum behavior of purely reactive CBF-based navigation while enabling safe, real-time, geometry-aware navigation.

Yi-Hsuan Chen, Salman Ghori, Ania Adil +2

Dept. of Aerospace Engineering, University of Maryland, College Park, MD, USA. · Computer, Electrical and Mathematical Science & Engineering Division (CEMSE), KAUST, Saudi Arabia. · Dept. Electrical and Computer Engineering and Dept. Computer Science, University of Maryland, College Park, MD, USA.

Safe Robot NavigationMotion PlanningConstrained Motion PlanningControl Barrier FunctionsModel Predictive Control
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Mar 31, 2026

Model Predictive Path Integral PID Control for Learning-Based Path Following

Classical proportional--integral--derivative (PID) control remains widely used in industrial control systems, while model predictive control (MPC) is actively studied to achieve higher performance for systems with nonlinear dynamics. Model predictive path integral (MPPI) control is a sampling-based MPC method that optimizes control inputs without gradient calculations and can handle non-differentiable models and objective functions. However, conventional MPPI directly samples control-input sequences, which can produce large temporal input increments and causes the optimization dimension to grow with the prediction horizon. This study proposes MPPI--PID control, which uses MPPI to optimize PID gains online instead of directly optimizing the control-input sequences. By replacing high-dimensional input-sequence optimization with low-dimensional gain-space optimization while retaining the PID structure, the proposed formulation improves sampling efficiency and promotes smoother control inputs. Theoretical analyses are provided for a unified path-integral update, the relation between optimization dimension and effective sample size, and the temporal correlation of input perturbations induced by the PID structure. The method is evaluated on a learning-based path following of a mini forklift using a residual-learning dynamics model that combines a physical model and a neural network identified from real-machine driving data. Numerical results show that MPPI--PID improves tracking performance over fixed-gain PID, yields smaller input increments than conventional MPPI, and maintains favorable performance under reduced sampling budgets.

Teruki Kato, Koshi Oishi, Seigo Ito

Toyota Central R&D Labs., Inc., Nagakute 480-1192, Japan

Nonlinear MPCResidual Dynamics LearningModel Predictive ControlFeedback ControlMPPI ControlOptimal Control+1
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Mar 30, 2026

Koopman Operator Framework for Modeling and Control of Off-Road Vehicle on Deformable Terrain

This work presents a hybrid physics-informed and data-driven modeling framework for predictive control of autonomous off-road vehicles operating on deformable terrain. Traditional high-fidelity terramechanics models are often too computationally demanding to be directly used in control design. Modern Koopman operator methods can be used to represent the complex terramechanics and vehicle dynamics in a linear form. We develop a framework whereby a Koopman linear system can be constructed using data from simulations of a vehicle moving on deformable terrain. For vehicle simulations, the deformable-terrain terramechanics are modeled using Bekker-Wong theory, and the vehicle is represented as a simplified five-degree-of-freedom (5-DOF) system. The Koopman operators are identified from large simulation datasets for sandy loam and clay using a recursive subspace identification method, where Grassmannian distance is used to prioritize informative data segments during training. The advantage of this approach is that the Koopman operator learned from simulations can be updated with data from the physical system in a seamless manner, making this a hybrid physics-informed and data-driven approach. Prediction results demonstrate stable short-horizon accuracy and robustness under mild terrain-height variations. When embedded in a constrained MPC, the learned predictor enables stable closed-loop tracking of aggressive maneuvers while satisfying steering and torque limits.

Kartik Loya, Phanindra Tallapragada

Department of Mechanical Engineering, Clemson University, Clemson, SC 29607 USA

Terrain-Aware Robot LocomotionVehicle DynamicsKoopman Operator LearningModel Predictive Control
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Mar 30, 2026

A Predictive Control Strategy to Offset-Point Tracking for Agricultural Mobile Robots

