Publications | Adeel Akhtar

2026

arXiv

Intrinsic Path Following on SO(3)

Adeel Akhtar

2026

@misc{akhtar2026intrinsicpathfollowingmathsfso3,
  author = {Akhtar, Adeel},
  title = {Intrinsic Path Following on {SO}(3)},
  year = {2026},
  archiveprefix = {arXiv},
  primaryclass = {math.OC},
  url = {https://arxiv.org/abs/2610.04332},
  tags = {intrinsic path following, SO(3), geometric control}
}

Under Review

On the Equivalence of Stochastic Control and Path Space Formulations for Schrödinger Bridges over Compact Connected Lie Groups

Hamza Mahmood, Georgiy A. Bondar, Abhishek Halder, and 1 more author

2026

Under review

arXiv Bib HTML PDF Code Website

@misc{mahmood2026equivalence,
  author = {Mahmood, Hamza and Bondar, Georgiy A. and Halder, Abhishek and Akhtar, Adeel},
  title = {On the Equivalence of Stochastic Control and Path Space Formulations for Schr{\"o}dinger Bridges over Compact Connected Lie Groups},
  year = {2026},
  note = {Under review},
  tags = {Schrodinger bridges, stochastic control, path space formulations, Lie groups}
}

IEEE L-CSS
Learning Neural Maximal Lyapunov Functions on SO(n)

Adeel Akhtar and Matthieu Barreau

IEEE Control Systems Letters, 2026

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Establishing stability guarantees for dynamical systems on Lie groups is a fundamental challenge, as classical Lyapunov methods developed for Euclidean spaces do not directly transfer to curved geometries. In this paper, we propose a framework for learning maximal Lyapunov functions for systems evolving on the special orthogonal group SO(n). Theoretically, we introduce a neural Lyapunov architecture based on the logarithmic map with proven approximation capabilities, and we formulate the learning problem via a Zubov-type characterization of the maximal region of attraction. A key technical contribution is the derivation of explicit, numerically tractable formulas for the derivative of the logarithmic map, enabling training through a two-phase algorithm that balances computational efficiency and accuracy. Empirically, we validate the approach on a low-dimensional nonlinear system.
@article{akhtar2026learning, author = {Akhtar, Adeel and Barreau, Matthieu}, title = {Learning Neural Maximal Lyapunov Functions on {SO}(n)}, journal = {IEEE Control Systems Letters}, year = {2026}, pages = {1711-1716}, doi = {10.1109/LCSYS.2026.3706470}, tags = {learning, Lyapunov functions, SO(n), Lie groups, neural Lyapunov functions} }
IEEE L-CSS
Schrödinger Bridge Over a Compact Connected Lie Group

Hamza Mahmood, Abhishek Halder, and Adeel Akhtar

IEEE Control Systems Letters, 2026

Abs DOI arXiv Bib HTML PDF Code Website

This work studies the Schrödinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while minimizing the control effort. We develop a coordinate-free formulation of this stochastic optimal control problem that respects the underlying geometric structure of the Lie group, thereby avoiding limitations associated with local parameterizations or embeddings in Euclidean spaces. We establish the existence and uniqueness of solution to the corresponding Schrödinger system. Our results are constructive in that they derive a geometric controller that optimally interpolates probability densities supported over the Lie group. To illustrate the results, we provide numerical examples on SO(2) and SO(3). The codes and animations are publicly available at https://gradslab.github.io/SbpLieGroups.
@article{mahmood2026schrodinger, author = {Mahmood, Hamza and Halder, Abhishek and Akhtar, Adeel}, title = {Schr{\"o}dinger Bridge Over a Compact Connected Lie Group}, journal = {IEEE Control Systems Letters}, year = {2026}, pages = {1141-1146}, doi = {10.1109/LCSYS.2026.3705293}, tags = {Schrodinger bridge, stochastic optimal control, Lie groups, Fokker-Planck equation} }

Under Review

Convergence of Primal-Dual Algorithms for Dynamics-Embedded Optimization With Koopman Linearization

S. Park and Adeel Akhtar

In , 2026

Under review

Bib

@inproceedings{park2026primaldual,
  author = {Park, S. and Akhtar, Adeel},
  title = {Convergence of Primal-Dual Algorithms for Dynamics-Embedded Optimization With Koopman Linearization},
  year = {2026},
  note = {Under review},
  tags = {optimization, primal-dual algorithms, Koopman linearization}
}

