arXiv subjects

Paulo Oliveira

Publications and source records attributed to Paulo Oliveira.

12 recordsLinked to original sources

arXiv2026

QuadRocket: An Aerial Robotic Testbed for Adaptive Thrust-Vector Control of Rocket-Like Vehicles

This paper presents QuadRocket, a quadrotor-based rocket prototype that provides a low-cost, low-risk platform for validating advanced thrust-vector control strategies for launch vehicle-type systems. The prototype consists of a cylindrical main body mounted on top of a quadrotor through a universal joint, forming a flying inverted pendulum with non-negligible inertia. For control design, the coupled system is modeled as a single axisymmetric rigid body actuated by a vectored force applied along its longitudinal axis. A reduced-attitude representation on the two sphere is adopted to explicitly exploit the vehicle's axial symmetry and to decouple yaw from the thrust-vector direction. On this model, we derive an adaptive backstepping controller that achieves almost global trajectory tracking in the presence of unknown constant disturbances, while a control-point transformation mitigates non minimum-phase behavior. The quadrotor is then treated as a thrust vector actuator, and a dynamic-surface-based attitude controller is designed to track the desired thrust-vector, accounting for actuation dynamics and avoiding explicit differentiation of virtual control signals. The complete architecture is evaluated in simulation and validated experimentally in an indoor motion-capture arena. Results demonstrate accurate trajectory tracking, effective disturbance compensation, and confirm the suitability of the QuadRocket as a versatile testbed for thrust-vector-controlled robotic vehicles.

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arXiv2026

Geometric Reduced-Attitude Tracking Under a Time-Varying Conic Constraint via Smooth Reference-Shaping

This letter studies reduced-attitude tracking for a rigid body on the 2-sphere S2 under a time-varying conic constraint. Using a kinematic model on S2, we first propose a geometric tracking law that guarantees almostglobal asymptotic and regionally exponential convergence in the unconstrained case, where the angular velocity serves as the control input. We then introduce a smooth reference-shaping mechanism that adjusts the desired direction so that the reference provided to the controller satisfies the time-varying conic constraint while preserving the smoothness required by the tracking law. The resulting approach yields smooth continuous feedback and retains the stability guarantees of the unconstrained controller, albeit at the expense of enforcing a soft version of the original constraint. Simulation results illustrate the effectiveness of the method and highlight its suitability for applications where deterministic behavior, smooth control action, and strong stability guarantees are preferred over hard constraint satisfaction.

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arXiv2026

The E-Rocket: Low-cost Testbed for TVC Rocket GNC Validation

This paper presents the E-Rocket, an electric-powered, low-cost rocket prototype for validation of Guidance, Navigation & Control (GNC) algorithms based on Thrust Vector Control (TVC). Relying on commercially available components and 3D printed parts, a pair of contra-rotating DC brushless motors is assembled on a servo-actuated gimbal mechanism that provides thrust vectoring capability. A custom avionics hardware and software stack is developed considering a dual computer setup which leverages the capabilities of the PX4 autopilot and the modularity of ROS 2 to accommodate for tailored GNC algorithms. The platform is validated in an indoor motion-capture arena using a baseline PID-based trajectory tracking controller. Results demonstrate accurate trajectory tracking and confirm the suitability of the E-Rocket as a versatile testbed for rocket GNC algorithms.

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arXiv2026

Robust Global Position and Heading Tracking on SE(3) via Saturated Hybrid Feedback

This letter presents a novel control solution to the robust global position and heading tracking problem for underactuated vehicles, equipped with single-axis thrust and full torque actuation, operating under strict, user-defined actuation limits. The architecture features a saturated position tracking controller augmented with two first-order filters. This formulation ensures the boundedness of the first and second derivatives, yielding less conservative bounds and systematically generating bounded attitude references whose limits are easily tuned via design parameters. To track these dynamic references, the inner loop comprises a saturated, modified Rodrigues parameter (MRP)-based controller paired with a hybrid dynamic path-lifting mechanism. This approach allows the attitude tracking law to be designed on a covering space of the configuration manifold. By leveraging a stability equivalence framework, the methodology establishes that the resulting interconnected system achieves robust global asymptotic and semi-global exponential tracking on SE(3), while complying with user-defined input saturation bounds. Numerical simulations validate the proposed solution.