Robots are increasingly being deployed in agriculture to support sustainable practices and improve productivity. They offer strong potential to enable precise, efficient, and environmentally friendly operations. However, most existing path-following controllers focus solely on the robot's center of motion and neglect the spatial footprint and dynamics of attached implements. In practice, implements such as mechanical weeders or spring-tine cultivators are often large, rigidly mounted, and directly interacting with crops and soil; ignoring their position can degrade tracking performance and increase the risk of crop damage. To address this limitation, we propose a closed-form predictive control strategy extending the approach introduced in [1]. The method is developed specifically for Ackermann-type agricultural vehicles and explicitly models the implement as a rigid offset point, while accounting for lateral slip and lever-arm effects. The approach is benchmarked against state-of-the-art baseline controllers, including a reactive geometric method, a reactive backstepping method, and a model-based predictive scheme. Real-world agricultural experiments with two different implements show that the proposed method reduces the median tracking error by 24% to 56%, and decreases peak errors during curvature transitions by up to 70%. These improvements translate into enhanced operational safety, particularly in scenarios where the implement operates in close proximity to crop rows.

Stephane Ngnepiepaye Wembe, Vincent Rousseau, Johann Laconte +1

Université Clermont Auvergne, INRAE, UR TSCF, 63000, Clermont-Ferrand, France · SABI AGRI, 63360, Saint-Beauzire, France

Robot Trajectory TrackingAgricultural RoboticsModel Predictive Control
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Mar 30, 2026

Cost-Matching Model Predictive Control for Efficient Reinforcement Learning in Humanoid Locomotion

In this paper, we propose a cost-matching approach for optimal humanoid locomotion within a Model Predictive Control (MPC)-based Reinforcement Learning (RL) framework. A parameterized MPC formulation with centroidal dynamics is trained to approximate the action-value function obtained from high-fidelity closed-loop data. Specifically, the MPC cost-to-go is evaluated along recorded state-action trajectories, and the parameters are updated to minimize the discrepancy between MPC-predicted values and measured returns. This formulation enables efficient gradient-based learning while avoiding the computational burden of repeatedly solving the MPC problem during training. The proposed method is validated in simulation using a commercial humanoid platform. Results demonstrate improved locomotion performance and robustness to model mismatch and external disturbances compared with manually tuned baselines.

Wenqi Cai, Kyriakos G. Vamvoudakis, Sébastien Gros +1

Electrical Engineering Program, New York University Abu Dhabi (NYUAD), 129188, UAE. · School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States. · Department of Engineering Cybernetics, Norwegian University of Science and Technology (NTNU), Trondheim, Norway.

Humanoid Robot LocomotionModel Predictive ControlModel-Based RL
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Mar 29, 2026

MPC as a Copilot: A Predictive Filter Framework with Safety and Stability Guarantees

Ensuring both safety and stability remains a fundamental challenge in learning-based control, where goal-oriented policies often neglect system constraints and closed-loop state convergence. To address this limitation, this paper introduces the Predictive Safety--Stability Filter (PS2F), a unified predictive filter framework that guarantees constraint satisfaction and asymptotic stability within a single architecture. The PS2F framework comprises two cascaded optimal control problems: a nominal model predictive control (MPC) layer that serves solely as a copilot, implicitly defining a Lyapunov function and generating safety- and stability-certified predicted trajectories, and a secondary filtering layer that adjusts external command to remain within a provably safe and stable region. This cascaded structure enables PS2F to inherit the theoretical guarantees of nominal MPC while accommodating goal-oriented external commands. Rigorous analysis establishes recursive feasibility and asymptotic stability of the closed-loop system without introducing additional conservatism beyond that associated with the nominal MPC. Furthermore, a time-varying parameterisation allows PS2F to transition smoothly between safety-prioritised and stability-oriented operation modes, providing a principled mechanism for balancing exploration and exploitation. The effectiveness of the proposed framework is demonstrated through comparative numerical experiments.

