arXiv subjects

Gennaro Notomista

Publications and source records attributed to Gennaro Notomista.

At least 19 recordsLinked to original sources

arXiv2026

$\alpha$-stability of Differentially Flat Systems with Application to Newton-Raphson Tracking Control for Vehicle Dynamics

This paper studies the $\alpha$-stability property of differentially flat nonlinear dynamical systems. The results build off the recently introduced notion of $\alpha$-stability, which is particularly amenable to characterize the ability of a system to track dynamic output reference signals. We consider systems controlled using the Newton-Raphson tracking controller, which results in closed-form control policies, therefore it is computationally efficient, and it has been shown to be effective to control a large variety of mobile robots, including autonomous vehicles. The main results of the paper consist in sufficient conditions for the $\alpha$-stability of differentially flat systems and for the equivalence between the proposed control algorithm and the Newton-Raphson tracking controller applied directly to the nonlinear dynamics. We demonstrate the behavior of the proposed controller applied to the kinematic unicycle and dynamic bicycle models.

math.DS↗

arXiv2026

Safe and Energy-Aware Decentralized PDE-Constrained Optimization-Based Control of Multi-UAVs for Persistent Wildfire Suppression

This paper presents a safe and energy-aware optimization-based control framework for multi-UAV wildfire suppression under localization and motion uncertainties. We first develop a centralized density-based controller that couples UAV motion and water deployment in a wildfire-specific control Lyapunov function. This framework is then extended to a decentralized setting suitable for large-scale operations using only local information. The controllers use control barrier function constraints to enforce both danger zone avoidance and the ability to reach a charging region. Simulations and real quadcopter experiments demonstrate the controller's effectiveness in fire suppression while preserving safety and energy sufficiency over multiple charge cycles.

eess.SY↗

arXiv2026

Safe and Energy-Aware Multi-Robot Density Control via PDE-Constrained Optimization for Long-Duration Autonomy

This paper presents a novel density control framework for multi-robot systems with spatial safety and energy sustainability guarantees. Stochastic robot motion is encoded through the Fokker-Planck Partial Differential Equation (PDE) at the density level. Control Lyapunov and control barrier functions are integrated with PDEs to enforce target density tracking, obstacle region avoidance, and energy sufficiency over multiple charging cycles. The resulting quadratic program enables fast in-the-loop implementation that adjusts commands in real-time. Multi-robot experiment and extensive simulations were conducted to demonstrate the effectiveness of the controller under localization and motion uncertainties.

eess.SY↗

arXiv2026

''It Is Much Safer to Be Sparse than Connected'': Safe Control of Robotic Swarm Density Dynamics with PDE-Optimization with State Constraints

This paper introduces a safety-critical optimization-based control strategy that leverages control Lyapunov and control barrier functions to guide the spatial density of robotic swarms governed by the Fokker-Planck equation to a predefined target distribution. In contrast to traditional open-loop state-constrained optimal control strategies, the proposed approach operates in closed-loop, and a Voronoi-based variant further enables distributed deployments. Theoretical guarantees of safety are derived, and numerical simulations demonstrate the performance of the proposed controllers. Finally, a multi-robot experiment showcases the real-world applicability of the proposed controllers under localization and motion noises, illustrating how it is much easier for a sparse swarm to satisfy safety specifications than it is for a densely packed one.

eess.SY↗

arXiv2026

Optimization-Free Constrained Control with Guaranteed Recursive Feasibility: A CBF-Based Reference Governor Approach

This letter presents a constrained control framework that integrates Explicit Reference Governors (ERG) with Control Barrier Functions (CBF) to ensure recursive feasibility without online optimization. We formulate the reference update as a virtual control input for an augmented system, governed by a smooth barrier function constructed from the softmin aggregation of Dynamic Safety Margins (DSMs). Unlike standard CBF formulations, the proposed method guarantees the feasibility of safety constraints by design, exploiting the forward invariance properties of the underlying Lyapunov level sets. This allows for the derivation of an explicit, closed-form reference update law that strictly enforces safety while minimizing deviation from a nominal reference trajectory. Theoretical results confirm asymptotic convergence, and numerical simulations demonstrate that the proposed method achieves performance comparable to traditional ERG frameworks.

eess.SY↗

arXiv2026

Optimization-based One-side Boundary Control of LWR Traffic Models

In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.

