This paper addresses the motion control problem for underactuated mechanical systems with full attitude control and one translational force input to manage the six degrees of freedom involved in the three-dimensional Euclidean space. These systems are often classified as second-order nonholonomic due to their completely nonintegrable acceleration constraints. To tackle this complex control problem, we propose two nonlinear model predictive control (NMPC) schemes that ensure closed-loop stability and recursive feasibility without terminal conditions. The system dynamics are modeled on the SE(3) manifold for a globally and unique description of rigid body configurations. One NMPC scheme also aims to reduce mission time as an economic criterion. The controllers' effectiveness is validated through numerical experiments on a quadrotor UAV.
Model Predictive Control (MPC) has been demonstrated to be effective in continuous control tasks. When a world model and a value function are available, planning a sequence of actions ahead of time leads to a better policy. Existing methods typically obtain the value function and the corresponding policy in a model-free manner. However, we find that such an approach struggles with complex tasks, resulting in poor policy learning and inaccurate value estimation. To address this problem, we leverage the strengths of MPC itself. In this work, we introduce Bootstrapped Model Predictive Control (BMPC), a novel algorithm that performs policy learning in a bootstrapped manner. BMPC learns a network policy by imitating an MPC expert, and in turn, uses this policy to guide the MPC process. Combined with model-based TD-learning, our policy learning yields better value estimation and further boosts the efficiency of MPC. We also introduce a lazy reanalyze mechanism, which enables computationally efficient imitation learning. Our method achieves superior performance over prior works on diverse continuous control tasks. In particular, on challenging high-dimensional locomotion tasks, BMPC significantly improves data efficiency while also enhancing asymptotic performance and training stability, with comparable training time and smaller network sizes. Code is available at https://github.com/wertyuilife2/bmpc.
A robust control strategy for autonomous vehicles can improve system stability, enhance riding comfort, and prevent driving accidents. This paper presents a novel interpolation tube-based constrained iterative linear quadratic regulator (itube-CILQR) algorithm for autonomous computer-vision-based vehicle lane-keeping. The goal of the algorithm is to enhance robustness during high-speed cornering on tight turns. The advantages of itube-CILQR over the standard tube-approach include reduced system conservatism and increased computational speed. Numerical and vision-based experiments were conducted to examine the feasibility of the proposed algorithm. The proposed itube-CILQR algorithm is better suited to vehicle lane-keeping than variational CILQR-based methods and model predictive control (MPC) approaches using a classical interior-point solver. Specifically, in evaluation experiments, itube-CILQR achieved an average runtime of 3.16 ms to generate a control signal to guide a self-driving vehicle; itube-MPC typically required a 4.67-times longer computation time to complete the same task. Moreover, the influence of conservatism on system behavior was investigated by exploring the interpolation variable trajectories derived from the proposed itube-CILQR algorithm during lane-keeping maneuvers.
When implementing model predictive control (MPC) for hybrid systems with a linear or a quadratic performance measure, a mixed-integer linear program (MILP) or a mixed-integer quadratic program (MIQP) needs to be solved, respectively, at each sampling instant. Recent work has introduced the possibility to certify the computational complexity of branch-and-bound (B&B) algorithms when solving MILP and MIQP problems formulated as multi-parametric MILPs (mp-MILPs) and mp-MIQPs. Such a framework allows for computing the worst-case computational complexity of standard B&B-based MILP and MIQP solvers, quantified by metrics such as the total number of LP/QP iterations and B&B nodes. These results are highly relevant for real-time hybrid MPC applications. In this paper, we extend this framework by developing parallel, domain-decomposition versions of the previously proposed algorithm, allowing it to scale to larger problem sizes and enable the use of high-performance computing (HPC) resources. Furthermore, to reduce peak memory consumption, we introduce two novel modifications to the existing (serial) complexity certification framework, integrating them into the proposed parallel algorithms. Numerical experiments show that the parallel algorithms significantly reduce computation time while maintaining the correctness of the original framework.
In model predictive control (MPC) for hybrid systems, solving optimization problems efficiently and with guarantees on worst-case computational complexity is critical to satisfy the real-time constraints in these applications. These optimization problems often take the form of mixed-integer linear programs (MILPs) or mixed-integer quadratic programs (MIQPs) that depend on system parameters. A common approach for solving such problems is the branch-and-bound (B&B) method. This paper extends existing complexity certification methods by presenting a unified complexity-certification framework for B&B-based MILP and MIQP solvers, specifically for the family of multi-parametric MILP and MIQP problems that arise in, e.g., hybrid MPC applications. The framework provides guarantees on worst-case computational measures, including the maximum number of iterations or relaxations B&B algorithms require to reach optimality. It systematically accounts for different branching and node selection strategies, as well as heuristics integrated into B&B, ensuring a comprehensive certification framework. By offering theoretical guarantees and practical insights for solver customization, the proposed framework enhances the reliability of B&B for real-time application. The usefulness of the proposed framework is demonstrated through numerical experiments on both random MILPs and MIQPs, as well as on MIQPs arising from a hybrid MPC problem.