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arXiv2025

Control and Navigation of a 2-D Electric Rocket

This work addresses the control and navigation of a simulated two-dimensional electric rocket. The model provides a simplified framework that neglects actuator dynamics and aerodynamic effects while capturing the complexities of underactuation and state coupling. Trajectory tracking is achieved through a modularized and layered control architecture, with employement of a Linear Quadratic Regulator (LQR) and Lyapunov theory. Full-state estimation is achieved through Kalman filtering techniques, part of the navigation module. The solutions are thoroughly evaluated in a custom-built MATLAB/Simulink testbed, simulating real-world conditions while maintaining a simplified setup. The results reveal limitations along the lateral axis, whose resolution is suggested for future work.

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arXiv2025

Pitch Plane Trajectory Tracking Control for Sounding Rockets via Adaptive Feedback Linearization

This paper proposes a pitch plane trajectory tacking control solution for suborbital launch vehicles relying on adaptive feedback linearization. Initially, the 2D dynamics and kinematics for a single-engine, thrust-vector-controlled sounding rocket are obtained for control design purposes. Then, an inner-outer control strategy, which simultaneously tackles attitude and position control, is adopted, with the inner-loop comprising the altitude and pitch control and the outer-loop addressing the horizontal (downrange) position control. Feedback linearization is used to cancel out the non-linearities in both the inner and outer dynamics. Making use of Lyapunov stability theory, an adaptation law, which provides online estimates on the inner-loop aerodynamic uncertainty, is jointly designed with the output tracking controller via adaptive backstepping, ensuring global reference tracking in the region where the feedback linearization is well-defined. The zero dynamics of the inner-stabilized system are then exploited to obtain the outerloop dynamics and derive a Linear Quadratic Regulator (LQR) with integral action, which can stabilize them as well as reject external disturbances. In the outermost loop, the estimate on the correspondent aerodynamic uncertainty is indirectly obtained by using the inner loop estimates together with known aerodynamics relations. The resulting inner-outer position control solution is proven to be asymptotically stable in the region of interest. Using a single-stage sounding rocket, propelled by a liquid engine, as reference vehicle, different mission scenarios are tested in a simulation environment to verify the adaptability of the proposed control strategy. The system is able to track the requested trajectories while rejecting external wind disturbances. Furthermore, the need to re-tune the control gains in between different mission scenarios is minimal to none.

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arXiv2024

Hybrid path-lifting algorithm and Equivalence of Stability results for MRP-based control strategies

The modified Rodrigues parameters (MRP) consist of two numerically different triplets that, by switching between them, yield a minimal globally non-singular attitude description with advantageous properties. The MRP space results from the Alexandroff compactification of the three-dimensional Euclidean space and is a double cover of $\mathrm{SO(3)}$. By capitalizing on instrumental properties of the covering map, this paper proposes a novel hybrid dynamic path-lifting mechanism to unambiguously and robustly extract the MRP from the attitude space. This hybrid solution allows applying an MRP-based feedback controller to the attitude dynamics in the base space while preserving its asymptotic and exponential stability properties. Furthermore, by profiting from the distinct characteristics of the MRP, the resulting interconnection is impervious to the unwinding phenomenon. The design and validation of an MRP-based controller exemplify the application of the proposed algorithm alongside the novel results for equivalence of stability between spaces. The solution renders the attitude space tracking dynamics robustly globally exponentially stable, demonstrating the potential of this novel methodology.

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arXiv2023

Thrust vector control and state estimation architecture for low-cost small-scale launchers

This paper proposes an integrated architecture for Thrust Vector Control (TVC) and state estimation for low-cost small-scale launchers, naturally unstable, and propelled by a solid motor. The architecture is based on a non-linear, six-degrees-of-freedom model for the generic thrust-vector-controlled launcher dynamics and kinematics, deduced and implemented in a realistic simulation environment. For estimation and control design purposes, a linearized version of the model is proposed. Single-nozzle TVC actuation is adopted, allowing for pitch and yaw control, with the control law being derived from the Linear Quadratic Regulator (LQR) with additional integral action (LQI). The control system is implemented through gain scheduling. Full state estimation is performed resorting to complementary kinematic filters, closely related to linear Kalman fitering theory. The architecture, composed by the navigation and control systems, is tested in simulation environment, demonstrating satisfactory attitude tracking performance and robustness to both external disturbances and model uncertainties.