Yunda Yan, Chenxi Tao, Jinya Su +2

Department of Computer Science, University College London, London WC1E 6BT, UK · School of Automation, Southeast University, Nanjing 210096, China · Department of Aeronautical and Automotive Engineering, Loughborough University, Leicestershire LE11 3TU, UK

Safety-Critical ControlModel Predictive Control
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Mar 25, 2026

Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling

The practical deployment of nonlinear model predictive control (NMPC) is often limited by online computation: solving a nonlinear program at high control rates can be expensive on embedded hardware, especially when models are complex or horizons are long. Learning-based NMPC approximations shift this computation offline but typically demand large expert datasets and costly training. We propose Sequential-AMPC, a sequential neural policy that generates MPC candidate control sequences by sharing parameters across the prediction horizon. For deployment, we wrap the policy in a safety-augmented online evaluation and fallback mechanism, yielding Safe Sequential-AMPC. Compared to a naive feedforward policy baseline across several benchmarks, Sequential-AMPC requires substantially fewer expert MPC rollouts and yields candidate sequences with higher feasibility rates and improved closed-loop safety. On high-dimensional systems, it also exhibits better learning dynamics and performance in fewer epochs while maintaining stable validation improvement where the feedforward baseline can stagnate.

Mihaela-Larisa Clement, Mónika Farsang, Agnes Poks +4

Institute of Computer Engineering, TU Wien, Vienna, Austria · AIT Austrian Institute of Technology, Vienna, Austria · Institute of Mechanics and Mechatronics, TU Wien, Vienna, Austria

Nonlinear MPCModel Predictive ControlPolicy LearningSafety-Critical ControlRecurrent Neural Networks
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Mar 20, 2026

High-Speed, All-Terrain Autonomy: Ensuring Safety at the Limits of Mobility

A novel local trajectory planner, capable of controlling an autonomous off-road vehicle on rugged terrain at high-speed is presented. Autonomous vehicles are currently unable to safely operate off-road at high-speed, as current approaches either fail to predict and mitigate rollovers induced by rough terrain or are not real-time feasible. To address this challenge, a novel model predictive control (MPC) formulation is developed for local trajectory planning. A new dynamics model for off-road vehicles on rough, non-planar terrain is derived and used for prediction. Extreme mobility, including tire liftoff without rollover, is safely enabled through a new energy-based constraint. The formulation is analytically shown to mitigate rollover types ignored by many state-of-the-art methods, and real-time feasibility is achieved through parallelized GPGPU computation. The planner's ability to provide safe, extreme trajectories is studied through both simulated trials and full-scale physical experiments. The results demonstrate fewer rollovers and more successes compared to a state-of-the-art baseline across several challenging scenarios that push the vehicle to its mobility limits.

James R. Baxter, Bogdan I. Epureanu, Paramsothy Jayakumar +1

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI · U.S. Army Ground Vehicle Systems Center, Warren, MI

Safe Motion PlanningOff-Road Robot NavigationModel Predictive ControlVehicle Dynamics
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Mar 20, 2026

Multi-Agent Motion Planning on Industrial Magnetic Levitation Platforms: A Hybrid ADMM-HOCBF approach

This paper presents a novel hybrid motion planning method for holonomic multi-agent systems. The proposed decentralised model predictive control (MPC) framework tackles the intractability of classical centralised MPC for a growing number of agents while providing safety guarantees. This is achieved by combining a decentralised version of the alternating direction method of multipliers (ADMM) with a centralised high-order control barrier function (HOCBF) architecture. Simulation results show significant improvement in scalability over classical centralised MPC. We validate the efficacy and real-time capability of the proposed method by developing a highly efficient C++ implementation and deploying the resulting trajectories on a real industrial magnetic levitation platform.

Bavo Tistaert, Stan Servaes, Alejandro Gonzalez-Garcia +4

Decentralized Multi-Agent Motion PlanningMotion PlanningSafe Motion PlanningModel Predictive Control
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Mar 20, 2026

Mixed-Integer vs. Continuous Model Predictive Control for Binary Thrusters: A Comparative Study

Binary on/off thrusters are commonly used for spacecraft attitude and position control during proximity operations. However, their discrete nature poses challenges for conventional continuous control methods. The control of these discrete actuators is either explicitly formulated as a mixed-integer optimization problem or handled in a two-layer approach, where a continuous controller's output is converted to binary commands using analog-to digital modulation techniques such as Delta-Sigma-modulation. This paper provides the first systematic comparison between these two paradigms for binary thruster control, contrasting continuous Model Predictive Control (MPC) with Delta-Sigma modulation against direct Mixed-Integer MPC (MIMPC) approaches. Furthermore, we propose a new variant of MPC for binary actuated systems, which is informed using the state of the Delta-Sigma Modulator. The two variations for the continuous MPC along with the MIMPC are evaluated through extensive simulations using ESA's REACSA platform. Results demonstrate that while all approaches perform similarly in high-thrust regimes, MIMPC achieves superior fuel efficiency in low-thrust conditions. Continuous MPC with modulation shows instabilities at higher thrust levels, while binary informed MPC, which incorporates modulator dynamics, improves robustness and reduces the efficiency gap to the MIMPC. It can be seen from the simulated and real-system experiments that MIMPC offers complete stability and fuel efficiency benefits, particularly for resource-constrained missions, while continuous control methods remain attractive for computationally limited applications.