Trajectory planning for automated vehicles commonly employs optimization over a moving horizon - Model Predictive Control - where the cost function critically influences the resulting driving style. However, finding a suitable cost function that results in a driving style preferred by passengers remains an ongoing challenge. We employ preferential Bayesian optimization to learn the cost function by iteratively querying a passenger's preference. Due to increasing dimensionality of the parameter space, preference learning approaches might struggle to find a suitable optimum with a limited number of experiments and expose the passenger to discomfort when exploring the parameter space. We address these challenges by incorporating prior knowledge into the preferential Bayesian optimization framework. Our method constructs a virtual decision maker from real-world human driving data to guide parameter sampling. In a simulation experiment, we achieve faster convergence of the prior-knowledge-informed learning procedure compared to existing preferential Bayesian optimization approaches and reduce the number of inadequate driving styles sampled.
This paper presents a safe model predictive control (SMPC) framework designed to ensure the satisfaction of hard constraints for systems perturbed by an external disturbance. Such safety guarantees are ensured, despite the disturbance, by online softening a subset of adjustable constraints defined by the designer. The selection of the constraints to be softened is made online based on a predefined priority assigned to each adjustable constraint. The design of a learning-based algorithm enables real-time computation while preserving the original safety properties. Simulations results, obtained from an automated driving application, show that the proposed approach provides guarantees of collision-avoidance hard constraints despite the unpredicted behaviors of the surrounding environment.
We propose Diffusion-Informed Model Predictive Control (D-I MPC), a generic framework for uncertainty-aware prediction and decision-making in partially observable stochastic systems by integrating diffusion-based time series forecasting models in Model Predictive Control algorithms. In our approach, a diffusion-based time series forecasting model is used to probabilistically estimate the evolution of the system's stochastic components. These forecasts are then incorporated into MPC algorithms to estimate future trajectories and optimize action selection under the uncertainty of the future. We evaluate the framework on the task of energy arbitrage, where a Battery Energy Storage System participates in the day-ahead electricity market of the New York state. Experimental results indicate that our model-based approach with a diffusion-based forecaster significantly outperforms both implementations with classical forecasting methods and model-free reinforcement learning baselines.
Manipulating deformable objects like cloth is challenging due to their complex dynamics, near-infinite degrees of freedom, and frequent self-occlusions, which complicate state estimation and dynamics modeling. Prior work has struggled with robust cloth state estimation, while dynamics models, primarily based on Graph Neural Networks (GNNs), are limited by their locality. Inspired by recent advances in generative models, we hypothesize that these expressive models can effectively capture intricate cloth configurations and deformation patterns from data. Building on this insight, we propose a diffusion-based generative approach for both perception and dynamics modeling. Specifically, we formulate state estimation as reconstructing the full cloth state from sparse RGB-D observations conditioned on a canonical cloth mesh and dynamics modeling as predicting future states given the current state and robot actions. Leveraging a transformer-based diffusion model, our method achieves high-fidelity state reconstruction while reducing long-horizon dynamics prediction errors by an order of magnitude compared to GNN-based approaches. Integrated with model-predictive control (MPC), our framework successfully executes cloth folding on a real robotic system, demonstrating the potential of generative models for manipulation tasks with partial observability and complex dynamics.
The proper disposal and repurposing of end-of-life electric vehicle batteries are critical for maximizing their environmental benefits. This study introduces a robust model predictive control (MPC) framework designed to optimize the battery discharging process during pre-treatment, ensuring both efficiency and safety. The proposed method explicitly incorporates temperature constraints to prevent overheating and potential hazards. By leveraging a control-oriented equivalent circuit model integrated with thermal dynamics, the MPC algorithm dynamically adjusts the discharging profile to maintain safe operating temperatures. Additionally, the robust controller is designed to account for model mismatches between the nonlinear battery dynamics and the linearized model, ensuring reliable performance under varying conditions. The effectiveness of this approach is demonstrated through simulations comparing the robust MPC method with conventional discharging strategies, including constant current-constant voltage (CC-CV) and constant current-constant temperature (CC-CT) methods. Results indicate that the robust MPC framework significantly reduces discharging time while adhering to safety constraints, offering a promising solution for the recycling and second-life applications of lithium-ion batteries.
