Model Predictive Control

We investigate interactive trajectory planning subject to uncertainty in the decisions of surrounding agents. To control the ego-agent, we aim to first learn the decision distribution and solve a Stochastic Model Predictive Control (SMPC) problem. To account for errors in the learned distribution, we show that it is possible to utilize Probably Approximately Correct (PAC) learning in combination with Distributionally Robust (DR) optimization to obtain a solution which accounts for the errors induced by the learning model. The results indicate that our PAC learning-based DR-MPC framework provides a method to interpolate between a robust MPC and an omnipotent SMPC, based on the available number of samples.

Flapping-wing micro aerial vehicles offer quieter and safer operation than rotary-wing drones, yet achieving precise autonomous control of bird-scale ornithopters remains challenging: lift, airspeed, and turning authority are tightly coupled and governed by only a few control inputs. Conventional cascaded controllers treat altitude, speed, and heading independently, producing persistent tracking errors during complex maneuvers, while time-parameterized trajectory tracking requires predefined speed profiles that existing methods cannot robustly produce for these coupled dynamics. We address both limitations simultaneously with a Model Predictive Contouring Control (MPCC) approach that tracks arc-length-parameterized trajectories while optimizing progress online, eliminating the need for predefined timing. However, MPCC requires a dynamical model that captures the coupled aerodynamics without exceeding the computational budget of real-time nonlinear optimization. Here, we propose a compact, continuously differentiable model that captures the dominant couplings of bird-scale ornithopters, enabling real-time predictive control. We validated the method with the XFly ornithopter flying along circular and three-dimensional racing trajectories and achieved a mean deviation from the reference trajectory between 6.5 and 9 cm at speeds up to 3 m/s, which represents an almost 10-fold improvement over prior ornithopter control methods.

Optimal control for safety-critical systems is often dependent on the conservativeness of constraints. Control Barrier Functions (CBFs) serve as a medium to represent such constraints, but constructing a minimally conservative CBF is a computationally intractable problem. Therefore, approaches that can guarantee safety while reducing conservatism will help improve the optimality of the system under consideration. Here, we present a Model Predictive Control (MPC) formulation using CBF as a terminal constraint, which is proven to improve feasibility and reachable sets with increasing prediction horizon. The constructive nature of the proofs allows for warm-starting the nonlinear optimization problem, thereby reducing the computational time substantially. Simulations are set up for a simple nonholonomic system to numerically validate the results, and it is observed that the number of infeasible points decreased by a factor of 1.7 to 2.7. The increase in reachable state space was demonstrated by the ability of the system to track trajectories that are entirely inside the unsafe region of the control barrier function.

Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.

A central challenge of visual control with model-based reinforcement learning (RL) is reliable long-horizon planning: long rollouts with learned latent dynamics exhibit branching futures and multi-modal action-value distributions. In addition, compounding model errors amplified by visual occlusions make deep imagination brittle. We present ELVIS, a latent model predictive controller (MPC) designed to make long-horizon planning practical. ELVIS plans in a Dreamer-style recurrent state space model (RSSM) and replaces standard unimodal model predictive path integral (MPPI) with a Gaussian-mixture MPPI that maintains multiple coherent hypotheses over long horizons, avoiding mode averaging under branching rollouts. In parallel, ELVIS stabilizes deep imagination with a shared uncertainty-aware lambda-return: an ensemble of latent critics defines an upper-confidence-bound (UCB) score that gates a time-varying lambda, adaptively trading off bootstrapping versus look-ahead to limit compounding error during planning. The same return is used both to train an actor-critic prior from imagined rollouts and to score candidate trajectories inside GMM-MPPI, aligning RL objectives with the planner's long-horizon optimization. On fourteen DeepMind Control Suite visual tasks, ELVIS establishes state-of-the-art performance compared with TD-MPC2 and DreamerV3. Finally, ELVIS transfers zero-shot to a real-world sand-spraying task with severe occlusions, improving surface-quality metrics and demonstrating robustness beyond simulation.

This paper presents a multi-phase whole-body model predictive control (MPC) approach for bipedal walking, combining a detailed whole-body model in the near horizon with a simplified single-rigid-body model in the later prediction steps. This reduces computational complexity while retaining prediction capabilities. The resulting nonlinear optimal control problem is solved entirely within the general-purpose, off-the-shelf nonlinear MPC framework acados, using sequential quadratic programming (SQP). Given a contact schedule and a target walking speed, the controller optimizes joint torques without depending on preselected footstep locations. The controller is validated in MuJoCo simulation on the 18-DoF bipedal robot HyPer-2.

