arXiv subjects

Francesco Borrelli

Publications and source records attributed to Francesco Borrelli.

At least 19 recordsLinked to original sources

arXiv2026

Racing a Wheeled Quadruped: Active Load Transfer Mitigation via Model Predictive Control

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

cs.RO↗

arXiv2026

SHIELD: Scalable Optimal Control with Certification using Duality and Convexity

We present SHIELD, a hierarchical algorithm that reduces both the decision-variable dimension and the constraint set in $\ell_1$-regularized convex programs. From strong convexity and Lagrangian duality, we derive certificates that \emph{safely} discard constraints and decision variables while guaranteeing that all removed constraints remain satisfied and all removed variables are null. To further accelerate the proposed algorithm, we propose a transformer-based deep neural network to guide the dual certificate inference. We validate SHIELD on stochastic model predictive control (SMPC) in complex, multi-modal traffic scenarios, comparing against a full-dimensional SMPC policy. Numerical simulations demonstrate order-of-magnitude computational speedups while preserving feasibility and closed-loop safety, highlighting the practicality of certifiably safe, lightweight MPC in complex driving scenes.

cs.RO↗

arXiv2026

Safe Adaptive-Sampling Control via Robust M-Step Hold Model Predictive Control

In adaptive-sampling control, the control frequency can be adjusted during task execution. Ensuring that these changes do not jeopardize the safety of the system being controlled requires attention. We introduce robust M-step hold model predictive control (MPC) to address this. Our formulation provides robust constraint satisfaction for an uncertain discrete-time system model with a fixed sampling time subject to an adaptable multi-step input hold (referred to as M-step hold). We show how to ensure recursive feasibility of the MPC utilizing M-step hold extensions of robust invariant sets, and demonstrate how to enable safe adaptive-sampling control via the online selection of M. We evaluate the utility of the robust M-step hold MPC formulation in a cruise control example.

eess.SY↗

arXiv2025

Constrained Policy Optimization via Sampling-Based Weight-Space Projection

Safety-critical learning requires policies that improve performance without leaving the safe operating regime. We study constrained policy learning where model parameters must satisfy rollout-based safety constraints that can be evaluated but not differentiated analytically. We propose SCPO, a sampling-based weight-space projection method that enforces safety directly in parameter space without requiring gradient access to the constraint functions. SCPO constructs a local safe region by combining rollout-based safety evaluations with smoothness bounds relating parameter perturbations to changes in safety metrics, and projects each gradient update via a convex QCQP. We establish a safe-by-induction guarantee: starting from any safe initialization, all intermediate policies remain safe given feasible projections. In constrained control settings with a stabilizing backup policy, SCPO further ensures closed-loop stability while enabling safe adaptation beyond the conservative backup. Experiments on constrained regression with harmful supervision and double-integrator imitation with a malicious expert show that SCPO rejects unsafe updates, maintains feasibility throughout training, and achieves meaningful objective improvement.

cs.LG↗

arXiv2025

Non Normalized Shared-Constraint Dynamic Games for Human-Robot Collaboration with Asymmetric Responsibility

This paper proposes a dynamic game formulation for cooperative human-robot navigation in shared workspaces with obstacles, where the human and robot jointly satisfy shared safety constraints while pursuing a common task. A key contribution is the introduction of a non-normalized equilibrium structure for the shared constraints. This structure allows the two agents to contribute different levels of effort towards enforcing safety requirements such as collision avoidance and inter-players spacing. We embed this non-normalized equilibrium into a receding-horizon optimal control scheme.

cs.RO↗

arXiv2025

Regulation-Aware Game-Theoretic Motion Planning for Autonomous Racing

This paper presents a regulation-aware motion planning framework for autonomous racing scenarios. Each agent solves a Regulation-Compliant Model Predictive Control problem, where racing rules - such as right-of-way and collision avoidance responsibilities - are encoded using Mixed Logical Dynamical constraints. We formalize the interaction between vehicles as a Generalized Nash Equilibrium Problem (GNEP) and approximate its solution using an Iterative Best Response scheme. Building on this, we introduce the Regulation-Aware Game-Theoretic Planner (RA-GTP), in which the attacker reasons over the defender's regulation-constrained behavior. This game-theoretic layer enables the generation of overtaking strategies that are both safe and non-conservative. Simulation results demonstrate that the RA-GTP outperforms baseline methods that assume non-interacting or rule-agnostic opponent models, leading to more effective maneuvers while consistently maintaining compliance with racing regulations.

eess.SY↗

arXiv2025

A learning model predictive control for virtual coupling in railroads

The objective of this paper is to present a novel intelligent train control system for virtual coupling in railroads based on a Learning Model Predictive Control (LMPC). Virtual coupling is an emerging railroad technology that reduces the distance between trains to increase the capacity of the line, whereas LMPC is an optimization-based controller that incorporates artificial intelligence methods to improve its control policies. By incorporating data from past experiences into the optimization problem, LMPC can learn unmodeled dynamics and enhance system performance while satisfying constraints. The LMPC developed in this paper is simulated and compared, in terms of energy consumption, with a general MPC, without learning capabilities. The simulations are divided into two main practical applications: a LMPC applied only to the rear trains (followers) and a LMPC applied to both the followers and the first front train of the convoy (leader). Within each application, the LMPC is independently tested for three railroad categories: metro, regional, and high-speed. The results show that the LMPC reduces energy consumption in all simulation cases while approximately maintaining speed and travel time. The effect is more pronounced in rail applications with frequent speed variations, such as metro systems, compared to high-speed rail. Future research will investigate the impact of using real-world data in place of simulated data.

