This paper provides new results for the tracking control of a quadrotor unmanned aerial vehicle (UAV). The UAV has four input degrees freedom, namely magnitudes rotor thrusts, that are used to six translational and rotational achieve asymptotic outputs, namely, three position variables center mass direction one body-fixed axis. A globally defined model rigid body dynamics is introduced as basis analysis. nonlinear controller developed on special Euclidean group SE(3) it shown have desirable...

Abstract This paper provides nonlinear tracking control systems for a quadrotor unmanned aerial vehicle ( UAV ) that are robust to bounded uncertainties. A mathematical model of is defined on the special E uclidean group, and output‐tracking controllers developed follow (i) an attitude command, (ii) position command center mass. The controlled system has desirable properties errors uniformly ultimately bounded, size ultimate bound can be reduced arbitrarily by parameters. Numerical examples...

This paper provides new results for control of complex flight maneuvers a quadrotor unmanned aerial vehicle (UAV). The are defined by concatenation modes or primitives, each which is achieved nonlinear controller that solves an output tracking problem. A mathematical model the UAV rigid body dynamics, on configuration space $\SE$, introduced as basis analysis. has four input degrees freedom, namely magnitudes rotor thrusts; mode solving asymptotic optimal Although many can be studied, we...

Journal Article Discrete Hamiltonian variational integrators Get access Melvin Leok, Leok * Department of Mathematics, University California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093–0112, USA *Corresponding author: mleok@math.ucsd.edu Search for other works by this author on: Oxford Academic Google Scholar Jingjing Zhang School Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China zhangjj@hpu.edu.cn IMA Numerical Analysis, Volume 31, Issue 4,...

We present a theory and applications of discrete exterior calculus on simplicial complexes arbitrary finite dimension. This can be thought as space. Our includes not only differential forms but also vector fields the operators acting these objects. allows us to address various interactions between (such Lie derivatives) which are important in applications. Previous attempts at have addressed forms. introduce notion circumcentric dual complex. The importance this field has been well...

Abstract Euler–Lagrange equations and variational integrators are developed for Lagrangian mechanical systems evolving on a product of two‐spheres. The geometric structure two‐spheres is carefully considered in order to obtain global motion. Both continuous motion completely avoid the singularities complexities introduced by local parameterizations or explicit constraints. We derive expressions two‐spheres, which more compact than existing written terms angles. Since derived from Hamilton's...

A 3D pendulum consists of a rigid body, supported at fixed pivot, with three rotational degrees freedom. The is acted on by gravitational force. dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the non-integrable case body asymmetric and center mass distinct from pivot location. full reduced models introduced used to study important features nonlinear dynamics: conserved quantities, equilibria, relative...

This paper considers safe control synthesis for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and safety constraints. We formulate novel robust (worst-case) Lyapunov function (CLF) barrier (CBF) constraints that take into account effect of case. show formulation leads to a second-order cone program (SOCP), which enables efficient stable synthesis. evaluate our approach PyBullet simulations an autonomous robot navigating unknown environments...

We develop a discrete analogue of Hamilton-Jacobi theory in the framework Hamiltonian mechanics. The resulting equation is only time. correspondence between and continuous mechanics naturally gives rise to Jacobi's solution equation. prove analogues geometric theorem. These results are readily applied optimal control setting, some well-known theory, such as Bellman equation, follow immediately. also apply linear systems, show that Riccati follows special case.

We develop a discrete analogue of Hamilton–Jacobi theory in the framework Hamiltonian mechanics. The resulting equation is only time. describe Jacobi's solution and also prove version geometric theorem. applied to linear systems yields Riccati as special case equation. apply optimal control problems, recover some well-known results, such Bellman (discrete-time HJB equation) dynamic programming its relation costate variable Pontryagin maximum principle. This relationship between exploited...

This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to variational integration with symmetry. The Runge–Kutta discretizations is considered, as well extent which symmetry discretization commute. These reduced methods allow direct simulation dynamical features such relative equilibria periodic orbits that can be obscured or difficult identify in unreduced dynamics. are demonstrated dynamics an Earth orbiting satellite a non-spherical J2...

This paper presents an analytical model and a geometric numerical integrator for tethered spacecraft that is composed of two rigid bodies connected by elastic tether. includes important dynamic characteristics in orbit, namely the nonlinear coupling between tether deformations, rotational dynamics bodies, reeling mechanism, orbital dynamics. A integrator, referred to as Lie group variational developed numerically preserve Hamiltonian structure presented its configuration manifold. The...