Franek Stark, Jakob Middelberg, Shubham Vyas

Robotics Innovation Center, German Research Center for Artificial Intelligence GmbH, Bremen, Germany · University of Bremen, Germany

Model Predictive ControlFeedback Control
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Mar 19, 2026

ADMM-Based Distributed MPC with Control Barrier Functions for Safe Multi-Robot Quadrupedal Locomotion

This paper proposes a fully decentralized model predictive control (MPC) framework with control barrier function (CBF) constraints for safety-critical trajectory planning in multi-robot legged systems. The incorporation of CBF constraints introduces explicit inter-agent coupling, which prevents direct decomposition of the resulting optimal control problems. To address this challenge, we reformulate the centralized safety-critical MPC problem using a structured distributed optimization framework based on the alternating direction method of multipliers (ADMM). By introducing a novel node-edge splitting formulation with consensus constraints, the proposed approach decomposes the global problem into independent node-local and edge-local quadratic programs that can be solved in parallel using only neighbor-to-neighbor communication. This enables fully decentralized trajectory optimization with symmetric computational load across agents while preserving safety and dynamic feasibility. The proposed framework is integrated into a hierarchical locomotion control architecture for quadrupedal robots, combining high-level distributed trajectory planning, mid-level nonlinear MPC enforcing single rigid body dynamics, and low-level whole-body control enforcing full-order robot dynamics. The effectiveness of the proposed approach is demonstrated through hardware experiments on two Unitree Go2 quadrupedal robots and numerical simulations involving up to four robots navigating uncertain environments with rough terrain and external disturbances. The results show that the proposed distributed formulation achieves performance comparable to centralized MPC while reducing the average per-cycle planning time by up to 51% in the four-agent case, enabling efficient real-time decentralized implementation.

Yicheng Zeng, Ruturaj S. Sambhus, Basit Muhammad Imran +3

Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA 24061, USA · The University of Texas at El Paso, El Paso, TX 79968, USA

Model Predictive ControlMulti-Robot Motion PlanningMulti-Robot CoordinationQuadruped Locomotion
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Mar 19, 2026

Lightweight Model Predictive Control for Spacecraft Rendezvous Attitude Synchronization

This work introduces two lightweight model predictive control (MPC) approaches for attitude tracking with reaction wheels during spacecraft rendezvous synchronization. Both approaches are based on a novel attitude deviation formulation, which enables the use of inherently linear constraints on angular velocity. We develop a single-loop and a dual-loop MPC; the latter embeds a stabilizing feedback controller within the inner loop, yielding a linear time-invariant system. Both controllers are implemented with CasADi - including automatic code generation - evaluated across various solvers, and validated within the Basilisk astrodynamics simulation framework. The experimental results demonstrate improved tracking accuracy alongside reductions in computational effort and memory consumption. Finally, embedded delivery to an ARM Cortex-M7 - representative of commercial off-the-shelf devices used in New Space platforms - confirms the real-time feasibility of these approaches and highlights their suitability for onboard attitude control in resource-constrained spacecraft rendezvous missions.

