相关论文: A Comparison Between Lie Group- and Lie Algebra- B…

After its introduction, impedance control has been utilized as a primary control scheme for robotic manipulation tasks that involve interaction with unknown environments. While impedance control has been extensively studied, the geometric…

This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to…

In this paper, we present an impedance control framework on the SE(3) manifold, which enables force tracking while guaranteeing passivity. Building upon the unified force-impedance control (UFIC) and our previous work on geometric impedance…

This paper shows how left and right actions of Lie groups on a manifold may be used to complement one another in a variational reformulation of optimal control problems equivalently as geodesic boundary value problems with symmetry. We…

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…

Lie algebras provide a useful framework for theoretical analysis in quantum machine learning, particularly in hybrid quantum-classical learning. From the viewpoint of function approximation, expectation values of parameterized quantum…

We demonstrate that the proper general setting for contrast (potential) functions in statistical and information geometry is the one provided by Lie groupoids and Lie algebroids. The contrast functions are defined on Lie groupoids and give…

We study safety-critical control on fully actuated mechanical systems by means of Zeroing Control Barrier Functions (ZCBFs) defined on Lie Groups. Specifically, we introduce and theoretically validate two classes of ZCBFs. The first…

The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the…

Most of the rigid-body systems which evolve on nonlinear Lie groups where Euclidean control designs lose geometric meaning. In this paper, we introduce a log-linear backstepping control law on SE2(3) that preserves full…

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…

Roughly ten years ago, the following "Gorenstein Interval Conjecture" (GIC) was proposed: Whenever $(1,h_1,\dots,h_i,\dots,h_{e-i},\dots,h_{e-1},1)$ and $(1,h_1,\dots,h_i+\alpha,\dots,h_{e-i}+\alpha,\dots,h_{e-1},1)$ are both Gorenstein…

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 studies the reduction by symmetry of variational problems on Lie groups and Riemannian homogeneous spaces. We derive the reduced equations of motion in the case of Lie groups endowed with a left-invariant metric, and on Lie…

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 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…

We investigate systems of equations, involving parameters from the point of view of both control theory and computer algebra. The equations might involve linear operators such as partial (q-)differentiation, (q-)shift, (q-)difference as…

We propose Geometric Pareto Control (GPC), a framework overcoming barriers of reinforcement learning in cyber-physical systems where governing physics is known. Reinforcement learning confronts barriers in safety-critical applications:…

We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…

We present a unified operator-theoretic framework for analyzing per-feature sensitivity in camera pose estimation on the Lie group SE(3). Classical sensitivity tools - conditioning analyses, Euclidean perturbation arguments, and Fisher…