math.OC↗

arXiv2025

Disentangled Control of Multi-Agent Systems

This paper develops a general framework with convergence guarantees for multi-agent control synthesis, which applies to a wide range of problems, including those with time-varying objective functions. The proposed framework achieves decentralization without inducing entangled dynamics among agents, and it naturally supports multi-objective robotics and real-time implementation. To demonstrate its generality and effectiveness, the framework is applied to three representative problems, namely time-varying leader-follower formation control, decentralized coverage control for time-varying density functions, which is a long-standing open problem, and safe formation navigation in a dense environment.

eess.SY↗

arXiv2025

Necessary and Sufficient Conditions for the Optimization-Based Concurrent Execution of Learned Robotic Tasks

In this work, we consider the problem of executing multiple tasks encoded by value functions, each learned through Reinforcement Learning, using an optimization-based framework. Prior works develop this framework but did not address when learned value functions can be concurrently executed. This work's main contributions consist of theorems which provide necessary and sufficient conditions to concurrently execute sets of learned tasks within subsets of the state space using the previously proposed min-norm controller. These theorems provide insight into when learned control tasks can be made concurrently executable, when they may already be so, and when concurrent execution is not possible under the proposed framework. We also extend the proposed framework to account for value functions trained with a discount factor, making it more compatible with standard RL practices.

eess.SY↗

arXiv2025

Safe Decentralized Density Control of Multi-Robot Systems using PDE-Constrained Optimization with State Constraints

In this paper, we introduce a decentralized optimization-based density controller designed to enforce set invariance constraints in multi-robot systems. By designing a decentralized control barrier function, we derived sufficient conditions under which local safety constraints guarantee global safety. We account for localization and motion noise explicitly by modeling robots as spatial probability density functions governed by the Fokker-Planck equation. Compared to traditional centralized approaches, our controller requires less computational and communication power, making it more suitable for deployment in situations where perfect communication and localization are impractical. The controller is validated through simulations and experiments with four quadcopters.

eess.SY↗

arXiv2025

Boundary Control for Stability and Invariance of Traffic Flow Dynamics: A Convex Optimization Approach

In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals, from which sets of invariance-preserving boundary controllers are derived. In combination with sets of stabilizing controllers, we reformulate the problem as a convex optimization program solved at each point in time to synthesize the boundary control inputs. We derive sufficient conditions for the existence of optimal controllers that ensure both stability and invariance.

math.OC↗

arXiv2025

Music-driven Robot Swarm Painting

This paper proposes a novel control framework for robotic swarms capable of turning a musical input into a painting. The approach connects the two artistic domains, music and painting, leveraging their respective connections to fundamental emotions. The robotic units of the swarm are controlled in a coordinated fashion using a heterogeneous coverage policy to control the motion of the robots which continuously release traces of color in the environment. The results of extensive simulations performed starting from different musical inputs and with different color equipments are reported. Finally, the proposed framework has been implemented on real robots equipped with LED lights and capable of light-painting.

cs.RO↗

arXiv2025

Extended Set-based Tasks for Multi-task Execution and Prioritization

The ability of executing multiple tasks simultaneously is an important feature of redundant robotic systems. As a matter of fact, complex behaviors can often be obtained as a result of the execution of several tasks. Moreover, in safety-critical applications, tasks designed to ensure the safety of the robot and its surroundings have to be executed along with other nominal tasks. In such cases, it is also important to prioritize the former over the latter. In this paper, we formalize the definition of extended set-based tasks, i.e., tasks which can be executed by rendering subsets of the task space asymptotically stable or forward invariant using control barrier functions. We propose a formal mathematical representation of such tasks that allows for the execution of more complex and time-varying prioritized stacks of tasks using kinematic and dynamic robot models alike. We present an optimization-based framework which is computationally efficient, accounts for input bounds, and allows for the stable execution of time-varying prioritized stacks of extended set-based tasks. The proposed framework is validated using extensive simulations, quantitative comparisons to the state-of-the-art hierarchical quadratic programming, and experiments with robotic manipulators.