Peter Stadler, Alexander Meinert, Niklas Baldauf +1

Space Applications Group, e:fs TechHub GmbH, 85080 Gaimersheim, Germany · Faculty of Electrical Engineering and Information Technology, Ingolstadt University of Applied Sciences, Germany

Spacecraft Attitude DeterminationModel Predictive ControlFeedback ControlSpacecraft Rendezvous and Proximity Operations
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Mar 19, 2026

Computationally Efficient Density-Driven Optimal Control via Analytical KKT Reduction and Contractive MPC

Efficient coordination for collective spatial distribution is a fundamental challenge in multi-agent systems. Prior research on Density-Driven Optimal Control (D2OC) established a framework to match agent trajectories to a desired spatial distribution. However, implementing this as a predictive controller requires solving a large-scale Karush-Kuhn-Tucker (KKT) system, whose computational complexity grows cubically with the prediction horizon. To resolve this, we propose an analytical structural reduction that transforms the T-horizon KKT system into a condensed quadratic program (QP). This formulation achieves O(T) linear scalability, significantly reducing the online computational burden compared to conventional O(T^3) approaches. Furthermore, to ensure rigorous convergence in dynamic environments, we incorporate a contractive Lyapunov constraint and prove the Input-to-State Stability (ISS) of the closed-loop system against reference propagation drift. Numerical simulations verify that the proposed method facilitates rapid density coverage with substantial computational speed-up, enabling long-horizon predictive control for large-scale multi-agent swarms.

Julian Martinez, Kooktae Lee

Department of Mechanical and Aerospace Engineering, Texas Tech University, Lubbock, TX 79409, USA

Input-to-State StabilityMulti-Agent ControlOptimal ControlModel Predictive ControlDynamical Systems
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Mar 19, 2026

Graph-of-Constraints Model Predictive Control for Reactive Multi-agent Task and Motion Planning

Sequences of interdependent geometric constraints are central to many multi-agent Task and Motion Planning (TAMP) problems. However, existing methods for handling such constraint sequences struggle with partially ordered tasks and dynamic agent assignments. They typically assume static assignments and cannot adapt when disturbances alter task allocations. To overcome these limitations, we introduce Graph-of-Constraints Model Predictive Control (GoC-MPC), a generalized sequence-of-constraints framework integrated with MPC. GoC-MPC naturally supports partially ordered tasks, dynamic agent coordination, and disturbance recovery. By defining constraints over tracked 3D keypoints, our method robustly solves diverse multi-agent manipulation tasks-coordinating agents and adapting online from visual observations alone, without relying on training data or environment models. Experiments demonstrate that GoC-MPC achieves higher success rates, significantly faster TAMP computation, and shorter overall paths compared to recent baselines, establishing it as an efficient and robust solution for multi-agent manipulation under real-world disturbances. Our supplementary video and code can be found at https://sites.google.com/view/goc-mpc/home .

Anastasios Manganaris, Jeremy Lu, Ahmed H. Qureshi +1

Department of Computer Science, Purdue University, West Lafayette, IN, USA, 47907.

Multi-Agent PlanningConstrained Motion PlanningMulti-Agent SystemsMulti-Robot CoordinationModel Predictive Control
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Mar 18, 2026

Real-Time Online Learning for Model Predictive Control using a Spatio-Temporal Gaussian Process Approximation

Learning-based model predictive control (MPC) can enhance control performance by correcting for model inaccuracies, enabling more precise state trajectory predictions than traditional MPC. A common approach is to model unknown residual dynamics as a Gaussian process (GP), which leverages data and also provides an estimate of the associated uncertainty. However, the high computational cost of online learning poses a major challenge for real-time GP-MPC applications. This work presents an efficient implementation of an approximate spatio-temporal GP model, offering online learning at constant computational complexity. It is optimized for GP-MPC, where it enables improved control performance by learning more accurate system dynamics online in real-time, even for time-varying systems. The performance of the proposed method is demonstrated by simulations and hardware experiments in the exemplary application of autonomous miniature racing.

Lars Bartels, Amon Lahr, Andrea Carron +1

Institute for Dynamic Systems and Control, ETH Zürich, CH-8092 Zürich, Switzerland.

Model Predictive ControlGaussian ProcessesGaussian Process RegressionResidual Dynamics LearningRobot Dynamics Learning
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Mar 17, 2026

Data-driven generalized perimeter control: Zürich case study

Urban traffic congestion is a key challenge for the development of modern cities, requiring advanced control techniques to optimize existing infrastructures usage. Despite the extensive availability of data, modeling such complex systems remains an expensive and time consuming step when designing model-based control approaches. On the other hand, machine learning approaches require simulations to bootstrap models, or are unable to deal with the sparse nature of traffic data and enforce hard constraints. We propose a novel formulation of traffic dynamics based on behavioral systems theory and apply data-enabled predictive control to steer traffic dynamics via dynamic traffic light control. A high-fidelity simulation of the city of Zürich, the largest closed-loop microscopic simulation of urban traffic in the literature to the best of our knowledge, is used to validate the performance of the proposed method in terms of total travel time and CO2 emissions.