Under Review

Decentralized Safe Path Following for Multiple Quadrotors on Intersecting Paths with Theoretical Guarantees

Hamza. Tariq and Adeel Akhtar

In , 2026

Under review

arXiv Bib HTML PDF

@inproceedings{tariq2026decentralized,
  author = {Tariq, Hamza. and Akhtar, Adeel},
  title = {Decentralized Safe Path Following for Multiple Quadrotors on Intersecting Paths with Theoretical Guarantees},
  year = {2026},
  note = {Under review},
  tags = {safe path following, multi-agent systems, quadrotors}
}

IEEE CDC

Modeling and Control of a Unicycle Robot on Manifolds

Adeel Akhtar and Mohamed Al Lawati

In Proceedings of the IEEE Conference on Decision and Control, 2026

Accepted

arXiv Bib HTML PDF

@inproceedings{akhtar2026unicyclemanifolds,
  author = {Akhtar, Adeel and Al Lawati, Mohamed},
  title = {Modeling and Control of a Unicycle Robot on Manifolds},
  booktitle = {Proceedings of the IEEE Conference on Decision and Control},
  year = {2026},
  note = {Accepted},
  tags = {unicycle robot, manifolds, geometric control}
}

IEEE CCTA
A Relaxed Quadratic-Program-based Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance

Hamza Tariq, Usman Ali, and Adeel Akhtar

In 2026 IEEE Conference on Control Technology and Applications (CCTA), 2026

Awarded Abs DOI arXiv Bib HTML PDF Code Website

Best Student Paper Award, IEEE CCTA 2026

Dynamic feedback linearization (DFL) is a classical technique for trajectory tracking of unicycle-type mobile robots, but the resulting DFL-based controller becomes singular when the linear velocity vanishes, rendering standard DFL-based controllers unsuitable for stop-and-reverse maneuvers. This paper proposes a quadratic-program (QP)-based optimal control framework that avoids this singularity, while establishing local Lipschitz continuity of the resulting feedback law. Our approach reformulates the DFL constraints as an equality-constrained QP with a slack variable, ensuring feasibility for all states and reference signals, including at points where the robot’s velocity vanishes. By introducing slack variables and tunable parameters, we demonstrate that the singular configuration can be avoided for a large class of reference trajectories. The effectiveness of the proposed approach for trajectory tracking is demonstrated through ROS2–Gazebo simulations on a TurtleBot3 Waffle robot. The code is available at https://gradslab.github.io/DFL_QP_Unicycle/.
@inproceedings{tariq2026relaxedqp, author = {Tariq, Hamza and Ali, Usman and Akhtar, Adeel}, title = {A Relaxed {Quadratic-Program-based} Framework for Trajectory Tracking of Unicycle Robots with Singularity Avoidance}, booktitle = {2026 IEEE Conference on Control Technology and Applications (CCTA)}, year = {2026}, address = {Vancouver, BC, Canada}, pages = {925--930}, publisher = {IEEE}, doi = {10.1109/CCTA62090.2026.11684166}, tags = {trajectory tracking, unicycle robot, quadratic programming, dynamic feedback linearization, singularity avoidance} }
IEEE CCTA
Quasi-Static Fault-Tolerant Feedback Control of a Quadrotor under Rotor Failure with Provable Safety Guarantees

Mohamed Al Lawati and Adeel Akhtar

In 2026 IEEE Conference on Control Technology and Applications (CCTA), 2026

Abs DOI Bib HTML Code Website

This project accompanies a nonlinear control framework for a quadrotor unmanned aerial vehicle experiencing a complete single-rotor failure. Given a geometric curve in three-dimensional space, the method characterizes and stabilizes the zero-dynamics manifold, also called the path-following manifold, which represents all feasible motions along the desired path. Stabilizing this manifold ensures path-invariance: if the UAV is initialized on the path with the appropriate transverse conditions, then the closed-loop vehicle remains on the path despite the rotor failure. The proposed quasi-static feedback controller achieves set stabilization without introducing additional dynamic controller states and provides local exponential convergence to the path-following manifold under regularity conditions. The approach is validated in a physics-based Drake simulation with Meshcat visualization.
@inproceedings{allawati2026quasistatic, author = {Al Lawati, Mohamed and Akhtar, Adeel}, title = {Quasi-Static Fault-Tolerant Feedback Control of a Quadrotor under Rotor Failure with Provable Safety Guarantees}, booktitle = {2026 IEEE Conference on Control Technology and Applications (CCTA)}, year = {2026}, address = {Vancouver, BC, Canada}, pages = {681--686}, publisher = {IEEE}, doi = {10.1109/CCTA62090.2026.11684234}, tags = {fault-tolerant control, quadrotor, rotor failure, path following, safety guarantees} }
IEEE ECC
A Geometric Solution of the Schrödinger Bridge Problem on SO(2) via Stochastic Optimal Control

