Model Predictive Control

Trajectory tracking performance of Uncrewed Aerial Vehicles (UAVs) degrades during high-speed and agile flight due to the depletion of the battery and subsequent loss of maximum available thrust. In applications such as drone racing, the consequent trajectory tracking error leads to a collision with obstacles and a subsequent failure to complete the race. In this paper, we present a novel method for integrating battery and propulsion system models into a Nonlinear Model Predictive Controller (NMPC) framework to enable real-time prediction of the voltage, consumed current, power, and maximum available thrust of the platform. This enables our approach to account for the dynamic variations in the maximum available thrust of the UAV caused by battery discharge, allowing it to plan for the depleting thrust and improve trajectory tracking performance. A trajectory planning algorithm is implemented to replan the trajectory in-flight based on evolving thrust limits. The accuracy of the proposed model is verified in real-world flight experiments, while the effectiveness of the replanning algorithm is evaluated in simulation. Compared to an uncompensated flight, our novel approach demonstrates achieves a collision-free flight to achieve a 6-fold decrease in tracking Root Mean Square Error (RMSE), a 46 % increase in flight distance, and a 100 % increase in flight time in an obstacle-ridden environment.

Safe autonomous navigation in shared environments requires the ability to anticipate and react to the latent behaviors of surrounding robots. In this paper, we propose SOWL-MPC, a safe learning-based predictive control strategy for a novel scenario, which we name ego-world robotic framework. In this setting, the control policy of the world robot is unknown and the ego exploits data to learn it and perform safe maneuvers. The proposed architecture combines an online learning mechanism based on Sparse Variational Gaussian Processes (SVGPs) with a receding-horizon control scheme. Relying solely on noisy state measurements, our approach infers a posterior distribution over the latent world policy, which is updated on streaming data via Online Variational Conditioning (OVC). The learned policy is propagated through the nonlinear world dynamics using an approximate moment propagation scheme, and fed to an uncertainty-aware Model Predictive Control (MPC), thus enabling safe maneuvering of the ego robot. The real-time feasibility and safety guarantees of SOWL-MPC are demonstrated through extensive Monte Carlo virtual experiments in ROS 2, and validated on real-world robotic hardware in an indoor arena.

This paper addresses defensive blocking in autonomous racing, where a vehicle must prevent a faster opponent from overtaking while operating near its dynamic limits. Different from lap-time minimization, we formulate defense as a spatial occupancy regulation problem via a hierarchical reinforcement-learning guided model predictive control framework. A Soft Actor-Critic strategic layer operates in the Frenet domain to generate geometry-aware defensive references, which are embedded into the nonlinear model predictive control formulation as spatial regularization under friction constraints. Evaluated on the Thunderhill West circuit in simulation, the framework increases average overtake time from 8.8 s to 14.6 s while significantly reducing opponent progress. Meanwhile, it allows the vehicle to utilize 83.4% of available tire force. The framework achieves a 33.3 ms mean solve time (13.9 ms std), supporting real-time high-speed adversarial interaction.

Safe steerable catheter control is fundamentally a problem of interaction dynamics: the tip must follow a planned motion, remain compliant against moving tissue, reject friction and hysteresis, and respect a clinically meaningful never-exceed contact-force bound. We formulate catheter--tissue interaction dynamics in the scalar tip-normal coordinate of a single-segment single-tendon catheter. A partial-physics feedforward cancels only the reliable nominal bending dynamics, exposing a configuration-invariant linear interaction-dynamics model whose input gain varies through the scalar catheter inertia. A predictive optimizer then regulates this interaction state subject to hard contact-force, tendon-force, and curvature constraints. An augmented Kalman filter compresses contact, friction, and modeling error into one sensor-free disturbance state, giving nominal offset-free regulation in free space while leaving force safety to the explicit constraint. The unconstrained and disturbance-free limit recovers classical catheter impedance as a special realization of the same interaction dynamics, rather than as the main design object. In a MuJoCo distributed-compliance simulation of an eight-link tendon-driven catheter, disturbance augmentation cuts free-space approach error by 90%, and only the force-constrained predictive interaction-dynamics controller reconciles tracking with the 0.5,N bound: the unconstrained controller drives contact force to 0.60,N against a penetrating target, while the constrained one holds 0.47,N at identical tracking. These results show that offset-free motion regulation and contact-force safety are coupled interaction-dynamics objectives, and that the explicit predictive constraint resolves their tension under stiff tissue contact. The bound also holds under $0.5$,mm, $1.2$,Hz cardiac motion. Hardware validation is future work.

Aquatic self-reconfigurable robots must assemble into desired shapes while ensuring safe interactions among multiple agents. This paper proposes a hybrid framework that combines distributed Model Predictive Control (MPC) with Control Barrier Functions (CBFs) for multi-agent shape formation and reconfiguration. Given a desired shape and target assignment, a distributed MPC scheme, solved via the Alternating Direction Method of Multipliers (ADMM), computes coordinated trajectories through local optimization and information exchange. To ensure safety in real time, distributed CBF-based filters are applied to enforce inter-agent collision avoidance. The proposed approach leverages the predictive capabilities of MPC to mitigate local minima, while CBFs provide formal safety guarantees despite the nonconvexity of the underlying optimization problem. Simulation results with up to 25 agents and experimental validation with four physical robots demonstrate the effectiveness and scalability of the framework.

We present a goal-agnostic control framework for partial differential equations (PDEs) built around an end-to-end joint-embedding predictive architecture (JEPA). A lightweight 2D vision-transformer (ViT) and action-conditioned latent dynamics are trained offline without a reward or downstream goal, before being frozen and reused by a model-predictive path integral (MPPI) controller. We minimize a control objective in the latent space, initially expressed via the $L^2$ distance and additionally illustrate the benefit of recasting the control objective in terms of an explicit physical observable when available. By instead minimizing the tracking error for a learned linear kinetic-energy (KE) probe on the frozen latent-state rollouts, we demonstrate the ability to reproduce the control of held-out trajectories with $R^2=0.989$, while requiring no change to the underlying world model. For a controlled 2D Navier--Stokes benchmark, using a KE-probe within MPPI planning improves the mean native reward from $-12.08\pm0.86$ for latent-$L^2$ tracking to $-10.90\pm0.91$ (95% CI), all while lowering last-quarter velocity-field RMSE from $0.0765$ to $0.0692$. Across three intentionally withheld, dissimilar, aperiodic targets, KE planning lowers late field RMSE by $53\%$ relative to latent-$L^2$ planning ($0.0220$ versus $0.0469$), winning across 30 paired comparisons. The same frozen model also supports stabilization around a steady-state configuration via direct regulation of KE, achieving $2.7\%$ mean relative error. While the latent probe proves brittle to measurement noise and missing pixels, our findings support the claim that latent dynamics can remain flexible and goal-agnostic, particularly when calibrated observables (granted they guarantee unique continuation) are a suitable objective for state control.

Real-world collision avoidance is a core motivation for studying the dynamics and control of high sideslip drifting in vehicles, yet the practical benefit of such maneuvers has so far primarily been tested in scenarios explicitly engineered to require drifting. In this work, we explore the question of if and when drifting may be optimal for safety in real-world winter driving conditions. We present a drift-capable nonlinear model predictive control (MPC) system designed to handle scenarios grounded in crash fatality data and deploy the controller in a high fidelity simulator across road departure and oncoming vehicle collision avoidance scenarios. The controller naturally initiates and sustains drifting maneuvers to stay on the road when hitting a patch of ice on the rear axle and to avoid an oncoming vehicle that has slid into its lane. Comparisons with a benchmark electronic stability control (ESC) system demonstrate how a drift-capable controller can trade off stability for controllability to precisely maneuver through dangerous winter driving scenarios. A Monte Carlo study over random ice patches further shows that the drift-capable controller achieves lower median lane error than ESC across several speeds, while revealing that drifting emerges predominantly at higher speeds.

