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In this paper, the dynamics of nonholonomic systems on Lie groups with a left-invariant kinetic energy and left-invariant constraints are considered. Equations of motion form a closed system of differential equations on the corresponding…
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…
We present the identification of the non-linear dynamics of a novel hovercraft design, employing end-to-end deep learning techniques. Our experimental setup consists of a hovercraft propelled by racing drone propellers mounted on a…
Unmanned vehicle navigation concerns estimating attitude, position, and linear velocity of the vehicle the six degrees of freedom (6 DoF). It has been known that the true navigation dynamics are highly nonlinear modeled on the Lie Group of…
Spacecraft operations are influenced by uncertainties such as dynamics modeling, navigation, and maneuver execution errors. Although mission design has traditionally incorporated heuristic safety margins to mitigate the effect of…
Alignment of the strapdown inertial navigation system (INS) has strong nonlinearity, even worse when maneuvers, e.g., tumbling techniques, are employed to improve the alignment. There is no general rule to attack the observability of a…
This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical…
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 provides new results for a robust adaptive tracking control of the attitude dynamics of a rigid body. Both of the attitude dynamics and the proposed control system are globally expressed on the special orthogonal group, to avoid…
This paper investigates the robust nonlinear close formation control problem. It aims to achieve precise position control at dynamic flight operation for a follower aircraft under the aerodynamic impact due to the trailing vortices…
This letter considers model predictive control of a tandem-rotor helicopter. The error is formulated using the matrix Lie group $SE_2(3)$. A reference trajectory to a target is calculated using a quartic guidance law, leveraging the…
Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently…
This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…
The control of free-floating robots requires dealing with several challenges. The motion of such robots evolves on a continuous manifold described by the Special Euclidean Group of dimension 3, known as SE(3). Methods from finite horizon…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The…
It is quite often claimed, and correctly so, that linear methods cannot achieve global stability results for attitude control, and conversely that nonlinear control is essential in order to achieve (almost) globally stable tracking of…
This paper presents nonlinear tracking control systems for a quadrotor unmanned aerial vehicle under the influence of uncertainties. Assuming that there exist unstructured disturbances in the translational dynamics and the attitude…
Previous results reported in the robotics literature show the relationship between time-delay control (TDC) and proportional-integral-derivative control (PID). In this paper, we show that incremental nonlinear dynamic inversion (INDI) -…
We consider the hovering control problem for a class of multi-rotor aerial platforms with generically oriented propellers. Given the intrinsically coupled translational and rotational dynamics of such vehicles, we first discuss some…