Hamza Mahmood and Adeel Akhtar

In 2026 European Control Conference (ECC), 2026

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We present a geometric coordinate-free solution to the isotropic Schrödinger bridge problem (SBP) for the kinematic equation on the Lie group SO(2). We consider the angular velocity of the system as the control input and assume that the given initial and terminal state probability density functions defined on SO(2) in our SBP are continuous and strictly positive. We solve the SBP by proving the existence and uniqueness of a solution to the so-called Schrödinger system of equations on SO(2), by showing that a fixed-point recursion is contractive in a complete metric space with respect to Hilbert’s projective metric. The geometric controller thus designed only uses the intrinsic geometric structure of SO(2) and does not embed it in the Euclidean plane to achieve the optimal density control. The numerical simulation verifies the validity of the theoretical construction of the Schrödinger bridge. The code and animations are publicly available at https://gitlab.com/a5akhtar/sbp.
@inproceedings{mahmood2026geometricbridge, author = {Mahmood, Hamza and Akhtar, Adeel}, title = {A Geometric Solution of the Schr{\"o}dinger Bridge Problem on {SO}(2) via Stochastic Optimal Control}, booktitle = {2026 European Control Conference (ECC)}, year = {2026}, pages = {2283--2288}, publisher = {IEEE}, tags = {Schrodinger bridge, SO(2), stochastic optimal control, Lie groups, Hilbert projective metric} }
IEEE ECC
Path-following Control of a Quadrotor using Quasi-Static Transverse Feedback Linearization

Mohamed Al Lawati and Adeel Akhtar

In 2026 European Control Conference (ECC), 2026

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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 x 3 decoupling matrix rather than a 4 x 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 https://gitlab.com/a5akhtar/quasistatic-tfl-uav/.
@inproceedings{allawati2026setstabilization, author = {Al Lawati, Mohamed and Akhtar, Adeel}, title = {Path-following Control of a Quadrotor using Quasi-Static Transverse Feedback Linearization}, booktitle = {2026 European Control Conference (ECC)}, year = {2026}, pages = {3454--3459}, publisher = {IEEE}, tags = {path following, quadrotor, quasi-static feedback linearization, transverse feedback linearization} }

2025

arXiv
A Safe Hybrid Control Framework for Car-like Robot With Guaranteed Global Path-Invariance Using a Control Barrier Function

Nan Wang, Adeel Akhtar, and Ricardo G. Sanfelice

2025

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This work proposes a hybrid framework for car-like robots with obstacle avoidance, global convergence, and safety, where safety is interpreted as path invariance, namely, once the robot converges to the path, it never leaves the path. Given a priori obstacle-free feasible path where obstacles can be around the path, the task is to avoid obstacles while reaching the path and then staying on the path without leaving it. The problem is solved in two stages. Firstly, we define a “tight” obstacle-free neighborhood along the path and design a local controller to ensure convergence to the path and path invariance. The control barrier function technology is involved in the control design to steer the system away from its singularity points, where the local path invariant controller is not defined. Secondly, we design a hybrid control framework that integrates this local path-invariant controller with any global tracking controller from the existing literature without path invariance guarantee, ensuring convergence from any position to the desired path, namely, global convergence. This framework guarantees path invariance and robustness to sensor noise. Detailed simulation results affirm the effectiveness of the proposed scheme.
@misc{wang2025safehybrid, author = {Wang, Nan and Akhtar, Adeel and Sanfelice, Ricardo G.}, title = {A Safe Hybrid Control Framework for Car-like Robot With Guaranteed Global Path-Invariance Using a Control Barrier Function}, year = {2025}, archiveprefix = {arXiv}, primaryclass = {cs.RO}, tags = {safe hybrid control, car-like robot, control barrier functions, path invariance, obstacle avoidance} }