eess.SY↗

arXiv2025

Value Iteration for Learning Concurrently Executable Robotic Control Tasks

Many modern robotic systems such as multi-robot systems and manipulators exhibit redundancy, a property owing to which they are capable of executing multiple tasks. This work proposes a novel method, based on the Reinforcement Learning (RL) paradigm, to train redundant robots to be able to execute multiple tasks concurrently. Our approach differs from typical multi-objective RL methods insofar as the learned tasks can be combined and executed in possibly time-varying prioritized stacks. We do so by first defining a notion of task independence between learned value functions. We then use our definition of task independence to propose a cost functional that encourages a policy, based on an approximated value function, to accomplish its control objective while minimally interfering with the execution of higher priority tasks. This allows us to train a set of control policies that can be executed simultaneously. We also introduce a version of fitted value iteration to learn to approximate our proposed cost functional efficiently. We demonstrate our approach on several scenarios and robotic systems.

cs.RO↗

arXiv2025

Energy-Aware Task Allocation for Teams of Multi-mode Robots

This work proposes a novel multi-robot task allocation framework for robots that can switch between multiple modes, e.g., flying, driving, or walking. We first provide a method to encode the multi-mode property of robots as a graph, where the mode of each robot is represented by a node. Next, we formulate a constrained optimization problem to decide both the task to be allocated to each robot as well as the mode in which the latter should execute the task. The robot modes are optimized based on the state of the robot and the environment, as well as the energy required to execute the allocated task. Moreover, the proposed framework is able to encompass kinematic and dynamic models of robots alike. Furthermore, we provide sufficient conditions for the convergence of task execution and allocation for both robot models.

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arXiv2024

Reactive Robot Navigation Using Quasi-conformal Mappings and Control Barrier Functions

This paper presents a robot control algorithm suitable for safe reactive navigation tasks in cluttered environments. The proposed approach consists of transforming the robot workspace into the \emph{ball world}, an artificial representation where all obstacle regions are closed balls. Starting from a polyhedral representation of obstacles in the environment, obtained using exteroceptive sensor readings, a computationally efficient mapping to ball-shaped obstacles is constructed using quasi-conformal mappings and Möbius transformations. The geometry of the ball world is amenable to provably safe navigation tasks achieved via control barrier functions employed to ensure collision-free robot motions with guarantees both on safety and on the absence of deadlocks. The performance of the proposed navigation algorithm is showcased and analyzed via extensive simulations and experiments performed using different types of robotic systems, including manipulators and mobile robots.

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arXiv2023

A Constrained-Optimization Approach to the Execution of Prioritized Stacks of Learned Multi-Robot Tasks

This paper presents a constrained-optimization formulation for the prioritized execution of learned robot tasks. The framework lends itself to the execution of tasks encoded by value functions, such as tasks learned using the reinforcement learning paradigm. The tasks are encoded as constraints of a convex optimization program by using control Lyapunov functions. Moreover, an additional constraint is enforced in order to specify relative priorities between the tasks. The proposed approach is showcased in simulation using a team of mobile robots executing coordinated multi-robot tasks.

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arXiv2022

Safe Reinforcement Learning Using Robust Control Barrier Functions

Reinforcement Learning (RL) has been shown to be effective in many scenarios. However, it typically requires the exploration of a sufficiently large number of state-action pairs, some of which may be unsafe. Consequently, its application to safety-critical systems remains a challenge. An increasingly common approach to address safety involves the addition of a safety layer that projects the RL actions onto a safe set of actions. In turn, a difficulty for such frameworks is how to effectively couple RL with the safety layer to improve the learning performance. In this paper, we frame safety as a differentiable robust-control-barrier-function layer in a model-based RL framework. Moreover, we also propose an approach to modularly learn the underlying reward-driven task, independent of safety constraints. We demonstrate that this approach both ensures safety and effectively guides exploration during training in a range of experiments, including zero-shot transfer when the reward is learned in a modular way.

eess.SY↗

arXiv2022

Resilience and Energy-Awareness in Constraint-Driven-Controlled Multi-Robot Systems

In the context of constraint-driven control of multi-robot systems, in this paper, we propose an optimization-based framework that is able to ensure resilience and energy-awareness of teams of robots. The approach is based on a novel, frame-theoretic, measure of resilience which allows us to analyze and enforce resilient behaviors of multi-robot systems. The properties of resilience and energy-awareness are encoded as constraints of a convex optimization program which is used to synthesize the robot control inputs. This allows for the combination of such properties with the execution of coordinated tasks to achieve resilient and energy-aware robot operations. The effectiveness of the proposed method is illustrated in a simulated scenario where a team of robots is deployed to execute two tasks subject to energy and resilience constraints.

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