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This paper examines the global convergence problem of SLAM algorithms, an issue that faces topological obstructions. This is because the state-space of attitude dynamics is defined on a non-contractible manifold: the special orthogonal…
This paper employs Geometric Algebra (GA) tools to model the dynamics of objects in 3-dimensional space, serving as a proof of concept to facilitate control design for trajectory tracking in underactuated systems. For control purposes, the…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
In this paper, we describe a geometric setting for higher-order lagrangian problems on Lie groups. Using left-trivialization of the higher-order tangent bundle of a Lie group and an adaptation of the classical Skinner-Rusk formalism, we…
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…
When implementing a non-continuous controller for a cyber-physical system, it may happen that the evolution of the closed-loop system is not anymore piecewise differentiable along the trajectory, mainly due to conditional statements inside…
This paper presents a geometric input-output analysis of hidden modes in distance-based formation control. We study the linearized dynamics under a gradient control law to characterize the system's structural limitations and their dynamic…
This tutorial presents a control-oriented introduction to aided inertial navigation systems using a Lie-group formulation centered on the extended Special Euclidean group SE_2(3). The focus is on developing a clear and…
In this paper, a robust control solution for a satellite equipped with a robotic manipulator is presented. First, the dynamic model of the system is derived based on quaternions to describe the evolution of the attitude of the base…
Despite extensive research on sliding mode control (SMC) design for quadrotors, the existing approaches suffer from certain limitations. Euler angle-based SMC formulations suffer from poor performance in high-pitch or -roll maneuvers.…
Many of the existing works on quadrotor control address the trajectory tracking problem by employing a cascade design in which the translational and rotational dynamics are stabilized by two separate controllers. The stability of the…
We introduce a new hybrid control strategy, which is conceptually different from the commonly used synergistic hybrid approaches, to efficiently deal with the problem of the undesired equilibria that precludes smooth vectors fields on…
The attitude of a rigid body evolves on the three-dimensional special orthogonal group, and it is often estimated by measuring reference directions, such as gravity or magnetic field, using an onboard sensor. As a single direction…
In this paper, we propose and demonstrate an adaptive-sliding mode control for trajectory tracking control of robot manipulators subjected to uncertain dynamics, vibration disturbance, and payload variation disturbance. Throughout this work…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
This paper presents a cascaded control architecture, based on nonlinear dynamic inversion (NDI), for rigid body attitude control. The proposed controller works directly with the rotation matrix parameterization, that is, with elements of…
This paper addresses the problem of estimating the attitude and angular velocity of a rigid object by exploiting its second order kinematic model. The approach is particularly useful in cases where angular velocity measurements are not…
Existing approaches to robust global asymptotic stabilization of a pair of antipodal points on unit $n$-sphere $\mathbb{S}^n$ typically involve the non-centrally synergistic hybrid controllers for attitude tracking on unit quaternion space.…
Over the past few decades, continuous quaternion-based attitude control has been proven highly effective for driving rotational systems that can be modeled as rigid bodies, such as satellites and drones. However, methods rooted in this…
This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the…