State-of-the-art model-based Reinforcement Learning (RL) approaches either use gradient-free, population-based methods for planning, learned policy networks, or a combination of policy networks and planning. Hybrid approaches that combine Model Predictive Control (MPC) with a learned model and a policy prior to leverage the advantages of both paradigms have shown promising results. However, these approaches typically rely on gradient-free optimization methods, which can be computationally expensive for high-dimensional control tasks. While gradient-based methods are a promising alternative, recent works have empirically shown that gradient-based methods often perform worse than their gradient-free counterparts. We propose Dream-MPC, a novel approach that generates few candidate trajectories from a rolled-out policy and optimizes each trajectory by gradient ascent using a learned world model, uncertainty regularization and amortization of optimization iterations over time by reusing previously optimized actions. Our results on 24 continuous control tasks show that Dream-MPC can significantly improve the performance of the underlying policy and can outperform gradient-free MPC and state-of-the-art baselines. Code and videos are available at https://dream-mpc.github.io.

Real-world control systems must achieve long-horizon objectives (liveness) while respecting continuous-time safety constraints, a combination that motivates hierarchical layered control architectures (LCAs). Existing LCA research, however, lacks (i) a uniform specification language across discrete planning and continuous execution, (ii) formal guarantees that specifications are preserved when interconnecting subsystems at heterogeneous time scales, and (iii) compositional separation between layers, owing to reliance on naive input-filtering laws. This paper addresses all three gaps by importing the safety--liveness decomposition into a heterogeneous assume--guarantee framework: \emph{safety is enforced by invariance} at the continuous-time layer, while \emph{liveness is achieved through refinement} at the discrete-time layer, with inter-layer coordination formalized via vertical refinement and timing-compatibility conditions. We instantiate this contract with a novel LCA combining an MPC planner, an input-to-state stabilizing (ISS) low-level controller, and a reference-governor bridge, and validate it on a Hybrid Energy Storage System (HESS) comprising a battery and a supercapacitor.

Domain randomization (DR) is widely used in policy learning to improve robustness to modeling error, but remains underexplored in contact-rich sampling-based predictive control (SPC), where rollout quality is highly sensitive to uncertainty. In this work, we take the first step by studying risk-aware DR in predictive sampling on a simple yet representative Push-T task, comparing average, optimistic, and pessimistic rollout aggregations under randomized model instances. Our initial results suggest that DR affects not only robustness to model error, but also the effective cost landscape seen by the sampling-based optimizer, by reshaping the basin of attraction around contact-producing actions. This opens up potential for exploring better grounded risk-aware contact-rich SPC under model uncertainty. Video: https://youtu.be/f1F0ALXxhSM

Autonomous driving technology has rapidly evolved over the past decade, offering significant improvements in transportation efficiency, safety, and cost reduction. While much of the progress has focused on highway driving and obstacle avoidance, low-speed maneuvers such as parking remain among the most difficult challenges for autonomous systems. This challenge is especially pronounced in trailer-truck transport vehicles due to their articulated motion and environmental constraints. This paper presents a proposed framework for autonomous truck parking that integrates perception, motion planning, control systems, and infrastructure awareness. By combining sensor fusion, Hybrid A* path planning, nonlinear model predictive control (NMPC), and data-driven parking systems, this work highlights the importance of system-level coordination for reliable and scalable autonomous parking solutions. As a proof-of-concept implementation, we adapted an open-source A* path planning simulation to incorporate a tractor-trailer kinematic model, demonstrating articulated vehicle path planning within a command-line simulation environment, with jackknife prevention identified as an area requiring further development.

This paper presents a novel model predictive control (MPC) approach for autonomous pick-and-place between moving platforms with a hook-equipped aerial manipulator. First, for accurate and rapid modeling of the complex dynamics, a digital twin model of the quadcopter equipped with a hook-based gripper, implemented in MuJoCo, is constructed and used as the predictive model for the MPC. To handle uncertainties of the predictive model (e.g. due to aerodynamics and uncertain payloads), a robust adaptive MPC approach is proposed. By systematic integration of zero-order robust optimization (zoRO) based uncertainty propagation and an extended Kalman filter (EKF) for parameter estimation, the MPC algorithm ensures robust constraint satisfaction, high performance, and computational efficiency. The effectiveness of the proposed method is evaluated in complex simulated scenarios and in real-world flight experiments.