Making optimal decisions under uncertainty is a shared problem among distinct fields. While optimal control is commonly studied in the framework of dynamic programming, it is approached with differing perspectives of the Bellman optimality condition. In one perspective, the Bellman equation is used to derive a global optimality condition useful for iterative learning of control policies through interactions with an environment. Alternatively, the Bellman equation is also widely adopted to derive tractable optimization-based control policies that satisfy a local notion of optimality. By leveraging ideas from the two perspectives, we present a local-global paradigm for optimal control suited for learning interpretable local decision makers that approximately satisfy the global Bellman equation. The benefits and practical complications in local-global learning are discussed. These aspects are exemplified through case studies, which give an overview of two distinct strategies for unifying reinforcement learning and model predictive control. We discuss the challenges and trade-offs in these local-global strategies, towards highlighting future research opportunities for safe and optimal decision-making under uncertainty.
Computing the receding horizon optimal control of nonlinear hybrid systems is typically prohibitively slow, limiting real-time implementation. To address this challenge, we propose a layered Model Predictive Control (MPC) architecture for robust stabilization of hybrid systems. A high level "hybrid" MPC is solved at a slow rate to produce a stabilizing hybrid trajectory, potentially sub-optimally, including a domain and guard sequence. This domain and guard sequence is passed to a low level "fixed mode" MPC which is a traditional, time-varying, state-constrained MPC that can be solved rapidly, e.g., using nonlinear programming (NLP) tools. A robust version of the fixed mode MPC is constructed by using tracking error tubes that are not guaranteed to have finite size for all time. Using these tubes, we demonstrate that the speed at which the fixed mode MPC is re-calculated is directly tied to the robustness of the system, thereby justifying the layered approach. Finally, simulation examples of a five link bipedal robot and a controlled nonlinear bouncing ball are used to illustrate the formal results.
Agile trajectory planning can improve the efficiency of multi-rotor Uncrewed Aerial Vehicles (UAVs) in scenarios with combined task-oriented and kinematic trajectory planning, such as monitoring spatio-temporal phenomena or intercepting dynamic targets. Agile planning using existing non-linear model predictive control methods is limited by the number of planning steps as it becomes increasingly computationally demanding. That reduces the prediction horizon length, leading to a decrease in solution quality. Besides, the fixed time-step length limits the utilization of the available UAV dynamics in the target neighborhood. In this paper, we propose to address these limitations by introducing variable time steps and coupling them with the prediction horizon length. A simplified point-mass motion primitive is used to leverage the differential flatness of quadrotor dynamics and the generation of feasible trajectories in the flat output space. Based on the presented evaluation results and experimentally validated deployment, the proposed method increases the solution quality by enabling planning for long flight segments but allowing tightly sampled maneuvering.
We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates and future observations into account. In other words, most current approaches separate state estimation from the optimal control problem. In this paper, we extend the popular ensemble Kalman filter to receding horizon optimal control problems in the spirit of nonlinear model predictive control. We provide an interacting particle approximation to the forward-backward stochastic differential equations arising from Pontryagin's maximum principle with the forward stochastic differential equation provided by the time-continuous ensemble Kalman-Bucy filter equations. The receding horizon control laws are approximated as linear and are continuously updated as in nonlinear model predictive control. We illustrate the performance of the proposed methodology for an inverted pendulum example.
Co-optimization of both vehicle speed and gear position via model predictive control (MPC) has been shown to offer benefits for fuel-efficient autonomous driving. However, optimizing both the vehicle's continuous dynamics and discrete gear positions may be too computationally intensive for a real-time implementation. This work proposes a learning-based MPC scheme to address this issue. A policy is trained to select and fix the gear positions across the prediction horizon of the MPC controller, leaving a significantly simpler continuous optimization problem to be solved online. In simulation, the proposed approach is shown to have a significantly lower computation burden and a comparable performance, with respect to pure MPC-based co-optimization.
This paper designs traffic signal control policies for a network of signalized intersections without knowing the demand and parameters. Within a model predictive control (MPC) framework, control policies consist of an algorithm that estimates parameters and a one-step MPC that computes control inputs using estimated parameters. The algorithm switches between different terminal sets of the MPC to explore different regions of the state space, where different parameters are identifiable. The one-step MPC minimizes a cost that approximates the sum of squares of all the queue lengths within a constant and does not require demand information. We show that the algorithm can estimate parameters exactly in finite time, and the one-step MPC renders maximum throughput in terms of input-to-state practical stability. Simulations indicate better transient performance regarding queue lengths under our proposed policies than existing ones.