math.OC↗

arXiv2025

Robust MPC for Uncertain Linear Systems -- Combining Model Adaptation and Iterative Learning

This paper presents a robust adaptive learning Model Predictive Control (MPC) framework for linear systems with parametric uncertainties and additive disturbances performing iterative tasks. The approach refines the parameter estimates online using set-membership estimation. Performance enhancement over iterations is achieved by learning the terminal cost from data. Safety is enforced using a terminal set, which is also learned iteratively. The proposed method guarantees recursive feasibility, constraint satisfaction, and a robust bound on the closed-loop cost. Numerical simulations on a mass-spring-damper system demonstrate improved computational efficiency and control performance compared to a robust adaptive MPC scheme without iterative learning of the terminal ingredients.

eess.SY↗

arXiv2025

Energy-Aware Lane Planning for Connected Electric Vehicles in Urban Traffic: Design and Vehicle-in-the-Loop Validation

Urban driving with connected and automated vehicles (CAVs) offers potential for energy savings, yet most eco-driving strategies focus solely on longitudinal speed control within a single lane. This neglects the significant impact of lateral decisions, such as lane changes, on overall energy efficiency, especially in environments with traffic signals and heterogeneous traffic flow. To address this gap, we propose a novel energy-aware motion planning framework that jointly optimizes longitudinal speed and lateral lane-change decisions using vehicle-to-infrastructure (V2I) communication. Our approach estimates long-term energy costs using a graph-based approximation and solves short-horizon optimal control problems under traffic constraints. Using a data-driven energy model calibrated to an actual battery electric vehicle, we demonstrate with vehicle-in-the-loop experiments that our method reduces motion energy consumption by up to 24 percent compared to a human driver, highlighting the potential of connectivity-enabled planning for sustainable urban autonomy.

eess.SY↗

arXiv2025

On Sampling Time and Invariance

Invariant sets define regions of the state space where system constraints are always satisfied. The majority of numerical techniques for computing invariant sets have been developed for discrete-time systems with a fixed sampling time. Understanding how invariant sets change with sampling time is critical for designing adaptive-sampling control schemes that ensure constraint satisfaction. We introduce M-step hold control invariance, a generalization of traditional control invariance, and show its practical use to assess the link between control sampling frequency and constraint satisfaction. We robustify M-step hold control invariance against model mismatches and discretization errors, paving the way for adaptive-sampling control strategies.

eess.SY↗

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.

cs.RO↗

arXiv2025

A Simple Approach to Constraint-Aware Imitation Learning with Application to Autonomous Racing

Guaranteeing constraint satisfaction is challenging in imitation learning (IL), particularly in tasks that require operating near a system's handling limits. Traditional IL methods, such as Behavior Cloning (BC), often struggle to enforce constraints, leading to suboptimal performance in high-precision tasks. In this paper, we present a simple approach to incorporating safety into the IL objective. Through simulations, we empirically validate our approach on an autonomous racing task with both full-state and image feedback, demonstrating improved constraint satisfaction and greater consistency in task performance compared to BC.

cs.LG↗

arXiv2025

Generalized Nash Equilibrium Solutions in Dynamic Games With Shared Constraints

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 presents a novel method based on the Mixed Complementarity Problem (MCP) formulation to compute non-normalized GNE, expanding the solution space. We also propose a systematic approach for selecting the optimal GNE based on predefined criteria, enhancing practical flexibility. Numerical examples illustrate the methods effectiveness, offering an alternative to traditional normalized solutions.

cs.RO↗

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.

eess.SY↗

arXiv2024

Learning Two-agent Motion Planning Strategies from Generalized Nash Equilibrium for Model Predictive Control

We introduce an Implicit Game-Theoretic MPC (IGT-MPC), a decentralized algorithm for two-agent motion planning that uses a learned value function that predicts the game-theoretic interaction outcomes as the terminal cost-to-go function in a model predictive control (MPC) framework, guiding agents to implicitly account for interactions with other agents and maximize their reward. This approach applies to competitive and cooperative multi-agent motion planning problems which we formulate as constrained dynamic games. Given a constrained dynamic game, we randomly sample initial conditions and solve for the generalized Nash equilibrium (GNE) to generate a dataset of GNE solutions, computing the reward outcome of each game-theoretic interaction from the GNE. The data is used to train a simple neural network to predict the reward outcome, which we use as the terminal cost-to-go function in an MPC scheme. We showcase emerging competitive and coordinated behaviors using IGT-MPC in scenarios such as two-vehicle head-to-head racing and un-signalized intersection navigation. IGT-MPC offers a novel method integrating machine learning and game-theoretic reasoning into model-based decentralized multi-agent motion planning.

cs.MA↗

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.

eess.SY↗

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.

eess.SY↗

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.

cs.RO↗