In legged locomotion, divergent components of motion (DCMs) have emerged as characteristic states for balance control. They isolate the unstable mode of the dynamics but, in existing formulations, apply only to reduced models such as the linear inverted pendulum. In this study, we show how DCMs can be more generally formulated as Koopman eigenfunctions. Whereas Koopman analysis typically targets eigenvalues near zero, which capture conserved or slowly varying quantities, our investigation leads us to deliberately search for unstable eigenpairs with large eigenvalues. The resulting Koopman DCMs are data-driven observables trained using only real-robot data. On a real biped, DCMs learned from one hour of robot data improve tracking of reference walking patterns. We further show how learned DCMs provide state-based viability constraints when combined with model predictive control.

Digital Twins rely on surrogate models to mirror physical systems in real time, yet these models can degrade as operating conditions evolve, a phenomenon known as concept drift. Maintaining surrogate fidelity under drift, particularly when models must also capture aleatoric uncertainty, remains an open challenge. Existing adaptive frameworks lack principled mechanisms for detecting when updates are needed, for efficiently adapting models from limited streaming data, and for certifying that updates genuinely improve predictive performance. Here we present an adaptive Digital Twin framework that integrates a Fisher score--based multivariate drift detector, Low-Rank Adaptation (LoRA) for parameter-efficient continual learning, and a Mann--Whitney $U$ test for online statistical validation. The framework monitors surrogate-model confidence via Fisher score vectors, triggers targeted fine-tuning of fewer than 1% of model parameters upon drift detection, and statistically certifies predictive improvement before deploying the updated surrogate. Applied to a stochastic linear system and a directed energy deposition additive manufacturing process as case studies, the framework successfully detects distributional shifts with short delays and restores both predictive accuracy and uncertainty quantification under abrupt and incremental drift. These results establish a statistically rigorous and computationally tractable pathway for sustaining the trustworthiness of neural-network--based Digital Twins throughout their operational life cycle.

Autonomous flight of aerial robots in narrow space remains challenging due to strong aerodynamic disturbances and limited flying space. Existing approaches mainly address aerodynamic disturbances at the control level, while motion planning typically relies on geometric constraints and fixed speed limits, leading to conservative or unsafe behaviors in confined environments. This paper presents a disturbance-aware planning and control framework (DAPCF) that integrates online disturbance estimation into the planning-control loop for quadrotor flight in narrow space. First, the dual-loop observers estimate 6-degree-of-freedom disturbance forces and torques in real time based on odometry and motor speed measurements. Then, a disturbance risk function is introduced that adaptively modulates the reference speed of the planner based on disturbance estimation, reducing velocity when disturbances exceed a threshold and restoring it under low-disturbance conditions. Finally, a motor-dynamics-based nonlinear model predictive controller (MDNMPC) with disturbance compensation is designed to ensure robust trajectory tracking under perturbed conditions. Experiments demonstrate that a quadrotor with a diagonal length of 0.39m can traverse straight, sloped, and curved tunnels as narrow as 0.6m, outperforming human pilots in both success rate and flight efficiency.

This paper presents a safety-critical distributed nonlinear model predictive control (DNMPC) framework for cooperative payload transportation by teams of quadrupedal robots. The proposed approach models the robotic team and the shared payload as a dynamically coupled networked system with rigid holonomic coupling constraints arising from cooperative transportation. To enable distributed real-time optimization, the centralized finite-horizon optimal control problem is decomposed into parallel local NMPC subproblems coordinated through the alternating direction method of multipliers (ADMM). The resulting distributed framework enforces consensus over both payload-state and interaction-wrench trajectories while explicitly incorporating acceleration-level holonomic coupling constraints within the distributed predictive control formulation. Safety-critical obstacle avoidance constraints for both the robotic agents and payload are enforced using higher-order control barrier functions (HOCBFs). The framework is validated through numerical simulations with teams of two, three, and four quadrupedal robots transporting shared payloads in cluttered environments. Real-time experiments on two- and three-robot teams demonstrate safe and robust transportation under payload uncertainty and external disturbances. Compared with centralized NMPC, the proposed framework achieves up to 23% reduction in average NLP solve time while maintaining comparable closed-loop performance. Ablation studies further demonstrate robustness to communication delays and show that explicit payload-state consensus and holonomic constraints substantially improve payload tracking and distributed coordination over existing wrench-only consensus formulations.

Autonomous rendezvous and proximity operations (RPO) in adversarial orbital environments require guidance architectures balancing target pursuit, safety preservation, and real-time adaptability under dynamically evolving interaction conditions. Although learning-based approaches show promise, their application to safety-critical orbital robotics remains limited by concerns regarding interpretability, robustness, and constraint awareness. This work presents an adaptive Model Predictive Control (MPC) framework for autonomous spacecraft RPO in multi-agent adversarial scenarios. The proposed architecture combines a constrained receding-horizon MPC formulation with a data-driven supervisory tuning layer that adjusts controller parameters from offline closed-loop evaluation and online interaction geometry. Relative motion follows Clohessy-Wiltshire (CW) dynamics, enabling computationally efficient finite-horizon prediction and real-time quadratic optimization. The MPC formulation incorporates actuator limits, predictive keep-out-zone constraints, slack-variable feasibility handling, and optional Control Barrier Function (CBF) safety filtering. Rather than generating thrust commands directly, the adaptive layer modifies interpretable MPC parameters, including tracking weights, safety penalties, minimum-separation objectives, and keep-out-zone objectives. The framework was evaluated in the official Kerbal Space Program Differential Game (KSPDG) Capture-the-Satellite environment through Monte Carlo simulations. Results demonstrate improved closed-loop robustness, adaptive maneuvering behavior, and rendezvous performance compared with fixed-parameter MPC while preserving safety-aware operation and real-time feasibility, providing a modular, interpretable foundation for adaptive spacecraft RPO.

The RLxF programme argues that learning signals should come from world feedback rather than from internal model proxies. We instantiate this position in safe model-based control and distil it into three concrete design principles. Empirically, across four world-model architectures spanning a 2x MSE range, MPC planning is statistically equivalent (TOST, n=200), and dynamics-based uncertainty penalties increase collision rates from 26% to 34%: the standard MBRL safety proxy is anti-correlated with safety in this regime. Replacing the model-internal proxy with three world-feedback signals (a sensor-derived margin via minimum lidar, a temporal signal via time-to-collision, and an outcome-supervised feedback model g_psi trained on prior collision labels, structurally analogous to outcome-trained reward models in RLHF) reduces collisions to 1-14% without retraining the world model or the planner. The mechanism is structural: model uncertainty has support over state-prediction space, whereas task risk has support over constraint boundaries, with empirical correlation r < 0.15. From this we extract three RLxF principles (ground risk in world outcomes, validate proxies before deployment, and substitute outcome-trained feedback models when direct world signals are unavailable) and argue they apply equally to model-based control and to verifier-based or RLHF approaches in LLM alignment.

This paper illustrates the Pick-to-Learn methodology applied to the calibration of a Model Predictive Control policy. While developed around a specific example, the presentation is meant to highlight a methodology of broad applicability. The example concerns an aircraft traveling from an origin point to a destination point in the presence of uncertain crosswinds and a low-connectivity zone that should be avoided. The MPC policy is parameterized by two hyperparameters, which are selected from data by the P2L procedure. Starting from a dataset of 400 wind realizations, also called scenarios, P2L identifies a final compression set containing only two informative scenarios. The resulting MPC policy avoids the low-connectivity zone on all available scenarios and, according to the P2L theory, satisfies a probabilistic risk bound of $4.8\%$ at confidence level $1-10^{-5}$, where the risk is the probability of entering the low-connectivity zone in a future flight under a new wind realization not included in the sample.

