arXiv subjects

Francesco Borrelli

Publications and source records attributed to Francesco Borrelli.

At least 37 records · Page 2Linked to original sources

arXiv2025

Approximate solution of stochastic infinite horizon optimal control problems for constrained linear uncertain systems

We propose a Model Predictive Control (MPC) with a single-step prediction horizon to approximate the solution of infinite horizon optimal control problems with the expected sum of convex stage costs for constrained linear uncertain systems. The proposed method aims to enhance a given sub-optimal controller, leveraging data to achieve a nearly optimal solution for the infinite horizon problem. The method is built on two techniques. First, we estimate the expected values of the convex costs using a computationally tractable approximation, achieved by sampling across the space of disturbances. Second, we implement a data-driven approach to approximate the optimal value function and its corresponding domain, through systematic exploration of the system's state space. These estimates are subsequently used to calculate the terminal cost and terminal set within the proposed MPC. We prove recursive feasibility, robust constraint satisfaction, and convergence in probability to the target set. Furthermore, we prove that the estimated value function converges to the optimal value function in a local region. The effectiveness of the proposed MPC is illustrated with detailed numerical simulations and comparisons with a value iteration method and a Learning MPC that minimizes a certainty equivalent cost.

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arXiv2025

Non-Normalized Solutions of Generalized Nash Equilibrium in Autonomous Racing

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used, this approach excludes other potentially valuable GNE. This paper addresses the limitations of normalized solutions in racing scenarios through three key contributions. First, we highlight the shortcomings of normalized solutions with a simple racing example. Second, we propose a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized Generalized Nash Equilibria (GNE). Third, we demonstrate that our proposed method overcomes the limitations of normalized GNE solutions and enables richer multi-modal interactions in realistic racing scenarios.

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arXiv2025

Scalable Multi-modal Model Predictive Control via Duality-based Interaction Predictions

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

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arXiv2024

Fast Stochastic MPC using Affine Disturbance Feedback Gains Learned Offline

We propose a novel Stochastic Model Predictive Control (MPC) for uncertain linear systems subject to probabilistic constraints. The proposed approach leverages offline learning to extract key features of affine disturbance feedback policies, significantly reducing the computational burden of online optimization. Specifically, we employ offline data-driven sampling to learn feature components of feedback gains and approximate the chance-constrained feasible set with a specified confidence level. By utilizing this learned information, the online MPC problem is simplified to optimization over nominal inputs and a reduced set of learned feedback gains, ensuring computational efficiency. In a numerical example, the proposed MPC approach achieves comparable control performance in terms of Region of Attraction (ROA) and average closed-loop costs to classical MPC optimizing over disturbance feedback policies, while delivering a 10-fold improvement in computational speed.

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arXiv2024

Multi-Objective Learning Model Predictive Control

Multi-Objective Learning Model Predictive Control is a novel data-driven control scheme which improves a linear system's closed-loop performance with respect to several convex control objectives over iterations of a repeated task. At each task iteration, collected system data is used to construct terminal components of a Model Predictive Controller. The formulation presented in this paper ensures that closed-loop control performance improves between successive iterations with respect to each objective. We provide proofs of recursive feasibility and performance improvement, and show that the converged policy is Pareto optimal. Simulation results demonstrate the applicability of the proposed approach.

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arXiv2024

Learning Hierarchical Control Systems for Autonomous Systems with Energy Constraints

This paper focuses on the design of hierarchical control architectures for autonomous systems with energy constraints. We focus on systems where energy storage limitations and slow recharge rates drastically affect the way the autonomous systems are operated. Using examples from space robotics and public transportation, we motivate the need for formally designed learning hierarchical control systems. We propose a learning control architecture which incorporates learning mechanisms at various levels of the control hierarchy to improve performance and resource utilization. The proposed hierarchical control scheme relies on high-level energy-aware task planning and assignment, complemented by a low-level predictive control mechanism responsible for the autonomous execution of tasks, including motion control and energy management. Simulation examples show the benefits and the limitations of the proposed architecture when learning is used to obtain a more energy-efficient task allocation.

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arXiv2024

Energy-efficient predictive control for connected, automated driving under localization uncertainty

This paper presents a data-driven Model Predictive Control (MPC) for energy-efficient urban road driving for connected, automated vehicles. The proposed MPC aims to minimize total energy consumption by controlling the vehicle's longitudinal motion on roads with traffic lights and front vehicles. Its terminal cost function and terminal constraints are learned from data, which consists of the closed-loop state and input trajectories. The terminal cost function represents the remaining energy-to-spend starting from a given terminal state. The terminal constraints are designed to ensure that the controlled vehicle timely crosses the upcoming traffic light, adheres to traffic laws, and accounts for the front vehicles. We validate the effectiveness of our method through both simulations and vehicle-in-the-loop experiments, demonstrating 19% improvement in average energy efficiency compared to conventional approaches that involve solving a long-horizon optimal control problem for speed planning and employing a separate controller for speed tracking.