Due to excellent mechanism characteristics of high rigidity, maneuverability and strength-to-weight ratio, 6 Degree-of-Freedom (DoF) Stewart structure is widely adopted to construct flight simulator platforms for replicating motion feelings during training pilots. Unlike conventional serial link manipulator based mechanisms, Upset Prevention and Recovery Training (UPRT) in complex flight status is often accompanied by large speed and violent rate of change in angular velocity of the simulator. However, Classical Washout Filter (CWF) based Motion Cueing Algorithm (MCA) shows limitations in providing rapid response to drive motors to satisfy high accuracy performance requirements. This paper aims at exploiting Model Predictive Control (MPC) based MCA which is proved to be efficient in Hexapod-based motion simulators through controlling over limited linear workspace. With respect to uncertainties and control solution errors from the extraction of Terminal Constraints (COTC), this paper proposes a Switchable Model Predictive Control (S-MPC) based MCA under model adaptive architecture to mitigate the solution uncertainties and inaccuracies. It is verified that high accurate tracking is achievable using the MPC-based MCA with COTC within the simulator operating envelope. The proposed method provides optimal tracking solutions by switching to MPC based MCA without COTC outside the operating envelope. By demonstrating the UPRT with horizontal stall conditions following Average Absolute Scale(AAS) evaluation criteria, the proposed S-MPC based MCA outperforms MPC based MCA and SWF based MCA by 42.34% and 65.30%, respectively.
In motion simulation, motion cueing algorithms are used for the trajectory planning of the motion simulator platform, where workspace limitations prevent direct reproduction of reference trajectories. Strategies such as motion washout, which return the platform to its center, are crucial in these settings. For serial robotic MSPs with highly nonlinear workspaces, it is essential to maximize the efficient utilization of the MSPs kinematic and dynamic capabilities. Traditional approaches, including classical washout filtering and linear model predictive control, fail to consider platform-specific, nonlinear properties, while nonlinear model predictive control, though comprehensive, imposes high computational demands that hinder real-time, pilot-in-the-loop application without further simplification. To overcome these limitations, we introduce a novel approach using deep reinforcement learning for motion cueing, demonstrated here for the first time in a 6-degree-of-freedom setting with full consideration of the MSPs kinematic nonlinearities. Previous work by the authors successfully demonstrated the application of DRL to a simplified 2-DOF setup, which did not consider kinematic or dynamic constraints. This approach has been extended to all 6 DOF by incorporating a complete kinematic model of the MSP into the algorithm, a crucial step for enabling its application on a real motion simulator. The training of the DRL-MCA is based on Proximal Policy Optimization in an actor-critic implementation combined with an automated hyperparameter optimization. After detailing the necessary training framework and the algorithm itself, we provide a comprehensive validation, demonstrating that the DRL MCA achieves competitive performance against established algorithms. Moreover, it generates feasible trajectories by respecting all system constraints and meets all real-time requirements with low...
Autonomous Underwater Vehicles (AUVs) play an essential role in modern ocean exploration, and their speed control systems are fundamental to their efficient operation. Like many other robotic systems, AUVs exhibit multivariable nonlinear dynamics and face various constraints, including state limitations, input constraints, and constraints on the increment input, making controller design challenging and requiring significant effort and time. This paper addresses these challenges by employing a data-driven Koopman operator theory combined with Model Predictive Control (MPC), which takes into account the aforementioned constraints. The proposed approach not only ensures the performance of the AUV under state and input limitations but also considers the variation in incremental input to prevent rapid and potentially damaging changes to the vehicle's operation. Additionally, we develop a platform based on ROS2 and Gazebo to validate the effectiveness of the proposed algorithms, providing new control strategies for underwater vehicles against the complex and dynamic nature of underwater environments.
The role played by physical activity in slowing down the progression of type-2 diabetes is well recognized. However, except for general clinical guidelines, quantitative real-time estimates of the recommended amount of physical activity, based on the evolving individual conditions, are {still missing} in the literature. The aim of this work is to provide a control-theoretical formulation of the exercise encoding all the exercise-related features (intensity, duration, period). Specifically, we design a feedback law in terms of recommended physical activity, following a model predictive control approach, based on a widespread compact diabetes progression model, suitably modified to account for the long-term effects of regular exercise. Preliminary simulations show promising results, well aligned with clinical evidence. These findings can be the basis for further validation of the control law on high-dimensional diabetes progression models to ultimately translate the predictions of the controller into meaningful recommendations.