Humanoid navigation in dynamic environments requires long-horizon planning while respecting short-horizon dynamic and safety constraints. Classical visibility-graph planners combined with model predictive control (MPC) can efficiently generate collision-free trajectories, but their performance depends on manually tuned parameters and accurate system modeling. In real robotic systems, control delays, state-estimation noise, and locomotion uncertainties can cause overshoot and constraint violations even when the nominal path is geometrically optimal. We propose RAVEN, a hierarchical reinforcement learning (RL)-MPC framework for robust humanoid navigation. Unlike prior approaches that use learning to tune cost weights or replace planning entirely, RAVEN employs RL to adapt the geometric construction of a visibility-graph planner by modifying obstacle inflation and related graph parameters. By directly reshaping the free-space geometry, the learned planner alters the topology of the global path to compensate for delay and tracking imperfections. A collision-free MPC layer then tracks the planned trajectory while explicitly enforcing velocity bounds and obstacle-avoidance constraints. By training under realistic delays and observation noise, RAVEN learns planning adaptations that improve robustness while retaining explicit long-horizon geometric planning and constrained optimization, in contrast to end-to-end learning approaches. We evaluate RAVEN against a manually tuned visibility-graph MPC baseline and a pure RL navigation policy. Results demonstrate reduced overshoot near obstacles, improved robustness in narrow passages, and more reliable navigation under delay and noise. These findings indicate that reinforcement-adaptive graph construction combined with constrained MPC provides an effective and interpretable alternative to end-to-end learning for robust humanoid navigation.

Autonomous racing overtaking requires balancing competitive performance with safety under nonlinear vehicle dynamics and real-time constraints. Model Predictive Control (MPC) combined with Control Barrier Functions (CBFs) provides a principled mechanism for certifying forward invariance of a safe set. However, commonly used fixed-decay discrete-time CBF formulations can become overly conservative in interactive racing scenarios, limiting overtaking performance and requiring manual tuning across track conditions. This paper proposes a hierarchical overtaking framework that explicitly separates maneuver-level decision making from safety-certified trajectory control, reducing conservatism while preserving safety. A high-level Mixed-Integer Quadratic Program (MIQP) resolves the combinatorial passing-side selection problem by selecting a feasible overtaking topology, while a nonlinear Frenet-frame MPC enforces vehicle dynamics and safety through embedded discrete-time CBF constraints. This decomposition isolates the combinatorial complexity of maneuver selection from the continuous trajectory optimization. To further mitigate the sensitivity of fixed-decay barrier constraints, a reinforcement learning policy adapts the discrete-time CBF decay parameter online, enabling context-dependent modulation of safety margins without directly controlling vehicle inputs. Simulation and scaled-hardware experiments show that no single fixed decay parameter achieves uniformly strong performance across tracks, whereas the adaptive strategy attains the highest aggregate success rate and consistently strong safety--performance trade-offs without per-track tuning, improving robustness to environment variation while maintaining safety constraint satisfaction in nominal operation.

High-speed off-road autonomy requires precise closed-loop control for a target vehicle while remaining robust across changing terrains. Recent forward kinodynamic (FKD) prediction foundation models suggest a promising path, starting from a generalist model and specializing it to the target platform. However, effective specialization remains challenging, as it often requires substantial real-world data, and models adapted to one setting can still overfit to specific terrains or driving regimes. We present OptCar (Optimized Car), a recipe for bridging the gap from generalist to specialist FKD models that preserves cross-terrain generalization while optimizing performance for a specific vehicle. $\texttt{OptCar}$ introduces a history-conditioned dynamics adaptation module that encodes recent state-action observations into a dynamics context token, and then fine-tunes the generalist model using limited real-world data together with targeted synthetic rollouts from environment-specific system identification. In closed-loop model predictive control (MPC) experiments across three terrains and an out-of-distribution cart-pulling task, the largest gains appear at 6m/s, the highest speed evaluated and the regime in which slip dominates tracking error. On vegetation and dirt, the most slip-diverse terrain, OptCar reduces 6m/s trajectory tracking error by roughly 55% relative to a fine-tuned AnyCar baseline, and remains the most accurate even when an unseen cart payload changes the dynamics. With only 5 minutes of real data per terrain, OptCar is competitive on road with a specialist trained on 30 minutes of road data, and substantially outperforms it once the terrain changes.

This study presents and validates a minimum-lap-time planning (MLTP) framework for motorsport applications that embeds robustness against both state disturbances and parameter uncertainty. The methodology builds upon a prior disturbance-aware framework that, at each track point, propagates stochastic vehicle dynamics over a short horizon and tightens tyre-friction constraints based on the worst-case scenario at horizon end. We extend the formulation to account for uncertainty in key vehicle parameters: moment of inertia, centre-of-mass position, and aerodynamic drag coefficient. To keep the extended formulation computationally tractable, a spatially selective, parsimonious activation strategy confines the robust constraints to the circuit segments where they are most critical. We demonstrate the improved driveability of the robust references by employing a model predictive controller (MPC) as a virtual test driver. For each reference, the same MPC drives a simulated FSAE (Formula SAE) car over 1000 runs on a representative Barcelona-Catalunya sector, with randomly realised impulsive disturbances and parameter scatter. We compare a nominal reference, planned without robustness, against its robust counterparts. The latter yield consistently fewer failed runs and, at a moderate sector-time cost, show tighter dispersion of key signals (vehicle inputs, axle saturations) around the reference values, evidence of better trackability.

Buildings are expected to shift cooling loads in response to grid conditions. Thermal energy storage (TES) enables this shift, but scheduling it well requires planning hours ahead under storage constraints. Model predictive control (MPC) and reinforcement learning are difficult to scale across buildings. This study instead adapts an open-weight reasoning model through reinforcement learning with verifiable rewards (RLVR). We convert exact offline dynamic-programming (DP) action values into dense rewards for every candidate action. Using only 30 training prompts, reinforcement fine-tuning (RFT) trains the model as an upper-level scheduler that outputs hourly heat-pump setpoints from text-based states and forecasts. Evaluation uses a deliberately simple office-building TES benchmark where exact DP is tractable and the optimum is known. RFT reduces the open-weight model's emissions from 70.5 to 61.2 kg-CO2, close to the DP optimum of 60.8 kg-CO2. GPT-5 nearly matches DP and MPC without task-specific training, while GPT-4o, a non-reasoning LLM, produces higher emissions than the no-storage baseline, so inference-time reasoning appears important. Trace analysis shows that RFT mainly stabilizes observable planning patterns (candidate comparison, look-ahead, and feasibility checking) rather than creating a new strategy. Robustness and generalization tests clarify what transfers: the reinforced planning patterns persist under forecast errors and an unseen TES condition and carry over to a battery task, but its different structure limits the gains. DP-based verifiable rewards offer a practical way to adapt open-weight reasoning models to building storage scheduling. These results motivate higher-fidelity tests of whole-building control and scalable verifiers for city-scale energy management.

This study introduces a unified control framework for fixed-wing unmanned aerial vehicles (UAVs) fitted with a pan-tilt (PT) camera, intended to perform an end-to-end mission spanning from initial target detection to accurate terminal engagement. The proposed system employs a three-phase strategy: a vision-based target acquisition phase, an NMPC-based tracking phase, and a terminal guidance phase. During tracking, the framework uses an Unscented Kalman Filter (UKF) to fuse YOLO-based visual detections with inertial measurements, enabling robust target state estimation under unknown dynamics. To ensure reliable visual contact, we introduce a constraint-aware Nonlinear Model Predictive Control (NMPC) strategy that incorporates Control Barrier Functions (CBFs) to explicitly prevent UAV self-occlusion -- a common limitation in fixed-wing tracking. Upon satisfying terminal engagement conditions, the system seamlessly transitions control to a quaternion-based Biased Proportional Navigation Guidance (BPNG) law, enforcing precise impact angle constraints. High-fidelity simulations demonstrate that the framework achieves stable, robust tracking and accurate terminal interception while strictly respecting the vehicle's dynamic limits and camera field-of-view constraints.

