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In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving…
We describe a new method to formulate classical Lagrangian mechanics on a finite-dimensional Lie group. This new approach is much more pedagogical than many previous treatments of the subject, and it directly introduces students to…
Model-based controllers can offer strong guarantees on stability and convergence by relying on physically accurate dynamic models. However, these are rarely available for high-dimensional mechanical systems such as deformable objects or…
In this paper, we present a learning-based tracking controller based on Gaussian processes (GP) for collision avoidance of multi-agent systems where the agents evolve in the special Euclidean group in the space SE(3). In particular, we use…
The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are…
In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce…
In this paper we will discuss some new developments in the design of numerical methods for optimal control problems of Lagrangian systems on Lie groups. We will construct these geometric integrators using discrete variational calculus on…
In the evolving landscape of high-speed agile quadrotor flight, achieving precise trajectory tracking at the platform's operational limits is paramount. Controllers must handle actuator constraints, exhibit robustness to disturbances, and…
We study whether second-order systems can be made to behave like prescribed first-order dynamical systems through feedback control. More precisely, we study whether prescribed vector fields on compact smooth manifolds, viewed geometrically…
This paper formalizes Hamiltonian-Informed Optimal Neural (Hion) controllers, a novel class of neural network-based controllers for dynamical systems and explicit non-linear model-predictive control. Hion controllers estimate future states…
We propose a new central synergistic hybrid approach for global exponential stabilization on the Special Orthogonal group SO(3). We introduce a new switching concept relying on a central family of (possibly) non-differentiable potential…
This paper presents a contact-aided inertial-kinematic floating base estimation for humanoid robots considering an evolution of the state and observations over matrix Lie groups. This is achieved through the application of a geometrically…
We extend the method of controlled Lagrangians with kinetic shaping to those mechanical systems on semidirect product Lie groups with broken symmetry, more specifically to the Euler--Poincar\'e equations with advected parameters. We find a…
In this paper, we present a novel cascade control structure with formal guarantees of uniform almost global asymptotic stability for the state tracking error dynamics of a quadcopter. The proposed approach features a model predictive…
This paper proposes a real-time neural network (NN) stochastic filter-based controller on the Lie Group of the Special Orthogonal Group $SO(3)$ as a novel approach to the attitude tracking problem. The introduced solution consists of two…
We extend the Euler Poincare formalism from Lie groups to Lie groupoids for optimal control problems. While Lie algebroids provide the standard infinitesimal framework, the groupoid formulation enables global trajectory reconstruction and…
This paper considers a combination of actuation tendons and measurement strings to achieve accurate shape sensing and direct kinematics of continuum robots. Assuming general string routing, a methodical Lie group formulation for the shape…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
The controllability issue of control-affine systems on smooth manifolds is one of the main problems in the theory, and it is recently known [Jouan P. Equivalence of control systems with linear systems on Lie groups and homogeneous spaces.…
This paper presents a theoretical framework for analyzing the stability of higher-order geometric nonlinear control laws for attitude control on the Special Orthogonal Group $\mathrm{SO(3)}$. In particular, the paper extends existing…