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We consider some generalizations of the classical nonholonomic integrator and give a geometric approach to characterize controllability for these systems. We use Stokes' theorem and results from complex analysis to obtain necessary and…
The steering control of an autonomous unicycle is considered. The underlying dynamical model of a single rolling wheel is discussed regarding the steady state motions and their stability. The unicycle model is introduced as the simplest…
In this paper we provide optimal control based strategies to explore the dynamic capabilities of a single-track car model which includes tire models and longitudinal load transfer. Using an explicit formulation of the holonomic constraints…
This is a survey article, from the viewpoint of the completeness of the Marsden- Weinstein reduction, to introduce briefly some recent developments of the symmetric reductions and Hamilton-Jacobi theory of the regular controlled Hamiltonian…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
In this letter, we investigate the formation control problem of mobile robots moving in the plane where, instead of assuming robots to be simple points, each robot is assumed to have the form of a disk with equal radius. Based on interior…
This paper formulates optimal control problems for rigid bodies in a geometric manner and it presents computational procedures based on this geometric formulation for numerically solving these optimal control problems. The dynamics of each…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
In this paper, we review the discrete Hamilton--Jacobi theory from a geometric point of view. In the discrete realm, the usual geometric interpretation of the Hamilton--Jacobi theory in terms of vector fields is not straightforward. Here,…
Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their…
We analyze discrete optimal control problems and their connection with back propagation and deep learning. We consider in particular the symmetric representation of the discrete rigid body equations developed via optimal control analysis…
Drift control is significant to the safety of autonomous vehicles when there is a sudden loss of traction due to external conditions such as rain or snow. It is a challenging control problem due to the presence of significant sideslip and…
The paper solves the problem of tracking control of a quadrotor with unmeasurable pitch and roll angles based on the geometric approach with the use of the enhanced extended observer and the internal model. The proposed approach makes it…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…
This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…
Limbless organisms of all sizes use undulating patterns of self-deformation to locomote. Geometric mechanics, which maps deformations to motions, provides a powerful framework to formalize and investigate the theoretical properties and…
There are numerous ways to control objects in the Stokes regime, with microscale examples ranging from the use of optical tweezers to the application of external magnetic fields. In contrast, there are relatively few explorations of…
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…