Sampling-based model predictive control methods like MPPI and CEM are essential for real-time control of nonlinear robotic systems, particularly where discontinuous dynamics preclude gradient-based optimization. However, these methods derive from information-theoretic objectives that are agnostic to the geometry of the control problem, leading to pathological behaviors such as mode-averaging when the cost landscape is complex. We present OT-MPC, a sampling-based algorithm that overcomes these limitations through an entropy-regularized optimal transport formulation. By computing an optimal coupling between candidate control sequences and low-cost proposals, OT-MPC refines candidates toward nearby promising samples while coordinating updates across the ensemble to maintain coverage of the solution space. We derive closed-form, gradient-free updates via the Sinkhorn algorithm, enabling real-time performance. Experiments on navigation, manipulation, and locomotion tasks demonstrate improved success rates over existing methods.

Autonomous spacecraft docking requires control policies that simultaneously ensure collision avoidance and target reachability under coupled, high-dimensional translational-rotational dynamics. Hamilton-Jacobi (HJ) reachability provides formal reach-avoid guarantees, but classical solvers are limited to low-dimensional systems. Learning-based approaches have begun to scale HJ analysis, yet they struggle in reach-avoid settings, especially where goal and failure sets are tightly coupled, as in docking. We propose a learning-based Backward Reach-Avoid Tube (BRAT) framework that addresses this challenge by tightly integrating HJ structure with MPC-based supervision. In the offline phase, we train a neural approximation of the HJ value function using PDE-based losses augmented with curriculum-driven MPC supervision, which provides informative value targets and stabilizes training in regions where purely PDE-based methods fail. In the online phase, the learned value function is deployed through two real-time controllers: (i) a value gradient-driven controller, and (ii) a value-function-augmented terminal MPC that explicitly enforces reachability at the horizon. We evaluate the proposed method on a 6D planar docking problem against grid-based ground truth and then scale to the full 13D system. Across both settings, our approach outperforms existing methods in success rate and computational efficiency.

This paper explores the benefits of computing arborescent trajectories (trajectory-trees) instead of commonly used sequential trajectories for partially observable robotic planning problems. In such environments, a robot infers knowledge from observations, and the optimal course of action depends on these observations. \revise{Trajectory-trees, optimized in belief space, naturally capture this dependency by branching where the belief state is expected to evolve into multiple distinct scenarios, such as upon receiving an observation. Unlike sequential trajectories, which model a single forward evolution of the system, trajectory-trees capture multiple possible contingencies.} First, we focus on Model Predictive Control (MPC) and demonstrate the benefits of planning tree-like trajectories. We formulate the control problem as the optimization of a tree with a single branching (PO-MPC). This improves performance by reducing control costs through more informed planning. To satisfy the real-time constraints of MPC, we develop an optimization algorithm called Distributed Augmented Lagrangian (D-AuLa), which leverages the decomposability of the PO-MPC formulation to parallelize and accelerate the optimization. We apply the method to both linear and non-linear MPC problems using autonomous driving examples. Second, we address Task And Motion Planning (TAMP), and introduce a planner (PO-LGP) reasoning on decision trees at task level, and trajectory-trees at motion-planning level. This approach builds upon the Logic-Geometric-Programming Framework (LGP) and extends it to partially observable problems. The experiments show the method's applicability to problems with a small belief state size, and scales to larger problems by optimizing explorative policies, which are used as macro-actions in an overarching task plan.

We study finite-horizon budget allocation as a closed-loop economic control problem and evaluate receding-horizon Model Predictive Control (MPC) relative to reactive budgeting policies. Budgets are allocated periodically under execution noise and operational constraints, while return efficiency may evolve over time. Using a controlled simulation framework motivated by digital marketing, we compare reactive pacing to MPC across environments with increasing degrees of non-stationarity. Our results show that non-stationarity alone does not justify predictive control. When return dynamics are stationary or evolve through unpredictable stochastic drift, MPC offers no systematic advantage over reactive baselines. By contrast, when return efficiency exhibits predictable structure over the planning horizon, that is captured through an underlying model, MPC consistently outperforms reactive budgeting by exploiting intertemporal trade-offs.

The Alternating Direction Method of Multipliers (ADMM) is a widely used method for structured convex optimization, and its practical performance depends strongly on the choice of penalty and relaxation parameters. Motivated by settings such as Model Predictive Control (MPC), where one repeatedly solves related optimization problems with fixed structure and changing parameter values, we propose learning online updates of the relaxation parameter to improve performance on problem classes of interest. This choice is computationally attractive in OSQP-like architectures, since adapting relaxation does not trigger the matrix refactorizations associated with penalty updates. We establish convergence guarantees for ADMM with time-varying penalty and relaxation parameters under mild assumptions, and show on benchmark quadratic programs that the resulting learned policies improve both iteration count and wall-clock time over baseline OSQP.