Alessio Rimoldi, Carlo Cenedese, Alberto Padoan +2

Automatic Control Laboratory, ETH Zürich · Delft Center for Systems and Control, TU Delft · Dep. of Electrical and Computer Engineering, UBC

Data-Driven ControlTraffic Signal ControlIntelligent Transportation SystemsModel Predictive Control
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Mar 17, 2026

Sampling-Based MuJoCo MPC for Double-Pendulum Sway Suppression on a Shipboard Crane

Transferring heavy payloads in maritime settings relies on efficient crane operation, limited by hazardous double-pendulum payload sway. This sway motion is further exacerbated in offshore environments by external perturbations from wind and ocean waves. Manual suppression of these oscillations on an underactuated crane system by human operators is challenging. Existing control methods struggle in such settings, often relying on simplified analytical models, while deep reinforcement learning (RL) approaches tend to generalise poorly to unseen conditions. Deploying a predictive controller onto compute-constrained, highly non-linear physical systems without relying on extensive offline training or complex analytical models remains a significant challenge. Here we show a complete real-time control pipeline centered on the MuJoCo MPC framework that leverages a cross-entropy method planner to evaluate candidate action sequences directly within a physics simulator. By using simulated rollouts, this sampling-based approach successfully reconciles the conflicting objectives of dynamic target tracking and sway damping without relying on complex analytical models. We demonstrate that the controller can run effectively on a resource-constrained embedded hardware, while outperforming traditional PID and RL baselines in counteracting external base perturbations. Furthermore, our system demonstrates robustness even when subjected to unmodeled physical discrepancies like the introduction of a second payload.

Oscar Pang, Lisa Coiffard, Paul Templier +3

Adaptive and Intelligent Robotics Lab, Department of Computing, Imperial College London, Exhibition Rd, London, SW7 2BX, United Kingdom

Robotic ControlRobust ControlModel Predictive Control
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Mar 15, 2026

VIP-Loco: A Visually Guided Infinite Horizon Planning Framework for Legged Locomotion

Perceptive locomotion for legged robots requires anticipating and adapting to complex, dynamic environments. Model Predictive Control (MPC) serves as a strong baseline, providing interpretable motion planning with constraint enforcement, but struggles with high-dimensional perceptual inputs and rapidly changing terrain. In contrast, model-free Reinforcement Learning (RL) adapts well across visually challenging scenarios but lacks planning. To bridge this gap, we propose VIP-Loco, a framework that integrates vision-based scene understanding with RL and planning. During training, an internal model maps proprioceptive states and depth images into compact kinodynamic features used by the RL policy. At deployment, the learned models are used within an infinite-horizon MPC formulation, combining adaptability with structured planning. We validate VIP-Loco in simulation on challenging locomotion tasks, including slopes, stairs, crawling, tilting, gap jumping, and climbing, across three robot morphologies: a quadruped (Unitree Go1), a biped (Cassie), and a wheeled-biped (TronA1-W). Through ablations and comparisons with state-of-the-art methods, we show that VIP-Loco unifies planning and perception, enabling robust, interpretable locomotion in diverse environments.

Aditya Shirwatkar, Satyam Gupta, Shishir Kolathaya

Robert Bosch Center for Cyber-Physical Systems, Indian Institute of Science, Bengaluru. · Robert Bosch Center for Cyber-Physical Systems and the Department of Computer Science & Automation, Indian Institute of Science, Bengaluru.

