Related papers: Sliding Motions on SO(3), Sliding Subgroups
The recently introduced energy-saving extension of the sub-optimal sliding mode control allows for control-off phases during the convergence to second-order equilibrium. This way, it enables for a lower energy consumption compared to the…
The dynamics simulation of multibody systems (MBS) using spatial velocities (non-holonomic velocities) requires time integration of the dynamics equations together with the kinematic reconstruction equations (relating time derivatives of…
We survey recent work on the geometry and dynamics of transverse subgroups of semi-simple Lie groups.
This paper proposes a novel nonlinear sliding mode state feedback controller for perturbed second-order systems. In analogy to a linear proportional-derivative (PD) feedback control, the proposed nonlinear scheme uses the output of interest…
In this paper we consider cases of existence of invariant measure, additional first integrals, and Poisson structure in a problem of rigid body's rolling without sliding on plane and sphere. The problem of rigid body's motion on plane was…
The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2,1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is…
We discuss smooth nonlinear control systems with symmetry. For a free and proper action of the symmetry group, the reduction of symmetry gives rise to a reduced smooth nonlinear control system. If the action of the symmetry group is only…
This paper develops a unified frequency-domain framework for the analysis of sliding-mode control systems, encompassing both discontinuous and Lipschitz-continuous implementations. Using describing function (DF) theory, closed-form…
A model invariant under a supersymmetric extension of the rotation group O(3) is mapped, using a stereographic projection, from the spherical surface S2 to two dimensional Euclidean space. The resulting model does not have a manifest local…
In this paper, we investigate the global robust stabilization of linear time-invariant systems by using event-triggered sliding mode control (SMC). Different from the practical sliding mode band, which is commonly used in previous studies…
We introduce a system where an elastic lattice of particles is moved slowly at a constant velocity under the influence of a local external potential, construct a rigid-body model through simplification processes, and show that the two…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
In digital sliding mode control implementations, discretization-induced chattering and inter-sample blindness can severely degrade the closed-loop performance, especially in case of fast perturbations. This paper addresses these challenges…
Contact-based motion planning for manipulation, object exploration or balancing often requires finding sequences of fixed and sliding contacts and planning the transition from one contact in the environment to another. However, most…
The purpose of this paper is to survey the structure of closed and transitive transformation groups acting on a closed surface. In particular, we prove a number of relations between groups acting on the sphere that contain the rotation…
In the half-space model of the hyperbolic three space with the hyperbolic metric, this same space can be seen as the Lie group, hence, a translation surface is a surface that is given by the product of two curves $\alpha$ and $\beta$ in…
Though the Chow group of 0-cycles on a K3 surface is quite large, we observe that the subgroup generated by product of divisors is cyclic.
In the present paper, a new type of ruled surfaces called osculating-type (OT)-ruled surface is introduced and studied. First, a new orthonormal frame is defined for OT-ruled surfaces. The Gaussian and the mean curvatures of these surfaces…
Accurate and robust positioning of rotor axle is essential for efficient and safe operation of high-speed rotational machines with active magnetic bearings. This study presents a cascaded nonlinear control strategy for vertical axial…
In this paper an adaptive sliding mode control approach for a quadrotor stabilization and trajectory tracking is presented. The closed loop control consists of three parts; the first part is quadrotor altitude and attitude stabilization,…