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arXiv2024

Euclidean and non-Euclidean Trajectory Optimization Approaches for Quadrotor Racing

We present two quadrotor raceline optimization approaches which differ in using Euclidean or non-Euclidean geometry to describe vehicle position. Both approaches use high-fidelity quadrotor dynamics and avoid the need to approximate gates using waypoints. We demonstrate both approaches on simulated racetracks with realistic vehicle parameters where we demonstrate 100x faster compute time than comparable published methods and improved solver convergence. We then extend the non-Euclidean approach to compute racelines in the presence of numerous static obstacles.

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arXiv2024

Data-Driven Multi-Modal Learning Model Predictive Control

We present a Learning Model Predictive Controller (LMPC) for multi-modal systems performing iterative control tasks. Assuming availability of historical data, our goal is to design a data-driven control policy for the multi-modal system where the current mode is unknown. First, we propose a novel method to select local data for constructing affine time-varying (ATV) models of a multi-modal system in the context of LMPC. Then we present how to build a sampled safe set from multi-modal historical data. We demonstrate the effectiveness of our method through simulation results of automated driving on a friction-varying track.

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arXiv2024

A Distributed Multi-Vehicle Coordination Algorithm for Navigation in Tight Environments

This work presents a distributed method for multi-vehicle coordination based on nonlinear model predictive control (NMPC) and dual decomposition. Our approach allows the vehicles to coordinate in tight spaces (e.g., busy highway lanes or parking lots) by using a polytopic description of each vehicle's shape and formulating collision avoidance as a dual optimization problem. Our method accommodates heterogeneous teams of vehicles (i.e., vehicles with different polytopic shapes and dynamic models can be part of the same team). Our method allows the vehicles to share their intentions in a distributed fashion without relying on a central coordinator and efficiently provides collision-free trajectories for the vehicles. In addition, our method decouples the individual-vehicles' trajectory optimization from their collision-avoidance objectives enhancing the scalability of the method and allowing one to exploit parallel hardware architectures. All these features are particularly important for vehicular applications, where the systems operate at high-frequency rates in dynamic environments. To validate our method, we apply it in a vehicular application, that is, the autonomous lane-merging of a team of connected vehicles to form a platoon. We compare our design with the centralized NMPC design to show the computational benefits of the proposed distributed algorithm.

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arXiv2024

Predictive Braking on a Nonplanar Road

We present an approach for predictive braking of a four-wheeled vehicle on a nonplanar road. Our main contribution is a methodology to consider friction and road contact safety on general smooth road geometry. We use this to develop an active safety system to preemptively reduce vehicle speed for upcoming road geometry, such as off-camber turns. Our system may be used for human-driven or autonomous vehicles and we demonstrate it with a simulated ADAS scenario. We show that loss of control due to driver error on nonplanar roads can be mitigated by our approach.

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arXiv2024

A General 3D Road Model for Motorcycle Racing

We present a novel control-oriented motorcycle model and use it for computing racing lines on a nonplanar racetrack. The proposed model combines recent advances in nonplanar road models with the dynamics of motorcycles. Our approach considers the additional camber degree of freedom of the motorcycle body with a simplified model of the rider and front steering fork bodies. We demonstrate the effectiveness of our model by computing minimum-time racing trajectories on a nonplanar racetrack.

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arXiv2024

Learning Hierarchical Control For Multi-Agent Capacity-Constrained Systems

This paper introduces a novel data-driven hierarchical control scheme for managing a fleet of nonlinear, capacity-constrained autonomous agents in an iterative environment. We propose a control framework consisting of a high-level dynamic task assignment and routing layer and low-level motion planning and tracking layer. Each layer of the control hierarchy uses a data-driven Model Predictive Control (MPC) policy, maintaining bounded computational complexity at each calculation of a new task assignment or actuation input. We utilize collected data to iteratively refine estimates of agent capacity usage, and update MPC policy parameters accordingly. Our approach leverages tools from iterative learning control to integrate learning at both levels of the hierarchy, and coordinates learning between levels in order to maintain closed-loop feasibility and performance improvement of the connected architecture.