Scenario-based model predictive control (SBMPC) is a variant of model predictive control (MPC) that explicitly accounts for uncertainty by optimizing control actions over multiple predicted scenarios. However, its computational complexity increases rapidly with the number of scenarios and prediction horizon, limiting is applicability to real-time planning and control. This paper presents a learning-accelerated Alternating Direction Method of Multipliers (ADMM) algorithm for efficiently solving SBMPC problems by leveraging parallel computing and Moreau envelope learning, while maintaining high solution accuracy. We reformulate the SBMPC problems into consensus forms that can be decomposed via ADMM, separating the scenario-dependent dynamics from non-anticipativity constraints and enabling parallel updates across scenarios and time steps. Building on this decomposition, we utilize existing learning-to-optimize schemes, which leverages Moreau envelope learning of the cost function to accelerate the primal update in ADMM, thereby reducing computation time. The proposed framework is evaluated on a microgrid energy management problem subject to load and renewable generation uncertainties. Comparisons with IPOPT and MadNLP, popular and modern nonlinear programming solvers, demonstrate substantial computational speedups while maintaining reliable closed-loop control performance.

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.

This paper introduces numerical optimizations for maximizing throughput on GPU when solving large batches (10,000 to over 100,000) of sequential quadratic programming (SQP) iterations, where all problems have the same structure. The optimizations are implemented in a toolbox WarpMPC for model-predictive control (MPC) in JAX and Warp. Based on the insight that all MPC problem instances in a batch share the same sparsity in time, cost, and constraints, we propose unrolling sparse linear factorizations and solves, which dominate alternating direction method of multipliers (ADMM) solver runtime. We avoid memory access bottlenecks and wasting computations via optimized memory layout, padding-reducing segmentation of the unrolled factorization, and dependency level scheduled backsolves, additionally accelerating sensitivity computation. We achieve throughputs of 8,000 to 250,000 SQP iterations per second on nonlinear cartpole, quadrotor, and humanoid robot benchmarks, outperforming baselines by 3$\times$ to 25$\times$. We illustrate practical usefulness by synthesizing a dataset and training a neural network approximation of an MPC in under 4 minutes that stabilizes a nano quadrotor in hardware experiments.

Autonomous-vehicle motion planners must resolve conflicts among safety, regulation, comfort, and efficiency in real time while exposing those decisions for audit. We present W-SQP, a weighted tiered-slack nonlinear model predictive controller (NMPC) that compiles nine driving-rule families into a four-tier shared-slack nonlinear program solved online with CasADi and IPOPT; the name denotes the weighted quadratic slack penalty, not a sequential-quadratic-programming solver. Strongly separated tier penalties bias residual violations toward lower-priority rules while leaving actuation bounds hard. The controller replans from its executed state at $10$,Hz and records per-rule residuals on every cycle. A $90$,ms solver-time limit returns an anytime iterate that is projected through the vehicle dynamics before execution; median and maximum observed wall-clock solve times were $28$ and $104$,ms. We evaluate W-SQP in closed loop on 150 Waymo Open Motion Dataset scenarios in Waymax against reactive and proposal-and-select baselines, and introduce a log-independent protocol that separates safety and regulatory compliance from resemblance to the recorded human trajectory. Under this protocol, W-SQP shows no systematic group-level deficit relative to expert replay on the log-independent safety and regulatory rules, with several localized regressions in the hardest, highest-divergence scenarios. The results characterize W-SQP as an auditable, priority-biased, anytime-capable NMPC prototype rather than a hard-real-time or formally safe controller.

A key limitation on the use of diffusion models in robotic planning is their inability to inherently enforce safety or dynamical constraints, which often results in physically infeasible or unsafe outputs. Hybrid approaches that employ model predictive control (MPC) to address this problem can be unstable, as poor trajectory initializations from the diffusion model prevent the MPC from converging to a safe and feasible solution. To overcome these challenges, we propose D-SafeMPC, which enhances the interaction between diffusion and control. Our method guides the reverse diffusion process with control barrier functions (CBFs) and control Lyapunov functions (CLFs) and employs an iterative-projection scheme where an MPC refines the trajectory at each denoising step. This steers sampling toward safe, goal-directed regions and provides reliable MPC warm starts. In simulations on a Franka manipulator across four scenarios (one static-obstacle and three dynamic-obstacle settings) and in a sim-to-real experiment on a physical Franka robot, D-SafeMPC improves safety, task success rates, and planning efficiency over state-of-the-art baselines. To facilitate reproducibility, our source code and experimental configurations are available in a repository at https://github.com/erdiphd/D-SafeMPC

Safe and socially compliant navigation remains a fundamental challenge for autonomous robots operating in human-populated environments. Beyond collision avoidance, robots must anticipate human motion and respect personal space to ensure human comfort. Model Predictive Control (MPC) offers a robust alternative to classical and data-driven methods, although its effectiveness strongly depends on accurate human motion prediction and efficient computation. This paper introduces SFM-NMPC, a Social Force Model-based Non-linear Model Predictive Control framework that embeds human motion prediction directly within the optimization loop. By incorporating the Social Force Model into the dynamic model of surrounding agents, the controller jointly predicts the trajectories of humans and robots over the prediction horizon, thereby enabling socially-aware planning. A tailored set of social cost functions guides the optimization toward human-compliant behaviors. Despite the increased model complexity, the proposed formulation runs in real time at 20 Hz. Extensive simulated testing in crowded environments demonstrates that SFM-NMPC outperforms state-of-the-art baselines in social compliance metrics while maintaining efficient and smooth navigation. Visual trajectory analysis and an ablation study further highlight the contribution of the embedded SFM dynamics and social cost terms, confirming the effectiveness of the proposed approach for real-world social navigation.

Latent world models are trained to predict future states in a learned representation and are then deployed inside a planner that selects actions by simulating them forward. Current practice adopts the prediction error, the single- or multi-step rollout loss on held-out data, as the training and model-selection objective, on the assumption that a lower prediction error yields better control. We show that this assumption is unreliable for a structural reason: a planner does not query the model on the training distribution but on the states that its candidate actions reach, which generally leave the data manifold, so an error averaged over the data cannot by itself govern control. We therefore reframe the objective as the discrepancy between the predicted and the true plan-cost at the plan the planner commits to, and prove that the planner's suboptimality is bounded by twice this discrepancy, whereas the data-averaged prediction error neither bounds nor tracks it. Under a linear-control premise the discrepancy separates into two terms. The first is a small on-manifold residual, on which the predicted and true dynamics agree and which a spectral tax prices through the non-normality of the latent transition operator. The second is an off-manifold divergence, on which an action carries the state off the manifold and the two dynamics diverge; this divergence is the binding term and is bounded by no data-averaged error. Synthetic operators confirm the pricing formulas, and latent model-predictive control experiments confirm the decoupling: across seeds, the single-step validation error is essentially uncorrelated with control success, whereas a fidelity score on the planner-reachable measure tracks it.

Autonomous navigation in dense and highly dynamic environments requires both physically feasible control and low-latency replanning. Optimization-based methods such as Model Predictive Control (MPC) explicitly handle robot kinematics and safety constraints, but repeated nonlinear optimization can limit real-time responsiveness. Deterministic behavior-cloning policies enable efficient inference but may fail to represent multimodal avoidance behaviors, whereas diffusion policies capture multimodality at the cost of time-consuming iterative denoising. We propose PIER-Flow (Physics-Informed Efficient Rectified Flow), a lightweight navigation policy for mobile robots. By distilling an MPC expert into a continuous-time Ordinary Differential Equation (ODE), PIER-Flow achieves single-step action generation through parallel latent sampling and lightweight feasibility selection. We introduce a physics-informed training objective to enforce kinematic consistency, paired with an asynchronous action chunking architecture for robust sim-to-real deployment. Extensive simulations demonstrate that PIER-Flow achieves a 98.85% success rate and zero collisions, with an average inference of $\sim$1.29 ms, which accelerates planning by 37.2$\times$ compared to MPC and over 800$\times$ against standard diffusion models. Crucially, real-world deployment on a resource-constrained edge computer further achieves an approximately stable inference latency of $\sim$5.3 ms, avoiding the latency spikes and freezing events observed with planning baselines.

