arXiv subjects

Hugo Matias

Publications and source records attributed to Hugo Matias.

5 recordsLinked to original sources

arXiv2026

CBF-based Probabilistic Safe Navigation under Unknown Nonlinear Obstacle Dynamics

Safe navigation for an ego vehicle in uncertain environments characterized by dynamic obstacles with unknown nonlinear dynamics is a challenging problem of significant practical interest. Existing approaches in the literature either lack formal safety guarantees, require full model knowledge, or fail to account for the risk associated with the vehicle's exact body geometry and the temporal evolution of uncertainty between sampling instants. In this paper, we propose a data-driven observer for the unknown obstacle dynamics that generates an alpha-confidence set flow, which is exactly transformed into a Control Barrier Function (CBF) to enforce (1-alpha)-probability safety. The proposed framework accommodates nonlinear ego vehicle dynamics of arbitrary relative degree, as demonstrated through case studies involving first- and second-order dynamics of an unmanned surface vehicle.

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arXiv2026

Safe Navigation under Uncertain Obstacle Dynamics using Control Barrier Functions and Constrained Convex Generators

This paper presents a sampled-data framework for the safe navigation of controlled agents in environments cluttered with obstacles governed by uncertain linear dynamics. Collision-free motion is achieved by combining Control Barrier Function (CBF)-based safety filtering with set-valued state estimation using Constrained Convex Generators (CCGs). At each sampling time, a CCG estimate of each obstacle is obtained using a finite-horizon guaranteed estimation scheme and propagated over the sampling interval to obtain a CCG-valued flow that describes the estimated obstacle evolution. However, since CCGs are defined indirectly - as an affine transformation of a generator set subject to equality constraints, rather than as a sublevel set of a scalar function - converting the estimated obstacle flows into CBFs is a nontrivial task. One of the main contributions of this paper is a procedure to perform this conversion, ultimately yielding a CBF via a convex optimization problem whose validity is established by the Implicit Function Theorem. The resulting obstacle-specific CBFs are then merged into a single CBF that is used to design a safe controller through the standard Quadratic Program (QP)-based approach. Since CCGs support Minkowski sums, the proposed framework also naturally handles rigid-body agents and generalizes existing CBF-based rigid-body navigation designs to arbitrary agent and obstacle geometries. While the main contribution is general, the paper primarily focuses on agents with first-order control-affine dynamics and second-order strict-feedback dynamics. Simulation examples demonstrate the effectiveness of the proposed method.

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arXiv2025

Hybrid Lyapunov and Barrier Function-Based Control with Stabilization Guarantees

Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs) can be combined, typically by means of Quadratic Programs (QPs), to design controllers that achieve performance and safety objectives. However, a significant limitation of this framework is the introduction of asymptotically stable equilibrium points besides the minimizer of the CLF, leading to deadlock situations even for simple systems and bounded convex unsafe sets. To address this problem, we propose a hybrid CLF-CBF control framework with global asymptotic stabilization and safety guarantees, offering a more flexible and systematic design methodology compared to current alternatives available in the literature. We further extend this framework to higher-order systems via a recursive procedure based on a joint CLF-CBF backstepping approach. The proposed solution is assessed through several simulation examples.

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arXiv2024

Convex MPC and Thrust Allocation with Deadband for Spacecraft Rendezvous

This paper delves into a rendezvous scenario involving a chaser and a target spacecraft, focusing on the application of Model Predictive Control (MPC) to design a controller capable of guiding the chaser toward the target. The operational principle of spacecraft thrusters, requiring a minimum activation time that leads to the existence of a control deadband, introduces mixed-integer constraints into the optimization, posing a considerable computational challenge due to the exponential complexity on the number of integer constraints. We address this complexity by presenting two solver algorithms that efficiently approximate the optimal solution in significantly less time than standard solvers, making them well-suited for real-time applications.

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arXiv2024

Model-Predictive Trajectory Generation for Aerial Search and Coverage

This paper introduces a trajectory planning algorithm for search and coverage missions with an Unmanned Aerial Vehicle (UAV) based on an uncertainty map that represents prior knowledge of the target region, modeled by a Gaussian Mixture Model (GMM). The trajectory planning problem is formulated as an Optimal Control Problem (OCP), which aims to maximize the uncertainty reduction within a specified mission duration. However, this results in an intractable OCP whose objective functional cannot be expressed in closed form. To address this, we propose a Model Predictive Control (MPC) algorithm based on a relaxed formulation of the objective function to approximate the optimal solutions. This relaxation promotes efficient map exploration by penalizing overlaps in the UAV's visibility regions along the trajectory. The algorithm can produce efficient and smooth trajectories, and it can be efficiently implemented using standard Nonlinear Programming solvers, being suitable for real-time planning. Unlike traditional methods, which often rely on discretizing the mission space and using complex mixed-integer formulations, our approach is computationally efficient and easier to implement. The MPC algorithm is initially assessed in MATLAB, followed by Gazebo simulations and actual experimental tests conducted in an outdoor environment. The results demonstrate that the proposed strategy can generate efficient and smooth trajectories for search and coverage missions.

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