AIAA

Acceleration Feedback Control for Atmospheric Reduced Gravity Flights

M. Aldosari, Y. H. Chen, Adeel Akhtar, and 1 more author

In AIAA SciTech Forum, 2025

DOI Bib HTML PDF

@inproceedings{aldosari2025acceleration,
  author = {Aldosari, M. and Chen, Y. H. and Akhtar, Adeel and Feron, Eric},
  title = {Acceleration Feedback Control for Atmospheric Reduced Gravity Flights},
  booktitle = {AIAA SciTech Forum},
  year = {2025},
  address = {Orlando, FL, USA},
  doi = {10.2514/6.2025-2082},
  tags = {flight control, acceleration feedback, reduced gravity}
}

IEEE ACC
Path Invariance of a Quadrotor System Under Cyber Attacks With Theoretical Guarantees

Hamza Mahmood, Usman Ali, and Adeel Akhtar

In Proceedings of the American Control Conference, 2025

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This paper presents a path-following controller for a quadrotor system to guarantee safe maneuvers, in terms of forward path invariance, in the presence of cyber-physical attacks. We assume that an adversarial agent can control any one of the rotors through a false data injection (FDI) type of attack. A feedback controller is designed using transverse feedback linearization which guarantees that the system follows a class of smooth curves under FDI attacks. Our proposed controller is computationally efficient, with a closed-form analytical expression, that not only mitigates the effect of bounded malicious signal but also ensures mission success. We provide theoretical guarantees of forward path invariance under FDI attacks with realistic assumptions and demonstrate the effectiveness of our approach through simulation.
@inproceedings{mahmood2025pathinvariance, author = {Mahmood, Hamza and Ali, Usman and Akhtar, Adeel}, title = {Path Invariance of a Quadrotor System Under Cyber Attacks With Theoretical Guarantees}, booktitle = {Proceedings of the American Control Conference}, year = {2025}, pages = {972--977}, publisher = {IEEE}, doi = {10.23919/ACC63710.2025.11107889}, tags = {path invariance, quadrotor, cyber attacks, false data injection, transverse feedback linearization} }

2023

IEEE ACC
Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)

Adeel Akhtar and Ricardo G. Sanfelice

In Proceedings of the American Control Conference, 2023

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This paper proposes global accelerated nonconvex geometric (GANG) optimization algorithms for optimizing a class of nonconvex functions on the compact Lie group SO(3). Nonconvex optimization is a challenging problem because the objective function may have multiple critical points, including saddle points. We propose two accelerated geometric algorithms to escape maxima and saddle points using random perturbations. The first algorithm uses the value of the Hessian of the objective function and random perturbations to escape the undesired critical points. In contrast, the second algorithm uses only the gradient information and random perturbations to escape maxima and saddle points. The efficacy of these geometric algorithms is verified in simulations.
@inproceedings{akhtar2023heavyball, author = {Akhtar, Adeel and Sanfelice, Ricardo G.}, title = {Global Accelerated Nonconvex Geometric Optimization Methods on {SO}(3)}, booktitle = {Proceedings of the American Control Conference}, year = {2023}, pages = {3554--3559}, publisher = {IEEE}, doi = {10.23919/ACC55779.2023.10155919}, tags = {geometric optimization, nonconvex optimization, Lie groups, SO(3), accelerated methods} }
IEEE TIE
Path Following of a Quadrotor With a Cable-Suspended Payload

Adeel Akhtar, Sajid Saleem, and Jinjun Shan

IEEE Transactions on Industrial Electronics, 2023

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This article addresses the design of a path following controller for a payload tethered to a quadrotor. Specifically, the goal is to design a smooth dynamic feedback controller that forces the suspended payload to converge and follow a large class of embedded curves. The given curve is treated as a smooth manifold, and set stabilization is used to find the maximal control invariant manifold. The controller design guarantees that once the aerial robot approaches the path, the payload never leaves the path. The performance of the proposed controller is verified through simulations with practical sensor noise and parametric uncertainties. Moreover, experimental implementation and verification of the proposed control scheme are performed on a Quanser UAV platform in an indoor flying arena.
@article{akhtar2023cablesuspended, author = {Akhtar, Adeel and Saleem, Sajid and Shan, Jinjun}, title = {Path Following of a Quadrotor With a Cable-Suspended Payload}, journal = {IEEE Transactions on Industrial Electronics}, year = {2023}, volume = {70}, number = {2}, pages = {1646--1654}, publisher = {IEEE}, doi = {10.1109/TIE.2022.3167130}, tags = {path following, quadrotor, cable-suspended payload, set stabilization, UAV} }