At the limit of handling, a stabilizing MPC depends on the yaw-rate reference it tracks and the stable-handling envelope it enforces, both operating-point-dependent and unknown a priori, so fixed or worst-case settings are either too conservative or unsafe. We learn this uncertainty with a conditional diffusion residual model and apply it to the controller's reference and constraints rather than its control law. Conditioned on the steering command, the model returns the residual's mean and a predictive spread: the mean re-sizes the tracked yaw reference, while the spread, propagated over the prediction horizon, tightens the stable-handling envelope through a one-sided chance back-off. Together these form the proposed diffusion-residual MPC (D-res), so caution is anticipated ahead of the tracking error rather than corrected after it by a high-gain loop. Because only two moments per command are needed, the generator is tabulated offline and the online controller adds a single table lookup to the baseline MPC, with no in-loop diffusion; it runs within the 100 Hz budget on an NVIDIA Jetson AGX Xavier (worst-case 4.08 ms per step). Across a 7-DOF model and high-fidelity CarMaker co-simulation spanning vehicle, tire, road, and maneuver diversity, D-res reduces peak side-slip where the fixed bicycle model is least accurate and restores directional stability on low-friction maneuvers, where the fixed reference over-commands the available grip.

Reinforcement learning (RL) enables the synthesis of control policies directly from data, making it highly appealing for complex cyber-physical systems (CPSs) and robotics. A persistent challenge, however, is ensuring strict, hard safety constraints during the active learning phase. In real-world physical systems, violating mechanical limits can cause irreversible damage, necessitating that exploration remains strictly within safe operational regions. We propose a generalized framework that combines the adaptive, high-performance nature of deep reinforcement learning (DRL) with the formal safety guarantees of model predictive control (MPC). Using a mathematical model of the system dynamics, offline MPC computations define a feasible state-action space, representing all safe combinations of system states and control inputs that guarantee constraint satisfaction. During training and deployment, the RL agent's instantaneous actions are projected onto this globally verified feasible set via a safety filter. We systematically evaluate our generalized approach on a non-linear 1-DoF laboratory testbed, demonstrating successful exploration and stable policy convergence on physical hardware.

Sampling-based model predictive control methods handle nonlinear dynamics and complex cost landscapes through Monte Carlo rollouts, yet typically employ fixed constraint penalties that do not adapt to model-plant mismatch. This paper proposes Residual-Conservative Model Predictive Path Integral Control (RC-MPPI), a sampling-based MPC framework that modulates safety conservatism online using the prediction-execution residual. RC-MPPI combines three coupled mechanisms: residual-dependent constraint tightening, adaptive safety-cost shaping, and residual-adaptive sampling modulation through exploration contraction and temperature relaxation. The temperature adaptation reflects a key insight: when the model is inaccurate, rollout cost evaluations become unreliable, and increasing temperature reduces overcommitment to apparent cost rankings. Under Lipschitz dynamics and sub-Gaussian disturbances, we derive probabilistic bounds on constraint violation and show that the joint effect of the adaptive mechanisms reduces violation probability as the residual grows. A rollout-cost uncertainty analysis further shows that model-plant mismatch perturbs MPPI importance weights in proportion to residual magnitude and inversely with temperature, providing theoretical justification for residual-adaptive temperature relaxation. Simulations on an LTI point-mass system and a planar 2R manipulator show improved safety margin, success rate, and control efficiency compared with vanilla MPPI under significant model-plant mismatch.

This paper proposes a novel method that extends the Model Predictive Path Integral (MPPI) method with motion primitives for additional structured sampling, which enhances the convergence towards a globally optimal solution. By evaluating motion primitives and perturbed control sequences in a real-time sampling-based optimization loop, this work addresses the limitations of the path planning capabilities of sampling-based controllers. The algorithm is implemented on a quadcopter simulator and tested on an obstacle field navigation task. It is demonstrated that the proposed approach enhances exploration of the control space while maintaining the fast, reactive behavior required for real-time control.

Optimization-based local planning and control require high-rate collision-avoidance constraint evaluation over a prediction horizon. In obstacle-dense environments, where feasible space is limited and the constraints become increasingly complex, the computational workload often dominates the control-cycle runtime. The resulting bottleneck motivates collision-avoidance constraints that combine computational efficiency with geometric fidelity. The proposed Polygonal Signed Distance Function (PSDF) is a geometry-exact signed distance function between a convex polygonal robot footprint and obstacles represented by their boundary edges. It is implemented as a weight-free, branch-free tensorized geometric pipeline enabling batched GPU execution and automatic differentiation. The PSDF is embedded into model predictive control by locally linearizing the stage-wise safety constraints within a sequential quadratic programming-based real-time iteration scheme, yielding the PSDF-embedded model predictive controller (PSDF-MPC). The design separates CPU/GPU computation so that the GPU evaluates batched PSDF values and gradients while the CPU solves a sparse quadratic program whose dimension is determined by system dimensions and horizon length, not by obstacle features. Microbenchmarks show that PSDF scales favorably against signed-distance query baselines. Closed-loop simulated and real-world navigation experiments, including comparisons with optimization-based baselines, demonstrate that PSDF-MPC maintains real-time feasibility and robust collision avoidance in dense polygonal environments.

Path planning is a fundamental component of autonomous vehicles, where achieving safe, comfortable, and dynamically feasible paths while ensuring computational efficiency remains a significant challenge. This paper presents a sequential path planning framework in which a rough path obtained from graph search is explicitly exploited to guide a Model Predictive Control (MPC)-based path refinement. A rough path is first obtained via Dijkstra search on a discretized grid and is then used to construct a spatially varying convex lateral safety corridor that explicitly captures obstacle avoidance constraints, transforming discrete obstacle avoidance decisions into continuous feasibility constraints for optimization. Within this corridor, an MPC problem is formulated to refine the path, enabling efficient optimization while maintaining path smoothness by penalizing the third-order spatial derivative of the lateral offset over a prediction horizon. The proposed algorithm is evaluated in multiple overtaking scenarios on both straight and curved roads, including cases with single and multiple target vehicles, using high-fidelity environment simulations (i.e., CarMaker). Compared with the previous study, which used polynomial fitting and a quadratic programming method, the proposed approach consistently achieves lower lateral acceleration, curvature, and jerk while reducing computational cost by 28.08% on straight roads and 29.52% on curved roads. These results demonstrate that exploiting graph-search structure within an MPC formulation provides an effective balance between path smoothness and computational efficiency for autonomous vehicles in structured driving environments.

A central challenge in many mobile multi-robot applications is that communication topologies are inherently time-varying. Agents may enter or exit the network and such changes cannot generally be restricted a priori. This work introduces a distributed multi-agent control algorithm based on local communication that supports anytime agent joining and leaving the communication network without centralized coordination. The method scales efficiently with the number of agents by relying on a distance-based neighbor definition and on contracts derived from predicted trajectories. The resulting contract constraints guarantee collision avoidance and constraint satisfaction. We validate the proposed method in an autonomous multi-agent driving scenario, demonstrating effective collision avoidance in high-speed, dynamic environments with agents moving in opposite directions, in both simulated and real-world experiments.

We establish finite-sample closed-loop stability guarantees for Model Predictive Path Integral (MPPI) control applied to discrete-time Linear Time-Invariant (LTI) systems with additive Gaussian process disturbances. The key observation is that, for unconstrained LTI/quadratic systems with the DARE terminal cost, the exact finite-horizon MPC law has the same first control action as the infinite-horizon LQR law for every planning horizon. Thus, finite-sample MPPI can be analyzed as a stochastic perturbation of LQR. First, we show that the MPPI control law approximates the LQR feedback with high probability. The approximation error decomposes into a Monte Carlo term that decreases with the sample count and an infinite-sample temperature bias that persists at finite temperature but vanishes as the temperature is reduced. The resulting constants are written in terms of the horizon-dependent stacked cost matrices, making explicit that the finite-sample certificate is parametrized by the selected planning horizon. Second, we use a Lyapunov perturbation argument to prove practical exponential stability in expectation. On sample paths that remain in a compact Lyapunov sublevel set over a finite operating horizon, the expected state norm decays exponentially up to three residual floors: a process-noise floor, an MPPI approximation floor, and a confidence floor from the per-step sampling failure probability. The sufficient sample threshold is explicit and computable from the DARE solution, LQR stability margin, MPPI sampling parameters, temperature, and planning horizon. In the joint limit of infinite samples and vanishing temperature bias, the result recovers the stochastic LQR stability bound.