Predictive safety filters (PSFs) leverage model predictive control to enforce constraint satisfaction during deep reinforcement learning (RL) exploration, yet their reliance on first-principles models or Gaussian processes limits scalability and broader applicability. Meanwhile, model-based RL (MBRL) methods routinely employ probabilistic ensemble (PE) neural networks to capture complex, high-dimensional dynamics from data with minimal prior knowledge. However, existing attempts to integrate PEs into PSFs lack rigorous uncertainty quantification. We introduce the Uncertainty-Aware Predictive Safety Filter (UPSi), a PSF that provides rigorous safety predictions using PE dynamics models by formulating future outcomes as reachable sets. UPSi introduces an explicit certainty constraint that prevents model exploitation and integrates seamlessly into common MBRL frameworks. We evaluate UPSi within Dyna-style MBRL on standard safe RL benchmarks and report substantial improvements in exploration safety over prior neural network PSFs while maintaining performance on par with standard MBRL. UPSi bridges the gap between the scalability and generality of modern MBRL and the safety guarantees of predictive safety filters.

This paper presents a sensitivity-based tube Nonlinear Model Predictive Control (NMPC) framework for cooperative aerial chains under bounded parametric uncertainty. We consider a planar two-vehicle chain connected by rigid links, modeled with input-rate actuation to enforce slew-rate and magnitude limits on thrust and torque. Robustness to uncertainty in link mass, length, and inertia is achieved by propagating first-order parametric state sensitivities along the horizon and using them to compute online constraint-tightening margins. We robustify an inter-link separation constraint, implemented via a smooth cosine embedding, and thrust-magnitude bounds. The method is implemented in MATLAB and evaluated with boundary-hugging maneuvers and Monte-Carlo uncertainty sampling. Results show improved constraint margins under uncertainty with tracking performance comparable to nominal NMPC.

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.

We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle can fail because control inputs influence the future quality of state estimates. State estimation requires an input-dependent Kalman filter whose gain and error covariance evolve as functions of the control inputs. To address this challenge, we propose a belief-space model predictive control ($\texttt{B-MPC}$) method that plans directly over both the estimated state and its error covariance. In particular, $\texttt{B-MPC}$ plans with a deterministic surrogate of the belief evolution defined by the input-dependent Kalman filter. Through numerical experiments in two synthetic settings, we show that $\texttt{B-MPC}$ can outperform both the separation-principle controller and its MPC variant in favorable regimes, and that these gains are accompanied by lower estimation covariance and more uncertainty-aware action choices.

This paper presents a trajectory planning method for articulated commercial vehicles, specifically tractor-semitrailers, based on Model Predictive Contouring Control (MPCC). Although MPCC has proven effective for passenger cars, it is generally ill-suited for tractor-semitrailers. These vehicles are significantly larger, the semitrailer follows a different path than the tractor, and reversing maneuvers are unstable and prone to jackknifing. Furthermore, practical driving scenarios often require scenario-dependent prioritization of different vehicle `anchor points', e.g., prioritizing the semitrailer position during docking or the tractor position when parking to charge. Therefore, we extend MPCC to enable scenario-dependent weighting of these anchor points and incorporate explicit road-boundary constraints for the front and rear tractor axles and the semitrailer axle, thereby ensuring that all considered wheels remain within the drivable area. The simulation results demonstrate the successful navigation of a representative logistic scenario in both forward and reverse direction. Furthermore, the influence of the optimization parameters on the trajectories is analyzed, providing insights into controlling the vehicle behavior. Finally, first tests using a full-scale prototype vehicle show the practical applicability of the approach.

Autonomous systems are increasingly deployed in real-world environments, where they must achieve high performance while maintaining safety under state and input constraints. Although Model Predictive Control (MPC) provides a principled framework for constrained optimal control, guaranteeing safety beyond its finite planning horizon remains a fundamental challenge. In this work, we augment MPC with a safety value function-based terminal constraint that enforces membership in a control-invariant safe set at the end of each planning horizon. This formulation enables real-time synthesis of trajectories that are both high-performing and provably safe. We show that, under an exact safety value function and a feasible initialization, the proposed MPC scheme is recursively feasible, thereby ensuring persistent safety. In contrast to traditional terminal set constructions that rely on local linearizations or conservative approximations, our approach incorporates a reachability-based safety value function for terminal constraints, yielding less conservative and more expressive safety guarantees. We validate the proposed framework through simulation and hardware experiments on a Flexiv Rizon 10s manipulator. Results demonstrate improved constraint satisfaction and robustness compared to standard state-constrained MPC and reactive safety filtering, while maintaining competitive task performance. The full implementation and experiments are available on the project website.