2022

IEEE CDC

Hybrid Geometric Controllers for Fully-Actuated Left-Invariant Systems on Matrix Lie Groups

Adeel Akhtar and Ricardo G. Sanfelice

In Proceedings of the IEEE Conference on Decision and Control, 2022

DOI Bib HTML PDF

@inproceedings{akhtar2022leftinvariant,
  author = {Akhtar, Adeel and Sanfelice, Ricardo G.},
  title = {Hybrid Geometric Controllers for Fully-Actuated Left-Invariant Systems on Matrix Lie Groups},
  booktitle = {Proceedings of the IEEE Conference on Decision and Control},
  year = {2022},
  pages = {1855--1860},
  publisher = {IEEE},
  doi = {10.1109/CDC51059.2022.9992659},
  tags = {hybrid geometric control, Lie groups, matrix Lie groups, left-invariant systems, global stabilization}
}

IEEE ACC
Coordinated Path Following for a Class of Underactuated Multi-Agent System Using Nested Set Stabilization

Adeel Akhtar

In Proceedings of the American Control Conference, 2022

Single-author paper

Awarded Abs DOI Bib HTML PDF Video

Single-author paper

This paper addresses the multi-agent coordinated path following problem consisting of a class of underactuated vehicles capable of following a class of closed embedded curves in the three-dimensional space and proposes a solution using a nested set stabilization approach. The stabilization of the first set restricts each agent to the assigned path following manifold and ensures that each system stays on the path indefinitely when initialized in the neighborhood of the path. Stabilizing the second set, contained inside the first, solves the position, velocity, acceleration, or jerk-related coordination constraints. The third set, contained in the second set, satisfies the yaw, or yaw-rate-related coordination constraints. The reduction theorem establishes the asymptotic stability of each nested set, and as a result, the multi-agent coordinated path following problem is solved.
@inproceedings{akhtar2022coordinated, author = {Akhtar, Adeel}, title = {Coordinated Path Following for a Class of Underactuated Multi-Agent System Using Nested Set Stabilization}, booktitle = {Proceedings of the American Control Conference}, year = {2022}, pages = {1230--1235}, publisher = {IEEE}, doi = {10.23919/ACC53348.2022.9867249}, note = {Single-author paper}, tags = {coordinated path following, multi-agent systems, underactuated systems, nested set stabilization} }
IEEE ACC
A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on S^1

Adeel Akhtar and Ricardo G. Sanfelice

In Proceedings of the American Control Conference, 2022

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This paper proposes a hybrid geometric control scheme for the classical problem of globally stabilizing a point-mass system on a unit circle, as it is impossible to design a smooth globally asymptotically stable controller for this problem. Unlike most existing solutions that rely on coordinates and rely on a particular controller construction, our proposed solution is coordinate free, or geometric, and belongs to a class of controllers that we also characterize. Specifically, we propose a geometric hybrid controller that uses a local geometric controller from the said class and an open-loop geometric controller. The system achieves global asymptotic stability when each controller from the local geometric class is combined with the geometric open-loop controller using a hybrid systems framework. Moreover, the hybrid geometric controller guarantees robust asymptotic stability. Simulations validate the stability properties of the proposed hybrid geometric controller.
@inproceedings{akhtar2022sphere, author = {Akhtar, Adeel and Sanfelice, Ricardo G.}, title = {A Class of Hybrid Geometric Controllers for Robust Global Asymptotic Stabilization on {S}^1}, booktitle = {Proceedings of the American Control Conference}, year = {2022}, pages = {874--879}, publisher = {IEEE}, doi = {10.23919/ACC53348.2022.9867666}, tags = {hybrid geometric control, unit circle, S1, robust stabilization, global asymptotic stability} }
IEEE TCST
Path Invariant Controllers for a Quadrotor With a Cable-Suspended Payload Using a Global Parameterization