Efficient flapping propulsion hinges on operating within a narrow Strouhal number window, a principle nature has converged upon for maximum thrust-to-power ratio. We translate this bioinspired empirical rule into real-time control, demonstrating it on an autonomous underwater vehicle driven by four soft fins. The proposed Strouhal-aware Model Predictive Control (MPC) enhances a quasi-steady hydrodynamic model with an explicit penalty for Strouhal deviation, solving the resulting nonconvex problem via a two-stage sampling and gradient optimization that runs onboard at 25 Hz. Pool and field trials show that the controller keeps each fin within the optimal Strouhal corridor (0.25-0.35) while precisely tracking commanded forces. This results in a mean reduction in mechanical power of 8.8% to 32% throughout the cruising range of 0.1 to 0.3 m/s. The proposed method also allows for a velocity of 0.4 m/s, which is unattainable for a baseline of the conventional inverse model. The results confirm that embedding first-principle flow physics into an MPC objective yields tangible endurance gains without sacrificing agility, offering a generic pathway to energy-aware locomotion in next-generation multifin robots.

While lightweight polyp segmentation is highly desirable for low-cost deployment, reported performance gains often stem from upgraded backbone encoders, complex decoders, or heavy refinement branches. Consequently, it remains difficult to isolate whether a lightweight correction mechanism is inherently effective on its own. We address this limitation by formulating refinement as a prediction-space recursive correction task, introducing a recursive controller that operates directly on backbone logits. Under a fixed recursion budget, this controller aggregates discrepancy and uncertainty evidence, updates a compact state tracking recent correction utility, and applies additive residual logit corrections. By design, this correction path remains small, host-portable, and deployment-explicit. Utilizing a unified Kvasir-trained protocol, we evaluate our approach across seven lightweight backbones on Kvasir-SEG and three transfer datasets, measuring segmentation accuracy (Dice/IoU) alongside deployment efficiency (parameters, GMACs, and peak memory). The controller yields consistent improvements in the source domain, achieves competitive performance against both training-side baselines and heavier structural refiners on representative hosts, and delivers selective transfer gains with minimal static overhead. Code is available at https://github.com/tyui99/Gain-Aware-Prediction-Space-Recursive-Controller.

The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Recently proposed data-driven techniques, like extended dynamic mode decomposition (EDMD), its kernelized variant, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.

This paper presents a novel layered planning and control framework based on multi-rate nonlinear model predictive control (MR-NMPC) that enables quadrupedal robots to perform hybrid bipedal locomotion with wall-assisted support in constrained environments. Real-time trajectory optimization for this locomotion presents significant challenges, as the controller must simultaneously plan for both the contact points and the continuous trajectories of the robot's center of mass (CoM) and orientation within the robot's nonlinear dynamics while accounting for unilateral contact constraints, underactuation, and the switching nature of the robot's dynamics. At the high level of the control framework, an MR-NMPC is proposed, which dynamically plans both the discrete-time trajectories of the contact points and the continuous-time trajectories of the CoM and orientation, using a single rigid body (SRB) dynamics model. By incorporating contact-point planning within the multi-rate optimal control framework, this approach enhances dynamic stability compared to heuristic foot placement strategies. At the low level of the control framework, a nonlinear whole-body controller (WBC) based on virtual constraints and a quadratic program enforces full-order dynamics and tracks the MR-NMPC references. The proposed approach is validated through extensive numerical simulations demonstrating the robust wall-assisted bipedal locomotion of a Unitree A1 quadrupedal robot on rough terrains and under external disturbances in a constrained environment. Comparative analysis shows that the proposed MR-NMPC achieves a 2.9 times higher success rate compared to conventional MPC with heuristic-based foot placement strategies in negotiating irregular terrain at high speeds.

World models can enable Model Predictive Control (MPC), but this requires dynamics prediction that is both fast enough for online use and expressive enough to represent uncertain futures. Diffusion models offer a natural mechanism for modeling uncertain dynamics, yet their iterative inference procedure makes them difficult to use for low-latency latent planning. We bridge this gap with Value Diffusion World Models (Valdi), combining end-to-end online training for MPC with a latent diffusion dynamics model. In preliminary experiments on the CarRacing environment, we show that Valdi, using a single diffusion step at both training and inference, matches a deterministic MLP baseline. Our experiments expose a trade-off between predictive multimodality and control performance in this setup. Code is available at https://github.com/Kit115/ValueDiffusionWorldModels.

Latent world models enable planning from high-dimensional observations by predicting future states in a compact latent space. However, these models are typically kept frozen at test time: when their predictions become inaccurate, planning can fail, especially under test-time distribution shift. To address this, we propose AdaJEPA, an adaptive latent world model that performs test-time adaptation within the closed loop of model predictive control (MPC). After training, AdaJEPA plans and executes the first action chunk, uses the observed next-state transition as a self-supervised adaptation signal, and replans with the updated model. This closed-loop update continuously recalibrates the world model without additional expert demonstrations. Across a range of goal-reaching tasks, AdaJEPA substantially improves planning success with as few as one gradient step per MPC replanning step.

This paper presents a novel non-linear mathematical model of an articulated tractor-trailer system that can be used, in combination with receding horizon techniques, to improve the performance of path tracking tasks of articulated systems. Due to its dual steering mechanisms, this type of vehicle can be very useful in precision agriculture, particularly for seeding, spraying and harvesting in small fields. The articulated tractor-trailer system model was embedded within a non-linear model predictive controller and the trailer position was monitored. When the kinematic of the trailer was considered, the deviation of trailer's position was reduced substantially alongside not only straight paths but also in headland turns. Using the proposed mathematical model, we were able to control the trailer's position itself rather than the tractor's position. The Robot Operating System (ROS) framework and Gazebo simulator were used to perform realistic simulations examples.

Accurate 4D trajectory prediction and closed-loop tracking are essential for Unmanned Aerial Vehicle (UAV) swarms to achieve safe and efficient operations in complex low-altitude environments such as urban airspaces, industrial sites, and indoor facilities. However, this task remains challenging due to intrinsic nonlinearity of UAV swarm dynamics and strict real-time constraints of swarm formation control. To address these challenges, we propose a unified framework that couples coarse-to-fine trajectory forecasting with uncertainty-aware Distributed Nonlinear Model Predictive Control (DNMPC). Our approach features two key innovations: 1) a dimension-decoupled trajectory prediction module that reduces computational complexity by forecasting axis-wise motion, and 2) a diffusion-based residual dynamics refinement module that captures temporally correlated dynamic uncertainties. These refined predictions are then integrated into a DNMPC loop to ensure formation stability. We also introduce a synchronized multi-scenario 4D UAV swarm dataset spanning six representative airspace scenarios. The dataset contains over \textbf{7,900} frames of synchronized three-UAV trajectories with frame-level annotations of speed intention and target sector. Extensive experiments demonstrate that our approach outperforms state-of-the-art baselines, reducing trajectory tracking error by up to \textbf{10-15%} and achieving sub-\textbf{0.07,m} average tracking error in complex urban and industrial environments, while maintaining real-time inference speeds of 34 FPS (sub-30 ms latency) suitable for agile flight.

The increasing integration of Electric Vehicles (EVs) has imposed a growing harmonic challenge on the power grid. For AC/DC Power Factor Correction (PFC) in single-phase On-Board Chargers (OBCs), Model Predictive Current Control (MPCC) improves the current quality by predicting and tracking the inductor current. However, finite control set MPCC selects switching states, resulting in discrete control actions and a limited optimisation space. Moreover, the MPCC cost function based on instantaneous current tracking error has limited capability to compensate for low-order harmonic disturbances induced by dead time, control delay, and model parameter mismatch. This paper proposes a duty cycle predictive MPCC incorporating a real-time harmonic estimation reference. The proposed method dynamically estimates the low-order harmonic components of the input current and corrects the MPCC reference current, enabling continuous duty cycle control and targeted suppression of dominant low-order harmonics. Simulation results on a single-phase OBC demonstrate that the proposed duty cycle predictive MPCC reduces the steady-state current THD_i from 11.47% to 6.10% compared with the switching state predictive MPCC. With the harmonic reference, the THD_i is further reduced to 2.85%.