Batch processes are inherently transient and typically nonlinear, motivating nonlinear model predictive control (NMPC). However, adopting NMPC is hindered by the cost and unavailability of dynamic models. Thus, we propose to use Gaussian Processes (GP) in a model-learning NMPC scheme (GP-MLMPC) for batch processes. We initialize the GP-MLMPC using data from a single initial trajectory, e.g., from a PI controller. We iteratively apply the NMPC embedded with GPs to run batches and update the GP with new observations from each iteration, thereby achieving batch-wise improvements. Using uncertainty quantification from the GPs, we formulate chance constraints to enforce safe operation to the required confidence levels. We demonstrate our approach in \textit{silico} on a semi-batch polymerization reactor for tracking and economic objectives over durations of two hours, and the reactor temperature is constrained in a range of $\pm2^\circ C$ around its setpoint. After only four batch iterations, tracking error from the GP-MLMPC scheme converged to a reduction of $83\%$, compared to the initial trajectory. Furthermore, under an economic objective, the GP-MLMPC resulted in a 17-fold increase in final product mass by iteration 8, compared to the initial trajectory. In both cases, the resulting GP-MLMPC performance is on par with the full-model NMPC, which shows that the optimal controller can be learned by the approach. By collecting samples around the optimal trajectory, the GP-MLMPC remains sample-efficient across iterations and achieves quick convergence. Thus, the proposed GP-MLMPC scheme presents a promising data-efficient approach for the control of nonlinear batch processes without mechanistic knowledge.

Variable impedance model predictive control (MPC) formulations often treat joint stiffness as an instantaneous decision variable. The resulting feasible set strictly contains the physically realizable set under first-order actuator dynamics. We identify this as a formulation error rather than a modeling approximation, formalize the distinction between the parameter-based feasible set F_param and the realizable set F_real, and characterize the regime of mismatch via the dimensionless parameter α = ωsT (actuator bandwidth times task timescale). For the 1D hopping monoped, we prove that below an analytical threshold α_crit derived in closed form from task physics, no admissible stiffness command realizes the parameter-based prediction. Numerical validation in 1D shows monotonic deviation growth as α decreases, with the predicted scaling holding across ten parameter combinations (log-log R2 = 0.986). Mechanism transfer to planar spring-loaded inverted pendulum dynamics confirms center-of-mass and stance-timing deviation as the primary consequence, with regime-dependent friction effects as a tertiary observable. A second threshold α_infeas < α_crit establishes a floor below which restricting the admissible stiffness range cannot repair realizability, closing the conservative-tuning objection. Augmenting the prediction state with stiffness closes the mismatch by construction.

The problem of controlling hybrid dynamical systems using model predictive control (MPC) is formulated and sufficient conditions for asymptotic stability of a set are provided. Hybrid dynamical systems are modeled in terms of hybrid equations, involving a differential equation and a difference equation with inputs and constraints. The proposed hybrid MPC algorithm uses a suitable prediction and control horizon construction inspired by hybrid time domains. Structural properties of the hybrid optimization problem, its feasible set, and its value function are provided. Checkable conditions to guarantee asymptotic stability of a set are provided. These conditions are given in terms of properties on the stage cost, terminal cost, and the existence of static state-feedback laws, related through a control Lyapunov function condition. Examples illustrate the results throughout the paper.

Landing UAVs on heaving marine platforms is challenging because relative vertical motion can generate large impact forces and cause rebound on touchdown. To address this, we develop an impact-aware Model Predictive Control (MPC) framework that models landing as a velocity-level rigid-body impact governed by Newton's restitution law. We embed this as a linear complementarity problem (LCP) within the MPC dynamics to predict the discontinuous post-impact velocity and suppress rebound. In simulation, restitution-aware prediction reduces pre-impact relative velocity and improves landing robustness. Experiments on a heaving-deck testbed show an 86.2% reduction in post-impact deflection compared to a tracking MPC.

The integration of Model Predictive Control (MPC) and Reinforcement Learning (RL) has emerged as a promising paradigm for constrained decision-making and adaptive control. MPC offers structured optimization, explicit constraint handling, and established stability tools, whereas RL provides data-driven adaptation and performance improvement in the presence of uncertainty and model mismatch. Despite the rapid growth of research on RL--MPC integration, the literature remains fragmented, particularly for control architectures built on linear or linearized predictive models. This paper presents a comprehensive Systematic Literature Review (SLR) of RL--MPC integrations for linear and linearized systems, covering peer-reviewed and formally indexed studies published until 2025. The reviewed studies are organized through a multi-dimensional taxonomy covering RL functional roles, RL algorithm classes, MPC formulations, cost-function structures, and application domains. In addition, a cross-dimensional synthesis is conducted to identify recurring design patterns and reported associations among these dimensions within the reviewed corpus. The review highlights methodological trends, commonly adopted integration strategies, and recurring practical challenges, including computational burden, sample efficiency, robustness, and closed-loop guarantees. The resulting synthesis provides a structured reference for researchers and practitioners seeking to design or analyze RL--MPC architectures based on linear or linearized predictive control formulations.