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arXiv2024

Eco-driving under localization uncertainty for connected vehicles on Urban roads: Data-driven approach and Experiment verification

This paper addresses the eco-driving problem for connected vehicles on urban roads, considering localization uncertainty. Eco-driving is defined as longitudinal speed planning and control on roads with the presence of a sequence of traffic lights. We solve the problem by using a data-driven model predictive control (MPC) strategy. This approach involves learning a cost-to-go function and constraints from state-input data. The cost-to-go function represents the remaining energy-to-spend from the given state, and the constraints ensure that the controlled vehicle passes the upcoming traffic light timely while obeying traffic laws. The resulting convex optimization problem has a short horizon and is amenable for real-time implementations. We demonstrate the effectiveness of our approach through real-world vehicle experiments. Our method demonstrates $12\%$ improvement in energy efficiency compared to the traditional approaches, which plan longitudinal speed by solving a long-horizon optimal control problem and track the planned speed using another controller, as evidenced by vehicle experiments.

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arXiv2024

A Sequential Quadratic Programming Approach to the Solution of Open-Loop Generalized Nash Equilibria for Autonomous Racing

Dynamic games can be an effective approach for modeling interactive behavior between multiple competitive agents in autonomous racing and they provide a theoretical framework for simultaneous prediction and control in such scenarios. In this work, we propose DG-SQP, a numerical method for the solution of local generalized Nash equilibria (GNE) for open-loop general-sum dynamic games for agents with nonlinear dynamics and constraints. In particular, we formulate a sequential quadratic programming (SQP) approach which requires only the solution of a single convex quadratic program at each iteration. The three key elements of the method are a non-monotonic line search for solving the associated KKT equations, a merit function to handle zero sum costs, and a decaying regularization scheme for SQP step selection. We show that our method achieves linear convergence in the neighborhood of local GNE and demonstrate the effectiveness of the approach in the context of head-to-head car racing, where we show significant improvement in solver success rate when comparing against the state-of-the-art PATH solver for dynamic games. An implementation of our solver can be found at https://github.com/zhu-edward/DGSQP.

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arXiv2024

Clustering Heuristics for Robust Energy Capacitated Vehicle Routing Problem (ECVRP)

The paper presents an approach to solving the Robust Energy Capacitated Vehicle Routing Problem (RECVRP), focusing on electric vehicles and their limited battery capacity. A finite number of customers, each with their own demand, have to be serviced by an electric vehicle fleet while ensuring that none of the vehicles run out of energy. The time and energy it takes to travel between any two points is modeled as a random variable with known distribution. We propose a Mixed Integer Program (MIP) for computing an exact solution and introduce clustering heuristics to enhance the solution speed. This enables efficient re-planning of routes in dynamic scenarios. The methodology transforms the RECVRP into smaller problems, yielding good quality solutions quickly compared to existing methods. We demonstrate the effectiveness of this approach using a well-known benchmark problem set as well as a set of randomly generated problems.

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arXiv2024

Learning Model Predictive Control with Error Dynamics Regression for Autonomous Racing

This work presents a novel Learning Model Predictive Control (LMPC) strategy for autonomous racing at the handling limit that can iteratively explore and learn unknown dynamics in high-speed operational domains. We start from existing LMPC formulations and modify the system dynamics learning method. In particular, our approach uses a nominal, global, nonlinear, physics-based model with a local, linear, data-driven learning of the error dynamics. We conducted experiments in simulation and on 1/10th scale hardware, and deployed the proposed LMPC on a full-scale autonomous race car used in the Indy Autonomous Challenge (IAC) with closed loop experiments at the Putnam Park Road Course in Indiana, USA. The results show that the proposed control policy exhibits improved robustness to parameter tuning and data scarcity. Incremental and safety-aware exploration toward the limit of handling and iterative learning of the vehicle dynamics in high-speed domains is observed both in simulations and experiments.

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arXiv2023

Monocular Camera Localization for Automated Vehicles Using Image Retrieval

We address the problem of finding the current position and heading angle of an autonomous vehicle in real-time using a single camera. Compared to methods which require LiDARs and high definition (HD) 3D maps in real-time, the proposed approach is easily scalable and computationally efficient, at the price of lower precision. The new method combines and adapts existing algorithms in three different fields: image retrieval, mapping database, and particle filtering. The result is a simple, real-time localization method using an image retrieval method whose performance is comparable to other monocular camera localization methods which use a map built with LiDARs. We evaluate the proposed method using the KITTI odometry dataset and via closed-loop experiments with an indoor 1:10 autonomous vehicle. The tests demonstrate real-time capability and a 10cm level accuracy. Also, experimental results of the closed-loop indoor tests show the presence of a positive feedback loop between the localization error and the control error. Such phenomena is analysed in details at the end of the article.

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