arXiv subjects

Mohamed Al Lawati

Publications and source records attributed to Mohamed Al Lawati.

3 recordsLinked to original sources

arXiv2026

Modeling and Control of a Unicycle Robot on Manifolds

This paper studies path-following control for a kinematic unicycle evolving on a smooth manifold embedded in $\mathbb{R}^3$. The objective is to stabilize a one-dimensional path on the manifold without imposing a temporal parameterization, thereby distinguishing the problem from trajectory tracking. Working in a geometric framework, we propose two feedback laws: a static controller for prescribed nonzero translational speed and a dynamic controller based on a dynamic extension of the translational speed. By lifting the path to the unit tangent bundle of the surface, we characterize the corresponding path-following manifold and establish its control invariance. We then show that the proposed controllers render the path-following manifold locally exponentially stable under suitable regularity conditions. A numerical simulation illustrates the proposed controller. Code and animations are publicly available at https://gradslab.github.io/UnicycleOnManifolds/.

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arXiv2026

Quasi-Static Fault-Tolerant Feedback Control of a Quadrotor under Rotor Failure with Provable Safety Guarantees

This paper presents a nonlinear control law for a quadrotor unmanned aerial vehicle (UAV) under single-rotor failure that guarantees set stabilization via quasi-static feedback (QSF). Given a geometric curve in three-dimensional space, we characterize and stabilize the zero-dynamics manifold, also known as the path-following manifold, which represents all feasible motions along the path. Stabilizing this manifold ensures path-invariance: a UAV with a failed rotor initialized on the path with an appropriate orientation remains on the path for all future time. Furthermore, local exponential convergence to the manifold is guaranteed under certain conditions, implying that, under the stated assumptions, rotor failure during flight does not cause transverse deviation from the path. The proposed controller thus provides theoretical safety guarantees, which are validated through numerical experiments in the Drake physics-based simulation engine. The code is publicly available at https://gradslab.github.io/quasistatic-ftc/.

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arXiv2026

Path-following Control of a Quadrotor using Quasi-Static Transverse Feedback Linearization

We propose a quasi-static transverse feedback linearization (QSTFL) controller for a quadrotor to follow a prescribed geometric path, rather than a time-parameterized trajectory. In contrast to existing dynamic-feedback approaches, the controller does not introduce additional controller states. The thrust input is computed algebraically from the current state, eliminating the need for thrust-derivative measurements and numerical integration. The proposed design renders the path-following manifold invariant, ensuring that trajectories initialized on the path remain on it for all future time, while simultaneously regulating tangential velocity and yaw. We establish a diffeomorphic coordinate transformation and prove local exponential stability of the path-following manifold. In addition, closed-form expressions are derived for the thrust and torque inputs. Compared with dynamic-feedback constructions, the controller requires inversion of only a $3\times 3$ decoupling matrix rather than a $4\times 4$ one, leading to a simpler control law and reduced computational complexity. Numerical simulations demonstrate the effectiveness of the proposed method. Code and animations are publicly available at \footnotesize{\texttt{\href{https://gitlab.com/a5akhtar/quasistatic-tfl-uav/}{https://gitlab.com/a5akhtar/quasistatic-tfl-uav/}}}.

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