Modern world models are becoming too complex to admit explicit dynamical descriptions. We study safety-critical contextual control, where a Planner must optimize a task objective using only feasibility samples from a black-box Simulator, conditioned on a context signal $ξ_t$. We develop a sample-based Penalized Predictive Control (PPC) framework grounded in online Riemannian optimization, in which the Simulator compresses the feasibility manifold into a score-based density $\hat{p}(u \mid ξ_t)$ that endows the action space with a Riemannian geometry guiding the Planner's gradient descent. The barrier curvature $κ(ξ_t)$, the minimum curvature of the conditional log-density $-\ln\hat{p}(\cdot\midξ_t)$, governs both convergence rate and safety margin, replacing the Lipschitz constant of the unknown dynamics. Our main result is a contextual safety bound showing that the distance from the true feasibility manifold is controlled by the score estimation error and a ratio that depends on $κ(ξ_t)$, both of which improve with richer context. Simulations on a dynamic navigation task confirm that contextual PPC substantially outperforms marginal and frozen density models, with the advantage growing after environment shifts.

Bimanual mobile manipulation requires a seamless integration between high-level semantic reasoning and safe, compliant physical interaction - a challenge that end-to-end models approach opaquely and classical controllers lack the context to address. This paper presents GenerativeMPC, a hierarchical cyber-physical framework that explicitly bridges semantic scene understanding with physical control parameters for bimanual mobile manipulators. The system utilizes a Vision-Language Model with Retrieval-Augmented Generation (VLM-RAG) to translate visual and linguistic context into grounded control constraints, specifically outputting dynamic velocity limits and safety margins for a Whole-Body Model Predictive Controller (MPC). Simultaneously, the VLM-RAG module modulates virtual stiffness and damping gains for a unified impedance-admittance controller, enabling context-aware compliance during human-robot interaction. Our framework leverages an experience-driven vector database to ensure consistent parameter grounding without retraining. Experimental results in MuJoCo, IsaacSim, and on a physical bimanual platform confirm a 60% speed reduction near humans and safe, socially-aware navigation and manipulation through semantic-to-physical parameter grounding. This work advances the field of human-centric cybernetics by grounding large-scale cognitive models into predictable, high-frequency physical control loops.

What appears effortless to a human waiter remains a major challenge for robots. Manipulating objects nonprehensilely on a tray is inherently difficult, and the complexity is amplified in dual-arm settings. Such tasks are highly relevant to service robotics in domains such as hotels and hospitality, where robots must transport and reposition diverse objects with precision. We present DART, a novel dual-arm framework that integrates nonlinear Model Predictive Control (MPC) with an optimization-based impedance controller to achieve accurate object motion relative to a dynamically controlled tray. The framework systematically evaluates three complementary strategies for modeling tray-object dynamics as the state transition function within our MPC formulation: (i) a physics-based analytical model, (ii) an online regression based identification model that adapts in real-time, and (iii) a reinforcement learning-based dynamics model that generalizes across object properties. Our pipeline is validated in simulation with objects of varying mass, geometry, and friction coefficients. Extensive evaluations highlight the trade-offs among the three modeling strategies in terms of settling time, steady-state error, control effort, and generalization across objects. To the best of our knowledge, DART constitutes the first framework for non-prehensile dual-arm manipulation of objects on a tray. Project Link: https://dart-icra.github.io/dart/

Modern datacenters schedule heterogeneous workloads across geo-distributed sites with diverse compute capacities, electricity prices, and thermal conditions. Compute utilization, heat generation, cooling demand, and energy consumption are tightly coupled, yet most existing schedulers abstract these effects and treat them independently. We present \textit{DataCenterGym}, a physics-grounded simulation environment for job scheduling in geo-distributed data centers, designed as a reusable testbed for future research. The simulator integrates compute queueing, building thermal dynamics, localized HVAC behavior, and temperature-dependent service degradation within a Gymnasium-compatible interface. We also develop a Hierarchical Model Predictive Control (H-MPC) scheduling algorithm that performs distributed job placement while explicitly accounting for thermal and power dynamics. Through experiments on nominal operation and workload sensitivity, we demonstrate how H-MPC improves scheduling performance relative to baseline schedulers.

