Related papers: Log-linear Backstepping control on $SE_2(3)$
For controller design for systems on manifolds embedded in Euclidean space, it is convenient to utilize a theory that requires a single global coordinate system on the ambient Euclidean space rather than multiple local charts on the…
One of the core advantages of SE2(3) Lie group framework for navigation modeling lies in the autonomy of error propagation. In the previous paper, the theoretical analysis of autonomy property of navigation model in inertial, earth and…
A novel, model free, approach to experimental closed-loop flow control is implemented on a separated flow. Feedback control laws are generated using genetic programming where they are optimized using replication, mutation and cross-over of…
This paper presents a differential geometric control approach that leverages SE(3) group invariance and equivariance to increase transferability in learning robot manipulation tasks that involve interaction with the environment.…
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…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
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…
This paper investigates the optimal co-design of logical and continuous controls for switched linear systems governed by controlled logical switching dynamics. Unlike traditional switched systems with arbitrary or state-dependent switching,…
The growing interest in space activities has led to the emergence of new space operators and innovative mission concepts. Small satellites such as CubeSats reduce mission costs and are typically deployed in constellations or formation…
This paper presents a geometric framework for analysis of dynamics of flapping wing micro aerial vehicles (FWMAV) which achieve locomotion in the special Euclidean group SE(3) using internal shape changes. We review the special structure of…
This paper presents a new geometric adaptive control system with state inequality constraints for the attitude dynamics of a rigid body. The control system is designed such that the desired attitude is asymptotically stabilized, while the…
Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on…
The PID controller is an elegant and versatile controller for set point tracking in double integrator systems of which mechanical systems evolving on Euclidean space constitute a large class. But since mechanical systems are typically…
In this paper, we propose an approach to designing online feedback controllers for input-saturated robotic systems evolving on Lie groups by extending the recently developed Sequential Action Control (SAC). In contrast to existing feedback…
This paper deals with the stabilization of a class of linear infinite-dimensional systems with unbounded control operators and subject to a boundary disturbance. We assume that there exists a linear feedback law that makes the origin of the…
The design of an invariant tracking control law for the kinematic car driving on a sphere is discussed. Using a Lie group framework a left-invariant description on SO(3) is derived. Basic geometric considerations allow a direct comparison…
Let H denote the 3-dimensional Heisenberg Lie group. The present paper classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups and expose a detailed study on the control behavior…
This paper presents the development of a sliding mode controller using the backstepping approach. The controller is employed to synthesize tracking errors and Lyapunov functions. A novel state-space representation is formulated by…
Robust control design is mainly devoted to guarantee closed-loop stability of a model-based control law in presence of parametric and structural uncertainties. The control law is usually a complex feedback law which is derived from a…
This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…