Adeel Akhtar, Sajid Saleem, and Jinjun Shan

IEEE Transactions on Control Systems Technology, 2022

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Payload delivery using unmanned aerial vehicles (UAVs) has attained central importance for smart logistics and transportation systems in the context of the fourth industrial revolution. This work considers the problem of designing a smooth dynamic feedback control law for a point mass payload suspended to a quadrotor and making the load to follow a large class of curves that includes both closed and non-closed curves. Typically, the load path following problem is solved using either a coordinate-free or a local-coordinate-based approach. However, in this article, we adopt an alternative methodology. First, we express the system dynamics in an extended Euclidean space using a global coordinate system. Second, we propose two families of functions that lead to the design of almost-global and local controllers in terms of region of convergence. We cast the load path following problem in the framework of set stabilization, and as a result, the proposed controllers make the given path an invariant manifold. The resulting controllers guarantee that once the suspended load converges to the path, it stays on the path indefinitely while satisfying other application-specific constraints. Finally, to complement the theoretical results, we provide a successful real-world experimental validation of the proposed controller on a Quanser QDrone UAV platform with a cable-suspended payload.
@article{akhtar2022pathinvariant, author = {Akhtar, Adeel and Saleem, Sajid and Shan, Jinjun}, title = {Path Invariant Controllers for a Quadrotor With a Cable-Suspended Payload Using a Global Parameterization}, journal = {IEEE Transactions on Control Systems Technology}, year = {2022}, volume = {30}, number = {5}, pages = {2002--2017}, publisher = {IEEE}, doi = {10.1109/TCST.2021.3133693}, tags = {path invariant control, quadrotor, cable-suspended payload, global parameterization, set stabilization} }

2021

IEEE TAC
Controller Class for Rigid Body Tracking on SO(3)

Adeel Akhtar and Steven L. Waslander

IEEE Transactions on Automatic Control, 2021

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In this article, we propose a novel family of Lie algebra valued functions on the special orthogonal group SO(3). Each function belonging to this family induces a novel controller that stabilizes a rigid body attitude. All controllers induced by the family form a controller class. This novel controller class contains both local and almost-global asymptotically stable controllers, and this article presents geometric stability results of the whole controller class.
@article{akhtar2021rigidbody, author = {Akhtar, Adeel and Waslander, Steven L.}, title = {Controller Class for Rigid Body Tracking on {SO}(3)}, journal = {IEEE Transactions on Automatic Control}, year = {2021}, volume = {66}, number = {5}, pages = {2234--2241}, publisher = {IEEE}, doi = {10.1109/TAC.2020.3008295}, tags = {geometric control, rigid body, SO(3), attitude control, coordinate-free control} }

2020

IEEE ACC
Feedback Linearizing Controllers on SO(3) Using a Global Parametrization

Adeel Akhtar, Sajid Saleem, and Steven L. Waslander

In Proceedings of the American Control Conference, 2020

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We present a methodology for studying the stabilization problem of a fully-actuated rotating rigid body. Since a rigid body attitude is represented by a rotation matrix in three dimensions, we exploit this fact and use each element of the rotation matrix as a parameter. This nine-parameter representation is global as well as unique, and results in a simplified set of nonlinear differential equations. We apply feedback linearization to design both local and almost global controllers. We also propose two novel definitions of feedback linearization functions, and prove that they lead to a well-defined vector relative degree and, as a result, almost-globally and locally stable controllers with bounded internal states. Using the proposed methodology, we present detailed examples of two such functions, demonstrating stabilization performance for each resulting controller on a rigid body system.
@inproceedings{akhtar2020feedbacklinearizing, author = {Akhtar, Adeel and Saleem, Sajid and Waslander, Steven L.}, title = {Feedback Linearizing Controllers on {SO}(3) Using a Global Parametrization}, booktitle = {Proceedings of the American Control Conference}, year = {2020}, pages = {1441--1446}, publisher = {IEEE}, doi = {10.23919/ACC45564.2020.9147963}, tags = {feedback linearization, SO(3), global parameterization, rigid body control} }
IEEE Access
Path Following for a Class of Underactuated Systems Using Global Parameterization

