This paper develops a correct-by-design controller for an autonomous vehicle interacting with opponent vehicles with unknown intentions. We define an intention-aware control problem incorporating epistemic uncertainties of the opponent vehicles and model their intentions as discrete-valued random variables. Then, we focus on a control objective specified as belief-space temporal logic specifications. From this stochastic control problem, we derive a sound deterministic control problem using stochastic expansion and solve it using shrinking-horizon model predictive control. The solved intention-aware controller allows a vehicle to adjust its behaviors according to its opponents' intentions. It ensures provable safety by restricting the probabilistic risk under a desired level. We show with experimental studies that the proposed method ensures strict limitation of risk probabilities, validating its efficacy in autonomous driving cases. This work provides a novel solution for the risk-aware control of interactive vehicles with formal safety guarantees.
With the increasing presence of autonomous vehicles (AVs) on public roads, developing robust control strategies to navigate the uncertainty of human-driven vehicles (HVs) is crucial. This paper introduces an advanced method for modeling HV behavior, combining a first-principles model with Gaussian process (GP) learning to enhance velocity prediction accuracy and provide a measurable uncertainty. We validated this innovative HV model using real-world data from field experiments and applied it to develop a GP-enhanced model predictive control (GP-MPC) strategy. This strategy aims to improve safety in mixed vehicle platoons by integrating uncertainty assessment into distance constraints. Comparative simulation studies with a conventional model predictive control (MPC) approach demonstrated that our GP-MPC strategy ensures more reliable safe distancing and fosters efficient vehicular dynamics, achieving notably higher speeds within the platoon. By incorporating a sparse GP technique in HV modeling and adopting a dynamic GP prediction within the MPC framework, we significantly reduced the computation time of GP-MPC, marking it only 4.6% higher than that of the conventional MPC. This represents a substantial improvement, making the process about 100 times faster than our preliminary work without these approximations. Our findings underscore the effectiveness of learning-based HV modeling in enhancing both safety and operational efficiency in mixed-traffic environments, paving the way for more harmonious AV-HV interactions.
Model Predictive Control (MPC) is a method to control nonlinear systems with guaranteed stability and constraint satisfaction but suffers from high computation times. Approximate MPC (AMPC) with neural networks (NNs) has emerged to address this limitation, enabling deployment on resource-constrained embedded systems. However, when tuning AMPCs for real-world systems, large datasets need to be regenerated and the NN needs to be retrained at every tuning step. This work introduces a novel, parameter-adaptive AMPC architecture capable of online tuning without recomputing large datasets and retraining. By incorporating local sensitivities of nonlinear programs, the proposed method not only mimics optimal MPC inputs but also adjusts to known changes in physical parameters of the model using linear predictions while still guaranteeing stability. We showcase the effectiveness of parameter-adaptive AMPC by controlling the swing-ups of two different real cartpole systems with a severely resource-constrained microcontroller (MCU). We use the same NN across both system instances that have different parameters. This work not only represents the first experimental demonstration of AMPC for fast-moving systems on low-cost MCUs to the best of our knowledge, but also showcases generalization across system instances and variations through our parameter-adaptation method. Taken together, these contributions represent a marked step toward the practical application of AMPC in real-world systems.
The transformation of fossil fuel-based district heating grids (DHGs) to CO$_2$-neutral DHGs requires the development of novel operating strategies. Model predictive control (MPC) is a promising approach, as knowledge about future heat demand and heat supply can be incorporated into the control, operating constraints can be ensured and the stability of the closed-loop system can be guaranteed. In this paper, we employ MPC for DHGs to control the system mass flows and injected heat flows. Following common practice, we derive terminal ingredients to stabilize given steady state temperatures and storage masses in the DHG. To apply MPC with terminal ingredients, it is crucial that the system under control is stabilizable. By exploiting the particular system structure, we give a sufficient condition for the stabilizability in terms of the grid topology and hence, for the applicability of the MPC scheme to DHGs. Furthermore, we demonstrate the practicability of the application of MPC to an exemplary DHG in a numerical case study.
AutoMPC is a Python package that automates and optimizes data-driven model predictive control. However, it can be computationally expensive and unstable when exploring large search spaces using pure Bayesian Optimization (BO). To address these issues, this paper proposes to employ a meta-learning approach called Portfolio that improves AutoMPC's efficiency and stability by warmstarting BO. Portfolio optimizes initial designs for BO using a diverse set of configurations from previous tasks and stabilizes the tuning process by fixing initial configurations instead of selecting them randomly. Experimental results demonstrate that Portfolio outperforms the pure BO in finding desirable solutions for AutoMPC within limited computational resources on 11 nonlinear control simulation benchmarks and 1 physical underwater soft robot dataset.
