arXiv subjects

Guilherme V. Raffo

Publications and source records attributed to Guilherme V. Raffo.

At least 19 recordsLinked to original sources

arXiv2026

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations

This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems. A key step in such algorithms is to propagate a set (often a zonotope or constrained zonotope) through a nonlinear function. Existing methods accomplish this through conservative linearization procedures that are known to lead to severe overestimation in many cases. Here, we propose an alternative that avoids linearization using the so-called factorable representation of nonlinear functions. We use a recursive polyhedral relaxation technique based on this representation that is well-established in the global optimization literature but has not previously been used for set-based estimation. This technique is combined with constrained zonotope (CZ) technology to avoid the limitations of recursive computations with polyhedra in halfspace representation. The resulting state estimation method is fully automated, has attractive computational complexity (with one caveat discussed herein), and can provide significantly tighter enclosures than those resulting from linearization procedures in many cases. Numerical examples highlight the advantages of this approach relative to existing CZ methods based on the Mean Value Theorem and Difference of Convex functions (DC) programming.

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arXiv2026

Safe whole-body backstepping control for quadcopter path-following

This paper presents a novel whole-body Backstepping control strategy for safe quadcopter path-following. The proposed approach introduces an integrated control scheme that combines a translational guidance controller with a rigid-body attitude controller. To guarantee asymptotic path convergence, the method utilizes a nominal Integrated Guidance and Control (IGC) based on Artificial Vector Fields (AVF). To ensure reactive safety and collision avoidance, the control law is modified using a smooth distance function within the High-Order Control Barrier Function (HOCBF) framework. The quadcopter dynamics are modeled using quaternion algebra to represent position, velocity, and attitude. By combining the Backstepping approach with HOCBF, the controller guarantees that the vehicle avoids obstacle sets while successfully converging to the target path when unobstructed. The proposed methodology is validated through software-in-the-loop simulations and real-world experimental results using the Crazyflie platform.

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arXiv2026

Model Predictive Supervisory Control for Hierarchical and Distributed UAS Traffic Management

This work proposes a hierarchical Model Predictive Supervisory Control (MPSC) framework for multi-agent systems with shared resources. MPSC integrates receding-horizon cost-optimal control with Supervisory control theory (SCT) based supervision that enforces safety, nonblockingness, and resource exclusivity. Scalability arises from hierarchical and scalable supervisor and automaton templates, enabling distributed execution without monolithic synthesis. Using this framework, this work develops an urban Unmanned aircraft system Traffic Management (UTM) model. The model supports pickup-and-delivery missions under time-varying demand efficiently.

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arXiv2026

Safe and robust tube-based path-following for robot navigation

In this paper, we propose a new robust navigation framework for path following tasks in robots operating within unknown, cluttered environments. Our approach ensures reactive safety through obstacle avoidance and guaranteed convergence to a target path, while simultaneously mitigating the impact of unknown-but-bounded disturbances using a tube-based control strategy. The methodology integrates key aspects in the robot navigation: (i) a nominal Integrated Guidance and Control scheme for path-following employing Artificial Vector Fields guidance and Backstepping control; (ii) a smooth distance function that enables a continuous control law formulation for seamless obstacle avoidance; (iii) a unified control objective that balances collision avoidance with path-following; and (iv) an adaptive control component to provide robustness against external disturbances. We provide formal proofs of safety and stability using barrier functions and Lyapunov stability theory. The effectiveness of the proposed framework is validated through extensive numerical simulations.

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arXiv2026

Model Predictive Planner for UAV Navigation in Non-Convex Air Corridors

This work presents a motion planning framework for UAV navigation in non-convex urban air corridors. The planner is based on a mixed-integer tracking model predictive control formulation that enforces corridor feasibility and dynamic consistency within a single optimization problem. To guarantee convergence to the target and mitigate the occurrence of local minima induced by non-convex geometry, a shortest-path-based offset cost with feasibility constraints is embedded directly into the planning problem. Numerical simulations show that the proposed formulation generates dynamically valid trajectories that satisfy the corridor constraints and converge to the target without relying on external global planning stages.

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arXiv2026

A cell-decomposition based path planner for 3D navigation in constrained workspaces

This paper proposes a cell decomposition algorithm for binary occupancy grids that ensures mutual complete visibility from each cell to at least one adjacent cell. This decomposition establishes a simplified framework for verifying path feasibility that can be easily embedded in optimization problems. To illustrate its utility, we formulate both second-order cone programs (SOCP) and their mixed-integer variant (MISOCP) within the proposed framework. Furthermore, we propose the KSP-SOCP method, which combines Yen's k-shortest path algorithm with the SOCP, achieving improved solutions compared to a standard SOCP approach while avoiding the computational burden of MISOCP. The cell decomposition algorithm, KSP-SOCP, and MISOCP approaches were evaluated in 9 city-like workspaces. The decomposition efficiently partitioned each map, enabling both optimization methods to compute feasible paths. The proposed KSP-SOCP achieved time performance comparable to the MISOCP while requiring less memory, making it highly suitable for large-scale problems.