Terrain-Aware Robot LocomotionVision-Based Robot ControlRL for Legged LocomotionModel Predictive Control
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Mar 15, 2026

Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds

State of the art quadrupedal locomotion approaches integrate Model Predictive Control (MPC) with Reinforcement Learning (RL), enabling complex motion capabilities with planning and terrain adaptive behaviors. However, they often face compounding errors over long horizons and have limited interpretability due to the absence of physical inductive biases. We address these issues by integrating Lagrangian Neural Networks (LNNs) into an RL MPC framework, enabling physically consistent dynamics learning. At deployment, our inverse dynamics infinite horizon MPC scheme avoids costly matrix inversions, improving computational efficiency by up to 4x with minimal loss of task performance. We validate our framework through multiple ablations of the proposed LNN and its variants. We show improved sample efficiency, reduced long-horizon error, and faster real time planning compared to unstructured neural dynamics. Lastly, we also test our framework on the Unitree Go1 robot to show real world viability.

Prakrut Kotecha, Aditya Shirwatkar, Shishir Kolathaya

the Robert Bosch Center for Cyber-Physical Systems, Indian Institute of Science, Bengaluru. · the Robert Bosch Center for Cyber-Physical Systems and the Department of Computer Science & Automation, Indian Institute of Science, Bengaluru.

Lagrangian Neural NetworksRL for Legged LocomotionPhysics-Informed RLRobot Dynamics LearningNeural Network ControlModel Predictive Control
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Mar 14, 2026

Implicit Maximum Likelihood Estimation for Real-time Generative Model Predictive Control

Diffusion-based models have recently shown strong performance in trajectory planning, as they are capable of capturing diverse, multimodal distributions of complex behaviors. A key limitation of these models is their slow inference speed, which results from the iterative denoising process. This makes them less suitable for real-time applications such as closed-loop model predictive control (MPC), where plans must be generated quickly and adapted continuously to a changing environment. In this paper, we investigate Implicit Maximum Likelihood Estimation (IMLE) as an alternative generative modeling approach for planning. IMLE offers strong mode coverage while enabling inference that is two orders of magnitude faster, making it particularly well suited for real-time MPC tasks. Our results demonstrate that IMLE achieves competitive performance on standard offline reinforcement learning benchmarks compared to the standard diffusion-based planner, while substantially improving planning speed in both open-loop and closed-loop settings. We further validate IMLE in a closed-loop human navigation scenario, operating in real-time, demonstrating how it enables rapid and adaptive plan generation in dynamic environments. Real-world videos and code are available at https://gmpc-imle.github.io/.

Grayson Lee, Minh Bui, Shuzi Zhou +3

School of Computing Science, Simon Fraser University, Burnaby, BC, Canada.

Maximum Marginal Likelihood EstimationModel Predictive ControlDiffusion-Based Planning
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Mar 14, 2026

LPV-MPC for Lateral Control in Full-Scale Autonomous Racing

Autonomous racing has attracted significant attention recently, presenting challenges in selecting an optimal controller that operates within the onboard system's computational limits and meets operational constraints such as limited track time and high costs. This paper introduces a Linear Parameter-Varying Model Predictive Controller (LPV-MPC) for lateral control. Implemented on an IAC AV-24, the controller achieved stable performance at speeds exceeding 160 mph (71.5 m/s). We detail the controller design, the methodology for extracting model parameters, and key system-level and implementation considerations. Additionally, we report results from our final race run, providing a comprehensive analysis of both vehicle dynamics and controller performance. A Python implementation of the framework is available at: https://tinyurl.com/LPV-MPC-acados

Hassan Jardali, Ihab S. Mohamed, Durgakant Pushp +1

Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN 47408 USA

Model Predictive ControlAutonomous DrivingAutonomous RacingVehicle Dynamics
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Mar 11, 2026

RL-Augmented MPC for Non-Gaited Legged and Hybrid Locomotion

We propose a contact-explicit hierarchical architecture coupling Reinforcement Learning (RL) and Model Predictive Control (MPC), where a high-level RL agent provides gait and navigation commands to a low-level locomotion MPC. This offloads the combinatorial burden of contact timing from the MPC by learning acyclic gaits through trial and error in simulation. We show that only a minimal set of rewards and limited tuning are required to obtain effective policies. We validate the architecture in simulation across robotic platforms spanning 50 kg to 120 kg and different MPC implementations, observing the emergence of acyclic gaits and timing adaptations in flat-terrain legged and hybrid locomotion, and further demonstrating extensibility to non-flat terrains. Across all platforms, we achieve zero-shot sim-to-sim transfer without domain randomization, and we further demonstrate zero-shot sim-to-real transfer without domain randomization on Centauro, our 120 kg wheeled-legged humanoid robot. We make our software framework and evaluation results publicly available at https://github.com/AndrePatri/AugMPC.