This paper presents an online smooth-path lane-change control framework. We focus on dense traffic where inter-vehicle space gaps are narrow, and cooperation with surrounding drivers is essential to achieve the lane-change maneuver. We propose a two-stage control framework that harmonizes Model Predictive Control (MPC) with Generative Adversarial Networks (GAN) by utilizing driving intentions to generate smooth lane-change maneuvers. To improve performance in practice, the system is augmented with an adaptive safety boundary and a Kalman Filter to mitigate sensor noise. Simulation studies are investigated in different levels of traffic density and cooperativeness of other drivers. The simulation results support the effectiveness, driving comfort, and safety of the proposed method.
Handling possible infeasibility and providing an execution time certificate are two pressing requirements of real-time Model Predictive Control (MPC). To meet these two requirements simultaneously, this paper proposes an $\ell_1$-penalty soft-constrained MPC formulation that is globally feasible and solvable with an execution time certificate using our proposed algorithm. This paper proves for the first time that $\ell_1$-penalty soft-constrained MPC problems can be equivalently transformed into a box-constrained quadratic programming (Box-QP) and then our previous execution-time-certified algorithm \cite{wu2023direct} (only limited to Box-QP) can be applied. However, our previous Box-QP algorithm \cite{wu2023direct}, which provides a theoretical execution-time certificate, is conservative in its iteration analysis, thus sacrificing computation efficiency. To this end, this paper proposes a novel $LDL^\top$ decomposition for the first time, to accelerate the computation of Newton step at each iteration. The speedup of our $LDL^\top$ decomposition comes from two-fold: \textit{i)} exploitation of the fact that the number of inequality constraints is generally larger than the number of variables in condensed MPC formulations, \textit{ii)} vectorized and parallel implementation based on based on its vector-wise operations, instead of element-wise operations of previous decomposition methods. Numerical experiments demonstrate great speedups of the proposed $LDL^\top$ decomposition (even up to 1000-fold, compared to the standard Choleksky method), which thus helps our solver achieve comparable computation performance to the state-of-the-art solvers such as IPOPT and OSQP. Code is available at \url{https://github.com/liangwu2019/L1-penalty-QP}.
Optimal control methods provide solutions to safety-critical problems but easily become intractable. Control Barrier Functions (CBFs) have emerged as a popular technique that facilitates their solution by provably guaranteeing safety, through their forward invariance property, at the expense of some performance loss. This approach involves defining a performance objective alongside CBF-based safety constraints that must always be enforced. Unfortunately, both performance and solution feasibility can be significantly impacted by two key factors: (i) the selection of the cost function and associated parameters, and (ii) the calibration of parameters within the CBF-based constraints, which capture the trade-off between performance and conservativeness. %as well as infeasibility. To address these challenges, we propose a Reinforcement Learning (RL)-based Receding Horizon Control (RHC) approach leveraging Model Predictive Control (MPC) with CBFs (MPC-CBF). In particular, we parameterize our controller and use bilevel optimization, where RL is used to learn the optimal parameters while MPC computes the optimal control input. We validate our method by applying it to the challenging automated merging control problem for Connected and Automated Vehicles (CAVs) at conflicting roadways. Results demonstrate improved performance and a significant reduction in the number of infeasible cases compared to traditional heuristic approaches used for tuning CBF-based controllers, showcasing the effectiveness of the proposed method.
The configuration of most robotic systems lies in continuous transformation groups. However, in mobile robot trajectory tracking, many recent works still naively utilize optimization methods for elements in vector space without considering the manifold constraint of the robot configuration. In this letter, we propose a geometric model predictive control (MPC) framework for wheeled mobile robot trajectory tracking. We first derive the error dynamics of the wheeled mobile robot trajectory tracking by considering its manifold constraint and kinematic constraint simultaneously. After that, we utilize the relationship between the Lie group and Lie algebra to convexify the tracking control problem, which enables us to solve the problem efficiently. Thanks to the Lie group formulation, our method tracks the trajectory more smoothly than existing nonlinear MPC. Simulations and physical experiments verify the effectiveness of our proposed methods. Our pure Python-based simulation platform is publicly available to benefit further research in the community.