Modeling tethered space systems is critical for advanced orbital operations. Flexible components such as tethers and space nets are integral to these systems but present significant control challenges due to their high dimensional, strongly coupled, and nonlinear dynamics. While data driven methods offer alternative modeling approaches, they frequently struggle with long term predictive stability and spatial generalization. To address this, we propose the Koopman Graph Dynamics (KGD) framework to learn the structural dynamics by integrating the global linear evolution of the Koopman operator with the local topological priors of Graph Neural Networks. Building upon this representation, we develop a KGD based Model Predictive Control strategy for tethered space systems. Subsequently, the ground experiments on flexible tether and space net demonstrate the high precision modeling capabilities of the proposed method. Crucially, the framework exhibits exceptional capacity for spatial transfer without retraining. Models trained exclusively on small configurations successfully predict and control significantly larger, unseen physical scales. Furthermore, the orbit simulations within a physics engine verify the effectiveness of the proposed approach for tethered space systems.

Model Predictive Control (MPC) is the standard predictive layer in hierarchical quadruped controllers, but the per-cycle QP solve limits the update rate achievable on embedded processors. Because legged gaits revisit a bounded region of state space, MPC solutions admit caching and reuse. This paper proposes \emph{Certified CacheMPC}: a Locality-Sensitive-Hashed cache of horizon contact-force trajectories, partitioned by contact mode, retrieved at query time and accepted only when an a-posteriori per-query certificate confirms primal feasibility and a Lagrangian dual-gap upper bound on cost suboptimality. A bounded-budget controller schedule combines top-$K$ certified retrieval, a deadline-bounded QP solve, and a shifted last-certified fallback. The framework is evaluated on a Unitree Go2 across $2{,}038$ usable cold-controller MuJoCo trials, including a $600$-trial $n\!=\!50$ campaign at three failure-boundary cells, and a first-deploy session on the on-robot NVIDIA Orin NX. The un-gated cache delivers a $25\times$ median solve-time speedup in simulation and an $18.7\times$ median speedup on hardware. At $n\!=\!50$ no statistically significant difference in closed-loop stable rate is detected between the cache variants and the no-cache baseline at any tested cell. The certificate's contribution to closed-loop safety is not resolvable at the present sample size.

This paper presents a hierarchical control framework using model predictive control (MPC) and reinforcement learning (RL) for active roll control to manage lateral load transfer during autonomous racing of a wheeled quadruped. The framework integrates offline time-optimal raceline generation, an online MPC planner that actively minimizes the lateral Load Transfer Ratio (LTR), and a low-level, whole-body RL policy deployed directly onto the robot's 16 actuators. The MPC is based on a vehicle dynamics bicycle model of the Unitree Go2-W platform. The robot's leg actuators act as active suspension where knee joints generate anti-roll torque to bank into turns. Physical track experiments demonstrate that active roll control reduces mean LTR by up to 44%, improves the fastest lap time by 8.7%, and boosts peak lateral acceleration capability by 21.3% to 1.98 $m/s^2$, maintaining robust high-speed stability beyond the range of a non-tilting baseline controller. Supplementary code and video can be found at https://github.com/meisman-ucb/go2w-roll-control-mpc

Soft robots are challenging to control due to their nonlinear and time-varying dynamics. Data-enabled predictive control (DeePC) offers a model-free alternative by directly leveraging measured input-output trajectories to construct a predictive controller. However, its receding-horizon formulation requires solving a constrained optimization problem at every sampling instant, which can be computationally demanding for real-time deployment on resource-limited robotic platforms. To address this limitation, we propose an adaptive reinforcement-learning-based event-triggered DeePC (RL-ET-DeePC) framework for soft robotic control. A model-free RL policy is trained to determine when to invoke the DeePC optimizer based on the current system state representation, thereby reducing unnecessary optimization calls while preserving closed-loop performance. Simulation results show that RL-ET-DeePC reduces optimization frequency by up to 66% compared to periodic DeePC, while maintaining comparable tracking accuracy. Hardware experiments on a three-dimensional cable-driven soft robotic arm demonstrate zero-shot transfer, achieving a 34% reduction in optimization frequency with tracking accuracy comparable to periodic DeePC and more consistent performance than a static threshold-based event-triggered baseline.

Model Predictive Control (MPC) is widely used in industrial and robotic systems for enforcing constraints and embedding domain knowledge through finite-horizon optimization-based planning. However, despite these strengths, an MPC scheme typically does not yield optimal policies for sequential decision-making problems formulated as Markov Decision Processes (MDPs). Recent combinations of MPC with Reinforcement Learning (RL) alleviate this issue by treating MPC as a parameterized model of the optimal policy of an MDP and adjusting its parameters using data. While these approaches typically consider classical MDPs, many real-world problems include future information--such as forecasts, prices, or reference trajectories--at decision time, which must be included in the MDP state for optimal decision-making. Current MPC-RL approaches do not directly account for this augmented-state structure, raising the question of how to incorporate future information into MPC to obtain an optimal policy. This work establishes the structural requirements under which a parameterized MPC can exactly represent the optimal value functions and policy of an MDP with future information. We further demonstrate that such a parameterized MPC can serve as a structured function approximator, with its parameters learned using RL. The approach is illustrated on a point-mass racing task with future reference information.

Linear Quadratic (LQ) control problems are at the heart of linear control theory and Model Predictive Control (MPC). While performant, standard approaches to solving such problems are inherently serial, limiting real-time scalability despite the parallel computing power available on modern multi-core CPUs. Contributing to addressing this challenge and motivated by ``divide and conquer'' strategies, we present a parallel-in-time approach that solves computationally demanding conic optimal control problems through the use of the alternating direction method of multipliers (ADMM). In particular, we formulate the inner primal update of ADMM as an LQ problem and split the reformulated problem along the time horizon. This enables us to derive a variant of the Riccati recursion using dynamic programming to solve each subproblem in parallel. Numerical benchmarks on two real-world applications demonstrate as much as a 5x speedup compared to existing related approaches on multi-core CPU hardware.

Robotics increasingly relies on GPUs for parallel simulation, large-scale learning, and neural-network inference. For model predictive control (MPC) to scale with this paradigm, solvers must run efficiently on this hardware while remaining fast, differentiable, and compatible with expressive MPC formulations used in robotics. We present TurboMPC, a differentiable MPC solver that runs entirely on the GPU and supports state and control inequality constraints, implicit integrators, cross-time-coupled costs, and slack variables. TurboMPC combines sequential quadratic programming (SQP), an alternating direction method of multipliers (ADMM) inner solver, implicit differentiation, and a co-designed JAX-CUDA implementation for efficiency and ease of use. In simulation, we validate TurboMPC on constrained planning, humanoid imitation learning, and reinforcement learning with neural-network cost function tasks, achieving up to $15\times$ and $58\times$ speedups over state-of-the-art CPU and GPU differentiable solvers, respectively. We deploy TurboMPC on a full-scale car for minimum-time racing and find that batched, GPU-accelerated tuning of MPC parameters via Bayesian optimization yields significantly faster driving than a hand-tuned baseline. TurboMPC also scales to planning horizons of over $8000$ knot points while maintaining control of the vehicle. We open-source TurboMPC at: https://github.com/ToyotaResearchInstitute/turbompc

Neural world models coupled with model predictive control (MPC) replan at every environment step to bound accumulated prediction error, but this incurs substantial computational overhead. Reusing a cached plan reduces this overhead, yet its effectiveness depends on how prediction mismatch propagates through the local dynamics. We analyze this trade-off with a perturbation-based dynamic-regret framework and show that stale-plan penalties scale with the reuse tolerance, the accumulated mismatch since the last replanning step, and the local dynamics sensitivity. Based on this structure, we propose AdaReP, a training-free wrapper that adapts the replanning tolerance online using the current deviation from the cached rollout and a local sensitivity estimate, without modifying the learned world model or planner. Across image-space planning, latent-space control, and real-world robotic manipulation, AdaReP substantially reduces planner-side computation while maintaining comparable task performance, including over 80% fewer queries on a 50-trial physical robot study.