Data-driven Model Predictive Control (MPC) has lately been the core research subject in the field of control theory. The combination of an optimal control framework with deep learning paradigms opens up the possibility to accurately track control tasks without the need for complex analytical models. However, the system dynamics are often nuanced and the neural model lacks the potential to understand physical properties such as inertia and conservation of energy. In this work, we propose a novel energy-based regularization loss function which is applied to the training of a neural model that learns the residual dynamics of an omnidirectional aerial robot. Our energy-based regularization encourages the neural network to cause control corrections that stabilize the energy of the system. The residual dynamics are integrated into the MPC framework and improve the positional mean absolute error (MAE) over three real-world experiments by 23% compared to an analytical MPC. We also compare our method to a standard neural MPC implementation without regularization and primarily achieve a significantly increased flight stability implicitly due to the energy regularization and up to 15% lower MAE. Our code is available under: https://github.com/johanneskbl/jsk_aerial_robot/tree/develop/neural_MPC.

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.

Brand advertising plays a critical role in building long-term consumer awareness and loyalty, making it a key objective for advertisers across digital platforms. Although real-time bidding has been extensively studied, there is limited literature on algorithms specifically tailored for brand auction ads that fully leverage their unique characteristics. In this paper, we propose a lightweight Model Predictive Control (MPC) framework designed for brand advertising campaigns, exploiting the inherent attributes of brand ads -- such as stable user engagement patterns and fast feedback loops -- to simplify modeling and improve efficiency. Our approach utilizes online isotonic regression to construct monotonic bid-to-spend and bid-to-conversion models directly from streaming data, eliminating the need for complex machine learning models. The algorithm operates fully online with low computational overhead, making it highly practical for real-world deployment. Simulation results demonstrate that our approach significantly improves spend efficiency and cost control compared to baseline strategies, providing a scalable and easily implementable solution for modern brand advertising platforms.

Contact-rich micromanipulation in microfluidic flow is challenging because small disturbances can break pushing contact and induce large lateral drift. We study planar cell pushing with a magnetic rolling microrobot that tracks a waypoint-sampled reference curve under time-varying Poiseuille flow in simulation. We propose a hybrid controller that augments a nominal MPC with a learned residual policy trained by SAC. The policy outputs a bounded 2D velocity correction that is contact-gated, so residual actions are applied only during robot-cell contact, preserving reliable approach behavior and stabilizing learning. All methods share the same actuation interface and speed envelope for fair comparisons. Simulation results show improved robustness and tracking accuracy over pure MPC and PID under nonstationary flow, with generalization from a clover training curve to unseen circle and square trajectories. A residual-bound sweep identifies an intermediate correction limit as the best trade-off, which we use in all benchmarks.

Triphibious robots capable of multi-domain motion and cross-domain transitions are promising to handle complex tasks across diverse environments. However, existing designs primarily focus on dual-mode platforms, and some designs suffer from high mechanical complexity or low propulsion efficiency, which limits their application. In this paper, we propose a novel triphibious robot capable of aerial, terrestrial, and aquatic motion, by a minimalist design combining a quadcopter structure with two passive wheels, without extra actuators. To address inefficiency of ground-support motion (moving on land/seabed) for quadcopter based designs, we introduce an eccentric Center of Gravity (CoG) design that inherently aligns thrust with motion, enhancing efficiency without specialized mechanical transformation designs. Furthermore, to address the drastic differences in motion control caused by different fluids (air and water), we develop a unified propulsion system based on Field-Oriented Control (FOC). This method resolves torque matching issues and enables precise, rapid bidirectional thrust across different mediums. Grounded in the perspective of living condition and ground support, we analyse the robot's dynamics and propose a Hybrid Nonlinear Model Predictive Control (HNMPC)-PID control system to ensure stable multi-domain motion and seamless transitions. Experimental results validate the robot's multi-domain motion and cross-mode transition capability, along with the efficiency and adaptability of the proposed propulsion system.

Autonomous driving requires reliable collision avoidance in dynamic environments. Nonlinear Model Predictive Controllers (NMPCs) are suitable for this task, but struggle in time-critical scenarios requiring high frequency. To meet this demand, optimization problems are often simplified via linearization, narrowing the horizon window, or reduced temporal nodes, each compromising accuracy or reliability. This work presents the first general convex obstacle avoidance formulation, enabled by a novel approach to integrating logic. This facilitates the incorporation of an obstacle avoidance formulation into convex MPC schemes, enabling a convex optimization framework with substantially improved computational efficiency relative to conventional nonconvex methods. A key property of the formulation is that obstacle avoidance remains effective even when obstacles lie outside the prediction horizon, allowing shorter horizons for real-time deployment. In scenarios where nonconvex formulations are unavoidable, the proposed method meets or exceeds the performance of representative nonconvex alternatives. The method is evaluated in autonomous vehicle applications, where system dynamics are highly nonlinear.