Grasping is a crucial task in robotics, necessitating tactile feedback and reactive grasping adjustments for robust grasping of objects under various conditions and with differing physical properties. In this paper, we introduce LeTac-MPC, a learning-based model predictive control (MPC) for tactile-reactive grasping. Our approach enables the gripper to grasp objects with different physical properties on dynamic and force-interactive tasks. We utilize a vision-based tactile sensor, GelSight, which is capable of perceiving high-resolution tactile feedback that contains information on the physical properties and states of the grasped object. LeTac-MPC incorporates a differentiable MPC layer designed to model the embeddings extracted by a neural network (NN) from tactile feedback. This design facilitates convergent and robust grasping control at a frequency of 25 Hz. We propose a fully automated data collection pipeline and collect a dataset only using standardized blocks with different physical properties. However, our trained controller can generalize to daily objects with different sizes, shapes, materials, and textures. The experimental results demonstrate the effectiveness and robustness of the proposed approach. We compare LeTac-MPC with two purely model-based tactile-reactive controllers (MPC and PD) and open-loop grasping. Our results show that LeTac-MPC has optimal performance in dynamic and force-interactive tasks and optimal generalizability. We release our code and dataset at https://github.com/ZhengtongXu/LeTac-MPC.
Optimal decision-making for trajectory tracking in partially observable, stochastic environments where the number of active localization updates -- the process by which the agent obtains its true state information from the sensors -- are limited, presents a significant challenge. Traditional methods often struggle to balance resource conservation, accurate state estimation and precise tracking, resulting in suboptimal performance. This problem is particularly pronounced in environments with large action spaces, where the need for frequent, accurate state data is paramount, yet the capacity for active localization updates is restricted by external limitations. This paper introduces ComTraQ-MPC, a novel framework that combines Deep Q-Networks (DQN) and Model Predictive Control (MPC) to optimize trajectory tracking with constrained active localization updates. The meta-trained DQN ensures adaptive active localization scheduling, while the MPC leverages available state information to improve tracking. The central contribution of this work is their reciprocal interaction: DQN's update decisions inform MPC's control strategy, and MPC's outcomes refine DQN's learning, creating a cohesive, adaptive system. Empirical evaluations in simulated and real-world settings demonstrate that ComTraQ-MPC significantly enhances operational efficiency and accuracy, providing a generalizable and approximately optimal solution for trajectory tracking in complex partially observable environments.
In coastal river systems, frequent floods, often occurring during major storms or king tides, pose a severe threat to lives and property. However, these floods can be mitigated or even prevented by strategically releasing water before extreme weather events with hydraulic structures such as dams, gates, pumps, and reservoirs. A standard approach used by local water management agencies is the "rule-based" method, which specifies predetermined pre-releases of water based on historical and time-tested human experience, but which tends to result in excess or inadequate water release. The model predictive control (MPC), a physics-based model for prediction, is an alternative approach, albeit involving computationally intensive calculations. In this paper, we propose a Forecast Informed Deep Learning Architecture, FIDLAR, to achieve rapid and optimal flood management with precise water pre-releases. FIDLAR seamlessly integrates two neural network modules: one called the Flood Manager, which is responsible for generating water pre-release schedules, and another called the Flood Evaluator, which assesses these generated schedules. The Evaluator module is pre-trained separately, and its gradient-based feedback is used to train the Manager model, ensuring optimal water pre-releases. We have conducted experiments using FIDLAR with data from a flood-prone coastal area in South Florida, particularly susceptible to frequent storms. Results show that FIDLAR is several orders of magnitude faster than currently used physics-based approaches while outperforming baseline methods with improved water pre-release schedules.
Safely exploring environments with a-priori unknown constraints is a fundamental challenge that restricts the autonomy of robots. While safety is paramount, guarantees on sufficient exploration are also crucial for ensuring autonomous task completion. To address these challenges, we propose a novel safe guaranteed exploration framework using optimal control, which achieves first-of-its-kind results: guaranteed exploration for non-linear systems with finite time sample complexity bounds, while being provably safe with arbitrarily high probability. The framework is general and applicable to many real-world scenarios with complex non-linear dynamics and unknown domains. We improve the efficiency of this general framework by proposing an algorithm, SageMPC, SAfe Guaranteed Exploration using Model Predictive Control. SageMPC leverages three key techniques: i) exploiting a Lipschitz bound, ii) goal-directed exploration, and iii) receding horizon style re-planning, all while maintaining the desired sample complexity, safety and exploration guarantees of the framework. Lastly, we demonstrate safe efficient exploration in challenging unknown environments using SageMPC with a car model.