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arXiv2026

Point-to-Cloud NMPC with Smooth Avoidance Constraints

This paper proposes a finite-horizon optimal control strategy for set-point tracking using a nonlinear model predictive control framework with integrated avoidance capabilities. The formulation employs a smooth point-to-cloud distance metric that ensures continuously differentiable and numerically well-conditioned gradients, even in the presence of regions with complex and nonconvex geometries. This smoothness allows safety constraints to be formulated consistently and differentiably through control barrier functions, resulting in a reliable avoidance behavior for the closed-loop system. Additionally, stationary artificial variables are introduced in the optimal control problem to preserve feasibility under changing set-points. The proposed approach is validated through numerical experiments of an aerial robot, demonstrating accurate tracking and smooth obstacle avoidance in complex environments.

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arXiv2026

Constrained Optimization on Matrix Lie Groups via Interior-Point Method

This paper proposes an interior-point framework for constrained optimization problems whose decision variables evolve on matrix Lie groups. The proposed method, termed the Matrix Lie Group Interior-Point Method (MLG-IPM), operates directly on the group structure using a minimal Lie algebra parametrization, avoiding redundant matrix representations and eliminating explicit dependence on Riemannian metrics. A primal-dual formulation is developed in which the Newton system is constructed through sensitivity and curvature matrices. Also, multiplicative updates are performed via the exponential map, ensuring intrinsic feasibility with respect to the group structure while maintaining strict positivity of slack and dual variables through a barrier strategy. A local analysis establishes quadratic convergence under standard regularity assumptions and characterizes the behavior under inexact Newton steps. Statistical comparisons against Riemannian Interior-Point Methods, specifically for optimization problems defined over the Special Orthogonal Group SO(n) and Special Linear Group SL(n), demonstrate that the proposed approach achieves higher success rates, fewer iterations, and superior numerical accuracy. Furthermore, its robustness under perturbations suggests that this method serves as a consistent and reliable alternative for structured manifold optimization.

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arXiv2025

Stabilizing NMPC Approaches for Underactuated Mechanical Systems on the SE(3) Manifold

This paper addresses the motion control problem for underactuated mechanical systems with full attitude control and one translational force input to manage the six degrees of freedom involved in the three-dimensional Euclidean space. These systems are often classified as second-order nonholonomic due to their completely nonintegrable acceleration constraints. To tackle this complex control problem, we propose two nonlinear model predictive control (NMPC) schemes that ensure closed-loop stability and recursive feasibility without terminal conditions. The system dynamics are modeled on the SE(3) manifold for a globally and unique description of rigid body configurations. One NMPC scheme also aims to reduce mission time as an economic criterion. The controllers' effectiveness is validated through numerical experiments on a quadrotor UAV.

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arXiv2025

Line zonotopes: A tool for state estimation and fault diagnosis of unbounded and descriptor systems

This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear static constraints on state variables - typical of descriptor systems - into their mathematical representation, leading to less conservative enclosures. However, for LDS that are unstable or not fully observable, a bounded representation cannot ensure a valid enclosure of the states over time. To address this limitation, we introduce line zonotopes, a new representation for unbounded sets that retains key properties of CZs, including polynomial time complexity reduction methods, while enabling the description of strips, hyperplanes, and the entire n-dimensional Euclidean space. This extension not only generalizes the use of CZs to unbounded settings but can also enhance set-based estimation and AFD in both stable and unstable scenarios. Additionally, we extend the AFD method for LDS from Rego et al. (2020) to operate over reachable tubes rather than solely on the reachable set at the final time of the considered horizon. This reduces conservatism in input separation and enables more accurate fault diagnosis based on the entire output sequence. The advantages of the proposed methods over existing CZ-based approaches are demonstrated through numerical examples.

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arXiv2025

Reachability Analysis of Nonlinear Discrete-Time Systems Using Polyhedral Relaxations and Constrained Zonotopes

This paper presents a novel algorithm for reachability analysis of nonlinear discrete-time systems. The proposed method combines constrained zonotopes (CZs) with polyhedral relaxations of factorable representations of nonlinear functions to propagate CZs through nonlinear functions, which is normally done using conservative linearization techniques. The new propagation method provides better approximations than those resulting from linearization procedures, leading to significant improvements in the computation of reachable sets in comparison to other CZ methods from the literature. Numerical examples highlight the advantages of the proposed algorithm.