Many aerial tasks involving quadrotors demand both instant reactivity and long-horizon planning for obstacle avoidance, energy efficiency, or trajectory tracking. High-fidelity models enable accurate control but are too slow for long horizons. Low-fidelity planners scale but cannot directly control the system, necessitating cascaded architectures. Prevailing hierarchical approaches plan with a simplified model and use a high-fidelity controller for tracking, yet this decomposition is inherently suboptimal. The controller is limited by the coarse plan, and conventional MPC alternatives shorten the horizon to stay real-time feasible. We present UNIQUE, an MPC architecture that replaces this hierarchical stacking with temporal cascading. The planning problem is formulated as the second-tail horizon of a single multi-phase MPC, rather than being solved separately. We align costs across horizons, derive feasibility constraints for the point-mass planning model, and introduce transition constraints that convert high-fidelity states into meaningful low-fidelity states. Parallel point-mass and mixed-integer solvers address nonconvexities while incorporating progressive 3D obstacle smoothing over the planning horizon. In simulations and real flights, under equal computational budgets, UNIQUE improves closed-loop tracking by up to 75% compared with standard MPC and hierarchical baselines. Ablations and Pareto analyses confirm performance gains across variations in horizon, constraint approximations, and smoothing schedules.

High-altitude balloons (HABs) are common in scientific research due to their wide range of applications and low cost. Because of their nonlinear, underactuated dynamics and the partial observability of wind fields, prior work has largely relied on model-free reinforcement learning (RL) methods to design near-optimal control schemes for station-keeping. These methods often compare only against hand-crafted heuristics, dismissing model-based approaches as impractical given the system complexity and uncertain wind forecasts. We revisit this assumption about the efficacy of model-based control for station-keeping by developing First-Order Model Predictive Control (FOMPC). By implementing the wind and balloon dynamics as differentiable functions in JAX, we enable gradient-based trajectory optimization for online planning. FOMPC outperforms a state-of-the-art RL policy, achieving a 24% improvement in time-within-radius (TWR) without requiring offline training, though at the cost of greater online computation per control step. Through systematic ablations of modeling assumptions and control factors, we show that online planning is effective across many configurations, including under simplified wind and dynamics models.

Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.

This work highlights the duality between state estimation and model predictive control. A model predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear prediction horizon length scalability. The proposed algorithms provide exceptional computational efficiency, adaptive time horizon lengths, and early optimization termination criteria. The use of Kalman smoothers as the backend optimization framework provides for a familiar implementation supported by strong theoretical guarantees. Additionally, a formulation is presented that separates linear model predictive control into purely reactive and anticipatory components, enabling any-time any-horizon observed control while ensuring controller stability for short time horizons. Finally, the method is extended to nonlinear systems and non-quadratic cost functions to obtain locally-optimal control of complex systems while maintaining linear prediction horizon scalability and adaptive-horizon capabilities.

Push recovery during locomotion will facilitate the deployment of humanoid robots in human-centered environments. In this paper, we present a unified framework for walking control and push recovery for humanoid robots, leveraging the arms for push recovery while dynamically walking. The key innovation is to use the environment, such as walls, to facilitate push recovery by combining Single Rigid Body model predictive control (SRB-MPC) with Hybrid Linear Inverted Pendulum (HLIP) dynamics to enable robust locomotion, push detection, and recovery by utilizing the robot's arms to brace against such walls and dynamically adjusting the desired contact forces and stepping patterns. Extensive simulation results on a humanoid robot demonstrate improved perturbation rejection and tracking performance compared to HLIP alone, with the robot able to recover from pushes up to 100N for 0.2s while walking at commanded speeds up to 0.5m/s. Robustness is further validated in scenarios with angled walls and multi-directional pushes.

This paper presents Adaptive Differentiable Model Predictive Contouring Control (AD-MPCC), a framework for autonomous racing that integrates differentiable MPCC with online parameter estimation to handle varying road-surface conditions. For online parameter estimation, we leverage a parameterized Pacejka Magic Formula together with a regularized moving-horizon estimation scheme with exponentially decaying weights to capture road interactions and update parameters in real time. Furthermore, we propose a differentiable MPCC (Diff-MPCC) framework that enables optimal adjustment of objective weights based on predefined long-horizon performance costs. To implement Diff-MPCC for online objective weight adaptation, we propose a Pacejka-informed machine learning model that is trained in a supervised manner using data generated by Diff-MPCC to tune the objective weights. Simulation results demonstrate that AD-MPCC reliably ensures safety and achieves faster lap times compared to baseline controllers in both single-surface and multiple-surface scenarios.