Adeel Akhtar, Sajid Saleem, and Steven L. Waslander

IEEE Access, 2020

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A large number of both aerial and underwater mobile robots fall in the category of underactuated systems that are defined on a manifold, which is not isomorphic to Euclidean space. Traditional approaches to designing controllers for such systems include geometric approaches and local coordinate-based representations. In this paper, we propose a global parameterization of the special orthogonal group, denoted by SO(3), to design path-following controllers for underactuated systems. In particular, we present a nine-dimensional representation of SO(3) that leads to controllers achieving path-invariance for a large class of both closed and non-closed embedded curves. On the one hand, this over-parameterization leads to a simple set of differential equations and provides a global non-ambiguous representation of systems as compared to other local or minimal parametric approaches. On the other hand, this over-parameterization also leads to uncontrolled internal dynamics, which we prove to be bounded and stable. The proposed controller, when applied to a quadrotor system, is capable of recovering the system from challenging situations such as initial upside-down orientation and also capable of performing multiple flips.
@article{akhtar2020underactuated, author = {Akhtar, Adeel and Saleem, Sajid and Waslander, Steven L.}, title = {Path Following for a Class of Underactuated Systems Using Global Parameterization}, journal = {IEEE Access}, year = {2020}, volume = {8}, pages = {34737--34749}, publisher = {IEEE}, doi = {10.1109/ACCESS.2020.2974153}, tags = {path following, underactuated systems, global parameterization, SO(3)} }

2018

Ph.D. Thesis

Nonlinear and Geometric Controllers for Rigid Body Vehicles

Adeel Akhtar

University of Waterloo, 2018

Bib HTML

@phdthesis{akhtar2018phdthesis,
  author = {Akhtar, Adeel},
  title = {Nonlinear and Geometric Controllers for Rigid Body Vehicles},
  school = {University of Waterloo},
  year = {2018},
  publisher = {UWSpace},
  tags = {geometric control, nonlinear control, rigid body vehicles, path following}
}

2015

IEEE T-RO
Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots

Adeel Akhtar, Steven L. Waslander, and Christopher Nielsen

IEEE Transactions on Robotics, 2015

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This paper presents an approach for designing path-following controllers for the kinematic model of car-like mobile robots using transverse feedback linearization with dynamic extension. This approach is applicable to a large class of paths and its effectiveness is experimentally demonstrated on a Chameleon R100 Ackermann steering robot. Transverse feedback linearization makes the desired path attractive and invariant, while the dynamic extension allows the closed-loop system to achieve the desired motion along the path.
@article{akhtar2015dynamic, author = {Akhtar, Adeel and Waslander, Steven L. and Nielsen, Christopher}, title = {Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots}, journal = {IEEE Transactions on Robotics}, year = {2015}, volume = {31}, number = {2}, pages = {269--279}, publisher = {IEEE}, doi = {10.1109/TRO.2015.2395711}, tags = {path following, mobile robots, transverse feedback linearization, car-like robots} }

2013

IEEE CDC
Fault Tolerant Path Following for a Quadrotor

Adeel Akhtar, Steven L. Waslander, and Christopher Nielsen

In Proceedings of the 52nd IEEE Conference on Decision and Control, Dec 2013

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This paper presents a path following controller for a quadrotor UAV experiencing a single rotor failure. A smooth, dynamic feedback control law is proposed that allows the quadrotor to follow both closed and non-closed embedded curves while maintaining a desired velocity profile along the path when one out of four motors is completely disabled due to failure. The nonlinear model of the quadrotor is transformed into a partially linear model by a coordinate and feedback transformation. A path following controller is designed for transformed system that guarantees invariance of the path. The uncontrolled nonlinear portion of the dynamics (internal dynamics) are shown to be bounded.
@inproceedings{akhtar2013faulttolerant, author = {Akhtar, Adeel and Waslander, Steven L. and Nielsen, Christopher}, title = {Fault Tolerant Path Following for a Quadrotor}, booktitle = {Proceedings of the 52nd IEEE Conference on Decision and Control}, year = {2013}, month = dec, pages = {847--852}, publisher = {IEEE}, doi = {10.1109/CDC.2013.6759988}, tags = {fault-tolerant control, quadrotor, path following} }

2012

IEEE CDC
Path Following for a Quadrotor Using Dynamic Extension and Transverse Feedback Linearization