Many recent vision-language-action (VLA) policies adopt an imagine-then-act design. A world-action model (WAM) first imagines a short future as a latent trajectory z~, on which the action is then conditioned. We identify this trusted imagination, rather than the reactive policy, as the exposed attack surface. A downstream oracle, such as a safety gate, a visual model-predictive-control (MPC) planner, or an imagine-then-check verifier, consumes z~ as a prediction of the future. The robustness of the policy therefore does not entail the robustness of systems that rely on the WAM. The underlying phenomenon is an asymmetry. Corrupting the imagination is easy, since it requires only displacing z~ from its natural-future manifold. Steering it precisely is hard, since it must reach a specified on-manifold target. We adopt a capability-based threat model with an L-infinity-bounded observation perturbation. The attacker applies projected gradient descent through the fully differentiable observation-to-imagination map. The same off-manifold property motivates a parameter-free denoiser detector. We evaluate three targets: RynnVLA-002, LingBot-VA, and LaDi-WM. Untargeted corruption is roughly 60x stronger than random and is detected at AUC 1.0. Targeted control remains bounded. An adaptive attacker evades detection only by forgoing corruption. The reactive policy remains robust to corrupted imagination. A native imagination-driven MPC, however, exhibits the first adversary-specific task failure (at epsilon=0.01, success 0.70 versus 0.05; Fisher p < 10^-4).

Actor-Critic Model Predictive Control (MPC) effectively addresses complex, non-convex control problems, but guaranteeing the closed-loop stability of sequence-based learning models within these pipelines remains challenging. This paper introduces a novel Transformer-Actor-Critic MPC architecture with formal robustness guarantees. First, we prove that Transformer networks can satisfy global incremental Input-to-State Stability ($δ$ISS). We then leverage Riemannian contraction theory to analyze the interconnected dynamics between the physical plant and the predictive neural network. Finally, we integrate these theoretical bounds as a training regularizer to yield a certifiably robust policy. The framework is validated on a nonlinear 3D drone model executing target-reaching and obstacle-avoidance maneuvers.

In this letter, we present a hierarchical control framework that enables wheeled bipedal robots to perform planar object sliding tasks with their wheeled legs. The proposed approach formulates a nonlinear model predictive controller (NMPC) based on a reduced-order three rigid bodies (TRB) dynamical model that explicitly accounts for the hip roll degree of freedom and multiple wheel-environment contact modes, which is essential for lateral stepping and pedipulation tasks. Within this framework, the NMPC simultaneously regulates robot locomotion and interaction forces, allowing the robot to stably execute both rolling and object manipulation behaviors. A trajectory-optimization-based robot-object motion planner is developed to generate reference motions that incorporate stick-slip transitions in ground-object contact. Two representative pedipulation motions, namely scooting and lateral sliding, are validated through real-world hardware experiments, in which the robot successfully retrieves a 1 kg object from under a desk and slides a 4 kg object over a distance of 0.228 m via scooting.

Conventional human-in-the-loop approaches typically involve users only when a robot encounters failure or uncertainty, treating humans primarily as tools for improving robot performance. However, in many human-centered robotics settings, interaction should support engagement by keeping users involved in decision-making rather than limiting them to failure-driven interventions. This is particularly compelling in physical caregiving, where mobility limitations can reduce users' ability to intervene or modulate the robot's behavior in the moment. As a result, failure-driven interaction policies may relegate users to passive observers for long stretches of the task. For example, a user with mobility limitations may feel less engaged when being continuously and passively fed by a robot. At the same time, overly frequent interaction can be tiring and increase the user's workload. To address this trade-off, we propose Engagement-aware MPC (E-MPC), a user-engagement-aware method that plans interaction to maintain engagement while respecting a workload constraint. E-MPC leverages a user interaction dynamics model that captures how user engagement evolves as a function of both the frequency and type of interaction. Rather than requesting input only when difficulties arise during task execution, the robot proactively considers the user's preferred level of engagement throughout the task, balancing autonomy and interaction while ensuring task success. We evaluate E-MPC in simulation with several ablations and baseline comparisons. Results demonstrate the effectiveness of our approach across diverse user personas. In addition, we conduct a real-world user study with participants with emulated mobility limitations on a robot-assisted bite acquisition system, showing that E-MPC improves user experience while maintaining task success.

Sampling-based Model Predictive Control (SMPC) is a promising strategy for contact-rich robotic manipulation, combining gradient-free optimization with massively parallel GPU simulation. Yet, most prior work relies on simplified dynamics or remains confined to simulation. We present an MPC framework that leverages JAX for large-scale parallelization and efficient computation, coupled with the high-fidelity MuJoCo MJX simulator, and deploy it on a Franka Research 3 executing the Push-T manipulation task through a complete real-to-sim-to-real pipeline. The MTP variant with structured global sampling outperforms unimodal baselines such as CEM, MPPI, and PS across tasks that require mode switching, both in simulation and on hardware. Furthermore, we evaluate online domain randomization within the MPC sample budget, showing that contact-initiation parameters yield interpretable adaptation signals, whereas global physics parameters provide feedback that is too weak for reliable exploitation at typical replanning frequencies. These findings highlight key challenges for sampling-based MPC in contact-rich manipulation-contact sensitivity, tight compute budgets, and the difficulty of obtaining informative domain-randomization signals in real time.

In skill-constrained production-inventory systems, the qualified human capacity available tomorrow depends on training decisions made today: production requires certified workers, certifications decay unless maintained, and training consumes the same scarce worker hours that production needs now. We study a closed-loop skill-constrained model predictive controller that, at every shift, solves a finite-horizon mixed-integer program over production, inventory, backlog, and training, with binary predicted certification, hard production eligibility, and an interpretable terminal value that prices certified-capacity gaps at the horizon boundary; only the first-period action is applied before replanning. On synthetic, seed-controlled SkillChain-Gym scenarios - announced and surprise new-skill shocks, demand shocks, absenteeism, forecast- and availability-quality modes, capacity-boundary and training-rate sweeps, and negative controls - we evaluate the controller against production-only and maintenance-only ablations, static cross-training insurance plans, and a strong reactive heuristic, under an ex-ante locked configuration and paired statistics. The result is regime dependence, not superiority: no policy class dominates. Predictive control helps when skill or labor bottlenecks are forecastable early enough for training to complete; lean static insurance remains hard to beat under surprise shocks, near the demand-capacity boundary, and wherever pre-shock slack makes insurance cheap. Attribution ablations separate certification maintenance, re-acquisition of lapsed certifications, and greenfield skill acquisition. Forecastability, not adaptivity per se, decides when predictive control pays.

Residential battery energy storage systems (BESS) are increasingly deployed alongside photovoltaic (PV) generation to reduce household energy costs under volatile time-of-use (TOU) tariffs. Model predictive control (MPC) is a widely adopted optimisation strategy for home energy management systems (HEMS), typically formulated to minimise net energy cost, subject to physical and operational constraints. However, battery degradation is rarely embedded in the optimisation objective, meaning its cost is unquantified and aggressive; high-cycle-count strategies could incur significant losses once deployed to physical systems. This paper presents a receding-horizon mixed-integer linear programming (MILP) baseline for a UK residential HEMS, using demand data from the REFIT dataset. A 3 by 3 sensitivity study is conducted across three battery sizes and three PV array sizes, with post-hoc degradation cost estimated using the Naumann stress model and rainflow cycle counting. Results show that degradation remains constant for each battery size and can exceed energy cost savings by up to 1,060 %. These results demonstrate that energy-cost-only optimisation systematically underestimates the true system cost, motivating a degradation-aware control formulation.