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arXiv2016

The Variational Attitude Estimator in the Presence of Bias in Angular Velocity Measurements

Estimation of rigid body attitude motion is a long-standing problem of interest in several applications. This problem is challenging primarily because rigid body motion is described by nonlinear dynamics and the state space is nonlinear. The extended Kalman filter and its several variants have remained the standard and most commonly used schemes for attitude estimation over the last several decades. These schemes are obtained as approximate solutions to the nonlinear optimal filtering problem. However, these approximate or near optimal solutions may not give stable estimation schemes in general. The variational attitude estimator was introduced recently to fill this gap in stable estimation of arbitrary rigid body attitude motion in the presence of uncertainties in initial state and unknown measurement noise. This estimator is obtained by applying the Lagrange-d'Alembert principle of variational mechanics to a Lagrangian constructed from residuals between measurements and state estimates with a dissipation term that is linear in the angular velocity measurement residual. In this work, the variational attitude estimator is generalized to include angular velocity measurements that have a constant bias in addition to measurement noise. The state estimates converge to true states almost globally over the state space. Further, the bias estimates converge to the true bias once the state estimates converge to the true states.

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arXiv2011

Approximate Maximum Likelihood Source Localization from Range Measurements Through Convex Relaxation

This work considers the problem of locating a single source from noisy range measurements to a set of nodes in a wireless sensor network. We propose two new techniques that we designate as Source Localization with Nuclear Norm (SLNN) and Source Localization with l1-norm (SL-l1), which extend to arbitrary real dimensions, including 3D, our prior work on 2D source localization formulated in the complex plane. Broadly, our approach is based on formulating a Maximum-Likelihood (ML) estimation problem for the source position, and then using convex relaxation techniques to obtain a semidefinite program (SDP) that can be globally and efficiently solved. SLNN directly approximates the Gaussian ML solution, and the relaxation is shown to be tighter than in other methods in the same class. We present an analysis of the convexity properties of the constraint set for the 2D complex version of SLNN (SLCP) to justify the observed tightness of the relaxation. In terms of global accuracy of localization, SLNN outperforms state-of-the-art optimization-based methods with either iterative or closed-form formulations. We propose the SL-l1 algorithm to address the Laplacian noise case, which models the presence of outliers in range measurements. We overcome the nondifferentiability of the Laplacian likelihood function by rewriting the ML problem as an exact weighted version of the Gaussian case, and compare two solution strategies. One of them is iterative, based on block coordinate descent, and uses SLNN as a subprocessing block. The other, attaining only slightly worse performance, is noniterative and based on an SDP relaxation of the weighted ML problem.

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arXiv2010

Robust Simultaneous Localization of Nodes and Targets in Sensor Networks Using Range-Only Measurements

Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to iteratively maximize a likelihood function (ML), which requires initialization with an approximate solution to avoid convergence towards local extrema. This paper develops methods for handling both Gaussian and Laplacian noise, the latter modeling the presence of outliers in some practical ranging systems that adversely affect the performance of localization algorithms designed for Gaussian noise. A modified Euclidean Distance Matrix (EDM) completion problem is solved for a block of target range measurements to approximately set up initial sensor/target positions, and the likelihood function is then iteratively refined through Majorization-Minimization (MM). To avoid the computational burden of repeatedly solving increasingly large EDM problems in time-recursive operation an incremental scheme is exploited whereby a new target/node position is estimated from previously available node/target locations to set up the iterative ML initial point for the full spatial configuration. The above methods are first derived under Gaussian noise assumptions, and modifications for Laplacian noise are then considered. Analytically, the main challenges to be overcome in the Laplacian case stem from the non-differentiability of $\ell_1$ norms that arise in the various cost functions. Simulation results confirm that the proposed algorithms significantly outperform existing methods for SLAT in the presence of outliers, while offering comparable performance for Gaussian noise.

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arXiv2010

A Sensor-based Long Baseline Position and Velocity Navigation Filter for Underwater Vehicles

This paper presents a novel Long Baseline (LBL) position and velocity navigation filter for underwater vehicles based directly on the sensor measurements. The solution departs from previous approaches as the range measurements are explicitly embedded in the filter design, therefore avoiding inversion algorithms. Moreover, the nonlinear system dynamics are considered to their full extent and no linearizations are carried out whatsoever. The filter error dynamics are globally asymptotically stable (GAS) and it is shown, under simulation environment, that the filter achieves similar performance to the Extended Kalman Filter (EKF) and outperforms linear position and velocity filters based on algebraic estimates of the position obtained from the range measurements.

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