Adeel Akhtar, Steven L. Waslander, and Christopher Nielsen

In Proceedings of the 51st IEEE Conference on Decision and Control, Dec 2012

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This work presents a path following controller for a quadrotor vehicle. A smooth, dynamic, feedback controller is designed that allows the quadrotor to follow both closed and non-closed embedded curves while maintaining a desired speed, a desired acceleration or while stabilizing desired points along the curves. The nonlinear dynamic model of the quadrotor is transformed into a linear system via a coordinate and feedback linearization transformation. Once transformed, a path following controller is designed that guarantees invariance of the path while enforcing the desired motion along the path.
@inproceedings{akhtar2012quadrotor, author = {Akhtar, Adeel and Waslander, Steven L. and Nielsen, Christopher}, title = {Path Following for a Quadrotor Using Dynamic Extension and Transverse Feedback Linearization}, booktitle = {Proceedings of the 51st IEEE Conference on Decision and Control}, year = {2012}, month = dec, pages = {3551--3556}, publisher = {IEEE}, doi = {10.1109/CDC.2012.6425945}, tags = {quadrotor, path following, transverse feedback linearization} }
AIAA
Relative Position-Based Visual Servoing Control for Quadrotors

M. Tribou, Adeel Akhtar, and Steven L. Waslander

In AIAA Guidance, Navigation, and Control Conference, Aug 2012

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This paper presents a position-based visual servoing control system that allows a quadrotor aerial robot with a single onboard camera to track a four degree of freedom relative pose trajectory with respect to a free-moving unknown target object composed of visual point features. The proposed vision system is able to estimate both the six degree of freedom relative motion and the target object model structure using only the images captured from the camera and recover scale using a minimal set of inter-feature point distances. An inner-loop attitude controller is used with an outer-loop position trajectory tracking control law to follow a relative trajectory with respect to the target object, while both bodies move in the inertial frame. The performance of the proposed algorithms are evaluated in simulation.
@inproceedings{tribou2012visualservoing, author = {Tribou, M. and Akhtar, Adeel and Waslander, Steven L.}, title = {Relative Position-Based Visual Servoing Control for Quadrotors}, booktitle = {AIAA Guidance, Navigation, and Control Conference}, year = {2012}, month = aug, publisher = {American Institute of Aeronautics and Astronautics}, doi = {10.2514/6.2012-5049}, tags = {visual servoing, quadrotor, vision-based control} }

2011

IEEE CDC-ECC

Path Following for a Car-Like Robot Using Transverse Feedback Linearization and Tangential Dynamic Extension

Adeel Akhtar and Christopher Nielsen

In Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, 2011

DOI Bib HTML

@inproceedings{akhtar2011carlike,
  author = {Akhtar, Adeel and Nielsen, Christopher},
  title = {Path Following for a Car-Like Robot Using Transverse Feedback Linearization and Tangential Dynamic Extension},
  booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference},
  year = {2011},
  pages = {7974--7979},
  publisher = {IEEE},
  doi = {10.1109/CDC.2011.6161413},
  tags = {path following, car-like robot, transverse feedback linearization, tangential dynamic extension}
}

M.A.Sc. Thesis

Dynamic Path Following Controllers for Planar Mobile Robots

Adeel Akhtar

University of Waterloo, 2011

Bib HTML

@mastersthesis{akhtar2011mastersthesis,
  author = {Akhtar, Adeel},
  title = {Dynamic Path Following Controllers for Planar Mobile Robots},
  school = {University of Waterloo},
  year = {2011},
  publisher = {UWSpace},
  tags = {path following, mobile robots, transverse feedback linearization, dynamic extension}
}

2007

WSEAS

Design, Implementation and Real-Time Digital Control of a Cart-Mounted Inverted Pendulum Using Atmel AVR Microcontroller

K. Altaf, Adeel Akhtar, S. Rehman, and 1 more author

In Proceedings of the 6th WSEAS International Conference on Signal Processing, Robotics and Automation, 2007

Bib

@inproceedings{altaf2007invertedpendulum,
  author = {Altaf, K. and Akhtar, Adeel and Rehman, S. and Iqbal, J.},
  title = {Design, Implementation and Real-Time Digital Control of a Cart-Mounted Inverted Pendulum Using Atmel AVR Microcontroller},
  booktitle = {Proceedings of the 6th WSEAS International Conference on Signal Processing, Robotics and Automation},
  year = {2007},
  address = {Corfu Island, Greece},
  tags = {inverted pendulum, real-time control, microcontroller}
}