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arXiv2025

ZETA: a library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems

This paper introduces ZETA, a new MATLAB library for Zonotope-based EsTimation and fAult diagnosis of discrete-time systems. It features user-friendly implementations of set representations based on zonotopes, namely zonotopes, constrained zonotopes, and line zonotopes, in addition to a basic implementation of interval arithmetic. This library has capabilities starting from the basic set operations with these sets, including propagations through nonlinear functions using various approximation methods. The features of ZETA allow for reachability analysis and state estimation of discrete-time linear, nonlinear, and descriptor systems, in addition to active fault diagnosis of linear systems. Efficient order reduction methods are also implemented for the respective set representations. Some examples are presented in order to illustrate the functionalities of the new library.

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arXiv2025

Joint State-Parameter Observer-Based Robust Control of a UAV for Heavy Load Transportation

This paper proposes a joint state-parameter observer-based controller for trajectory tracking of an octocopter unmanned aerial vehicle (OUAV), for transportation of a heavy load with unknown mass and size. The multi-body dynamic model of the OUAV with a rigidly attached load is obtained, effectively considering the effects of the load parameters into the dynamics of the system. A robust nonlinear W-infinity control strategy is designed for optimal trajectory tracking of the OUAV, with information of the states and load parameters provided by a joint estimation unscented Kalman filter. The effectiveness of the proposed strategy is corroborated by numerical results.

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arXiv2023

Set-Point Tracking MPC with Avoidance Features

This work proposes a finite-horizon optimal control strategy to solve the tracking problem while providing avoidance features to the closed-loop system. Inspired by the set-point tracking model predictive control (MPC) framework, the central idea of including artificial variables into the optimal control problem is considered. This approach allows us to add avoidance features into the set-point tracking MPC strategy without losing the properties of an enlarged domain of attraction and feasibility insurances in the face of any changing reference. Besides, the artificial variables are considered together with an avoidance cost functional to establish the basis of the strategy, maintaining the recursive feasibility property in the presence of a previously unknown number of regions to be avoided. It is shown that the closed-loop system is recursively feasible and input-to-state-stable under the mild assumption that the avoidance cost is uniformly bounded over time. Finally, two numerical examples illustrate the controller behavior.

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arXiv2022

Set-based state estimation for discrete-time constrained nonlinear systems: an approach based on constrained zonotopes and DC programming

This paper proposes a new state estimator for discrete-time nonlinear dynamical systems with unknown-but-bounded uncertainties and state linear inequality and nonlinear equality constraints. Our algorithm is based on constrained zonotopes (CZs) and on a DC programming approach (DC stands for difference of convex functions). Recently, mean value extension and first-order Taylor extension have been adapted from zonotopes to propagate CZs over nonlinear mappings. Although the resulting algorithms (called CZMV and CZFO) reach better precision than the original zonotopic versions, they carry the sensitivity to the wrapping and dependency effects inherited from interval arithmetic. These interval issues can be mitigated with DC programming since the approximation error bounds are obtained solving optimization problems. A direct benefit of this technique is the elimination of the dependency effect. Our set-membership filter (called CZDC) offers an alternative solution to CZMV and CZFO. In order to demonstrate the effectiveness of the proposed approach, CZDC is experimented over two numerical examples.

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arXiv2022

Joint state and parameter estimation based on constrained zonotopes

This note presents a new method for set-based joint state and parameter estimation of discrete-time systems using constrained zonotopes. This is done by extending previous set-based state estimation methods to include parameter identification in a unified framework. Unlike in interval-based methods, the existing dependencies between states and model parameters are maintained from one time step to the next, thus providing a more accurate estimation scheme. In addition, the enclosure of states and parameters is refined using measurements through generalized intersections, which are properly captured by constrained zonotopes. The advantages of the new approach are highlighted in two numerical examples.

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arXiv2020

Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes

This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.

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arXiv2019

Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

This paper presents new methods for set-valued state estimation of nonlinear discrete-time systems with unknown-but-bounded uncertainties. A single time step involves propagating an enclosure of the system states through the nonlinear dynamics (prediction), and then enclosing the intersection of this set with a bounded-error measurement (update). When these enclosures are represented by simple sets such as intervals, ellipsoids, parallelotopes, and zonotopes, certain set operations can be very conservative. Yet, using general convex polytopes is much more computationally demanding. To address this, this paper presents two new methods, a mean value extension and a first-order Taylor extension, for efficiently propagating constrained zonotopes through nonlinear mappings. These extend existing methods for zonotopes in a consistent way. Examples show that these extensions yield tighter prediction enclosures than zonotopic estimation methods, while largely retaining the computational benefits of zonotopes. Moreover, they enable tighter update enclosures because constrained zonotopes can represent intersections much more accurately than zonotopes.

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