Andrea Patrizi, Carlo Rizzardo, Arturo Laurenzi +3

All authors are with the Humanoids and Human-Centred Mechatronics (HHCM) lab, Istituto Italiano di Tecnologia (IIT), Via San Quirico 19d, 16163 Genova · Andrea Patrizi is also with the Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genova, Via All’Opera Pia 13, 16145 Genova.

Robot LocomotionLegged RoboticsRL for Legged LocomotionModel Predictive Control
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Mar 11, 2026

Parallel-in-Time Nonlinear Optimal Control via GPU-native Sequential Convex Programming

Real-time solution of nonlinear optimal control problems remains challenging on embedded robotic hardware, where conventional solvers often rely on global sparse linear algebra or sequential recursions that are difficult to map efficiently to massively parallel processors. This paper presents ucenter, a GPU-native Sequential Convex Programming (SCP) framework for nonlinear optimal control. At each SCP iteration, nonlinear dynamics are linearized around a nominal trajectory, and the resulting convexified subproblem is solved by a consensus Alternating Direction Method of Multipliers (ADMM) scheme. The temporal splitting replaces global sparse Karush-Kuhn-Tucker factorizations with independent per-node dense solves, closed-form dynamic consistency updates, and analytical projections onto convex constraint sets. Both the outer SCP loop and the inner ADMM subproblem are executed entirely on the GPU, enabling efficient optimization. The proposed solver is evaluated on quadrotor obstacle avoidance and Mars powered descent problems using an NVIDIA Jetson AGX Orin edge platform. Benchmarking against a CPU-parallel iLQR baseline in randomized environments reveals that the GPU implementation achieves over 100 Hz batched planning throughput, a 4.1x speedup, and a 51% reduction in energy consumption, while consistently maintaining low nonlinear dynamics defects. The framework exposes reusable GPU-parallel optimization primitives that can be specialized to a wide variety of complex nonlinear optimal control settings, as demonstrated by the scenario-based robust MPC and batched Monte Carlo generation tasks.

Yilin Zou, Zhong Zhang, Maxime Robic +1

School of Aerospace Engineering, Tsinghua University, 100084 Beijing, China. · Department of Aerospace Science and Technology, Politecnico di Milano, 20156 Milan, Italy.

Optimal ControlGPU AccelerationNonconvex OptimizationModel Predictive Control
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Mar 10, 2026

Hierarchical Task Model Predictive Control for Sequential Mobile Manipulation Tasks

Mobile manipulators are envisioned to serve more complex roles in people's everyday lives. With recent breakthroughs in large language models, task planners have become better at translating human verbal instructions into a sequence of tasks. However, there is still a need for a decision-making algorithm that can seamlessly interface with the high-level task planner to carry out the sequence of tasks efficiently. In this work, building on the idea of nonlinear lexicographic optimization, we propose a novel Hierarchical-Task Model Predictive Control framework that is able to complete sequential tasks with improved performance and reactivity by effectively leveraging the robot's redundancy. Compared to the state-of-the-art task-prioritized inverse kinematic control method, our approach has improved hierarchical trajectory tracking performance by 42% on average when facing task changes, robot singularity and reference variations. Compared to a typical single-task architecture, our proposed hierarchical task control architecture enables the robot to traverse a shorter path in task space and achieves an execution time 2.3 times faster when executing a sequence of delivery tasks. We demonstrated the results with real-world experiments on a 9 degrees of freedom mobile manipulator.

Xintong Du, Siqi Zhou, Angela P. Schoellig

Learning Systems and Robotics Lab (www.learnsyslab.org) at the Technical University of Munich, Germany, and the University of Toronto Institute for Aerospace Studies, Canada · University of Toronto Robotics Institute · Munich Institute of Robotics and Machine Intelligence (MIRMI) +1

Hierarchical Robot ControlMobile ManipulationModel Predictive ControlRobot Trajectory Tracking
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