Related papers: Log-linear Backstepping control on $SE_2(3)$
We demonstrate that the error dynamics of a thrusting spacecraft are nearly group affine on the $SE_2(3)$ Lie group, and the nonlinearity can be bounded, or removed with the application of a dynamic inversion control law. A numerical…
In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie…
This paper presents an approach that employs log-linearization in Lie group theory and the Newton-Euler equations to derive exact linear error dynamics for a multi-rotor model, and applies this model with a novel log-linear dynamic…
Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are…
Mechanical control systems such as aerial, marine, space, and terrestrial robots often naturally admit a state-space that has the structure of a Lie group. The kinetic energy of such systems is commonly invariant to the induced action by…
Trajectory tracking for the kinematic unicycle has been heavily studied for several decades. The unicycle admits a natural $\SE(2)$ symmetry, a key structure exploited in many of the most successful nonlinear controllers in the literature.…
This paper presents the integration and experimental validation of advanced control strategies for quadcopters based on Lie groups. We build upon recent theoretical developments on SE2(3)-based controllers and introduce a novel SE2(3) model…
Control systems of interest are often invariant under Lie groups of transformations. For such control systems, a geometric framework based on Lie symmetry is formulated, and from this a sufficient condition for dynamic feedback…
This paper reports on a new error-state Model Predictive Control (MPC) approach to connected matrix Lie groups for robot control. The linearized tracking error dynamics and the linearized equations of motion are derived in the Lie algebra.…
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…
In this paper, we extend the popular integral control technique to systems evolving on Lie groups. More explicitly, we provide an alternative definition of "integral action" for proportional(-derivative)-controlled systems whose…
This paper provides new results for a 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 complexities and…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
Through assembling the navigation parameters as matrix Lie group state, the corresponding inertial navigation system (INS) kinematic model possesses a group-affine property. The Lie logarithm of the navigation state estimation error…
This paper provides nonlinear tracking control systems for a quadrotor unmanned aerial vehicle (UAV) that are robust to bounded uncertainties. A mathematical model of a quadrotor UAV is defined on the special Euclidean group, and nonlinear…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system…
This paper presents a subsystem-based adaptive control framework for serial flexible manipulators with an arbitrary number of links, in which the elastic deformation PDE of each link is carried through the entire control design without…
In real-world robotics applications, accurate models of robot dynamics are critical for safe and stable control in rapidly changing operational conditions. This motivates the use of machine learning techniques to approximate robot dynamics…
This paper addresses the motion control problem for underactuated mechanical systems with full attitude control and one translational force input to manage the six degrees of freedom involved in the three-dimensional Euclidean space. These…