Reinforcement learning algorithms need exploration to learn. However, unsupervised exploration prevents the deployment of such algorithms on safety-critical tasks and limits real-world deployment. In this paper, we propose a new algorithm called Ensemble Model Predictive Safety Certification that combines model-based deep reinforcement learning with tube-based model predictive control to correct the actions taken by a learning agent, keeping safety constraint violations at a minimum through planning. Our approach aims to reduce the amount of prior knowledge about the actual system by requiring only offline data generated by a safe controller. Our results show that we can achieve significantly fewer constraint violations than comparable reinforcement learning methods.
This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.
We propose a hierarchical architecture designed for scalable real-time Model Predictive Control (MPC) in complex, multi-modal traffic scenarios. This architecture comprises two key components: 1) RAID-Net, a novel attention-based Recurrent Neural Network that predicts relevant interactions along the MPC prediction horizon between the autonomous vehicle and the surrounding vehicles using Lagrangian duality, and 2) a reduced Stochastic MPC problem that eliminates irrelevant collision avoidance constraints, enhancing computational efficiency. Our approach is demonstrated in a simulated traffic intersection with interactive surrounding vehicles, showcasing a 12x speed-up in solving the motion planning problem. A video demonstrating the proposed architecture in multiple complex traffic scenarios can be found here: https://youtu.be/-pRiOnPb9_c. GitHub: https://github.com/MPC-Berkeley/hmpc_raidnet
State estimation for legged robots is challenging due to their highly dynamic motion and limitations imposed by sensor accuracy. By integrating Kalman filtering, optimization, and learning-based modalities, we propose a hybrid solution that combines proprioception and exteroceptive information for estimating the state of the robot's trunk. Leveraging joint encoder and IMU measurements, our Kalman filter is enhanced through a single-rigid body model that incorporates ground reaction force control outputs from convex Model Predictive Control optimization. The estimation is further refined through Gated Recurrent Units, which also considers semantic insights and robot height from a Vision Transformer autoencoder applied on depth images. This framework not only furnishes accurate robot state estimates, including uncertainty evaluations, but can minimize the nonlinear errors that arise from sensor measurements and model simplifications through learning. The proposed methodology is evaluated in hardware using a quadruped robot on various terrains, yielding a 65% improvement on the Root Mean Squared Error compared to our VIO SLAM baseline. Code example: https://github.com/AlexS28/OptiState
Hybrid dynamical systems are ubiquitous as practical robotic applications often involve both continuous states and discrete switchings. Safety is a primary concern for hybrid robotic systems. Existing safety-critical control approaches for hybrid systems are either computationally inefficient, detrimental to system performance, or limited to small-scale systems. To amend these drawbacks, in this paper, we propose a learning-enabled approach to construct local Control Barrier Functions (CBFs) to guarantee the safety of a wide class of nonlinear hybrid dynamical systems. The end result is a safe neural CBF-based switching controller. Our approach is computationally efficient, minimally invasive to any reference controller, and applicable to large-scale systems. We empirically evaluate our framework and demonstrate its efficacy and flexibility through two robotic examples including a high-dimensional autonomous racing case, against other CBF-based approaches and model predictive control.
Distributed model predictive control (MPC) is currently being investigated as a solution to the important control challenge presented by networks of hybrid dynamical systems. However, a benchmark problem for distributed hybrid MPC is absent from the literature. We propose distributed control of a platoon of autonomous vehicles as a comparison benchmark problem. The problem provides a complex and adaptable case study, upon which existing and future approaches to distributed MPC for hybrid systems can be evaluated. Two hybrid modeling frameworks are presented for the vehicle dynamics. Five hybrid MPC controllers are then evaluated and extensively assessed on the fleet of vehicles. Finally, we comment on the need for new efficient and high performing distributed MPC schemes for hybrid systems.
Sampling-based Model Predictive Control (MPC) has been a practical and effective approach in many domains, notably model-based reinforcement learning, thanks to its flexibility and parallelizability. Despite its appealing empirical performance, the theoretical understanding, particularly in terms of convergence analysis and hyperparameter tuning, remains absent. In this paper, we characterize the convergence property of a widely used sampling-based MPC method, Model Predictive Path Integral Control (MPPI). We show that MPPI enjoys at least linear convergence rates when the optimization is quadratic, which covers time-varying LQR systems. We then extend to more general nonlinear systems. Our theoretical analysis directly leads to a novel sampling-based MPC algorithm, CoVariance-Optimal MPC (CoVo-MPC) that optimally schedules the sampling covariance to optimize the convergence rate. Empirically, CoVo-MPC significantly outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor agile control tasks. Videos and Appendices are available at \url{https://lecar-lab.github.io/CoVO-MPC/}.