We address the controller design and the trajectory generation for a quadrotor maneuvering in three dimensions in a tightly constrained setting typical of indoor environments. In such settings, it is necessary to allow for significant excursions of the attitude from the hover state and small angle approximations cannot be justified for the roll and pitch. We develop an algorithm that enables the real-time generation of optimal trajectories through a sequence of 3-D positions and yaw angles, while ensuring safe passage through specified corridors and satisfying constraints on velocities, accelerations and inputs. A nonlinear controller ensures the faithful tracking of these trajectories. Experimental results illustrate the application of the method to fast motion (5–10 body lengths/second) in three-dimensional slalom courses.

Minimum snap trajectory generation and control for quadrotors

From the Publisher:
This graduate text provides an authoritative account of neural network (NN) controllers for robotics and nonlinear systems and gives the first textbook treatment of a general and streamlined design procedure for NN controllers. Stability proofs and performance guarantees are provided which illustrate the superior efficiency of the NN controllers over other design techniques when the system is unknown. New NN properties, such as robustness and passivity are introduced, and new weight tuning algorithms are presented. Neural Network Control of Robot Manipulators and Nonlinear Systems provides a welcome introduction to graduate students, and an invaluable reference to professional engineers and researchers in control systems.

/pdf/neural-network-control-of-robot-manipulators-and-nonlinear-2lgcy2ydnw.pdf

Neural Network Control of Robot Manipulators and Nonlinear Systems

Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems

This article provides a tutorial introduction to modeling, estimation, and control for multirotor aerial vehicles that includes the common four-rotor or quadrotor case.

Multirotor Aerial Vehicles: Modeling, Estimation, and Control of Quadrotor

A class of inherently nonlinear control problems has been identified, the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system. Models are presented for mechanical systems with nonholonomic constraints represented both by differential-algebraic equations and by reduced state equations. Control issues for this class of systems are studied and a number of fundamental results are derived. Although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback, a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested. >

Control and stabilization of nonholonomic dynamic systems

Stabilizing feedback laws for internally actuated multibody systems in space

Hybrid feedback control laws are constructed for stabilization of wheeled vehicles consisting of tractors with trailers. The equations of motion are first transformed into a special canonical form, known as the multi-input extended power form. A hybrid stabilization technique developed by Kolmanovsky et al. (1995) is applied to develop the controller structure. These controllers operate by switching at discrete time-instants between various time-periodic feedback functions. Implementation issues are briefly addressed for several wheeled vehicle examples.

Stabilization of wheeled vehicles by hybrid nonlinear time-varying feedback laws

This paper provides global formulations of Lagrangian and Hamiltonian variational dynamics evolving on the product of an arbitrary number of two-spheres. Four types of Euler-Lagrange equations and Hamilton's equations are developed in a coordinate-free fashion on two-spheres, without relying on local parameterizations that may lead to singularities and cumbersome equations of motion. The proposed intrinsic formulations of Lagrangian and Hamiltonian dynamics are novel in that they incorporate the geometry of two-spheres, resulting in equations of motion that are expressed compactly, and they are useful in analysis and computation of the global dynamics.

/pdf/global-formulations-of-lagrangian-and-hamiltonian-mechanics-1uyikgh40a.pdf

Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres

A source of space station attitude disturbances is identified The attitude disturbance is driven by internal space station motions and is a direct result of conservation of angular momentum Three examples are used to illustrate the effect: a planar three link system, a rigid carrier body with two moveable masses, and a nonplanar five link system Simulation results are given to show the magnitude of the attitude change in each example Factors which accentuate or attenuate this disturbance effect are discussed

/pdf/space-station-attitude-disturbance-arising-from-internal-4851xcune9.pdf

Space Station Attitude Disturbance Arising from Internal Motions

An attitude control problem for a tethered spacecraft is studied. The tethered spacecraft is viewed as a multi-body spacecraft consisting of a base body, a massless tether that connects the base body and an end mass, and tether actuator dynamics. Moments about the pitch and roll axes of the base spacecraft arise by control of the point of attachment of the tether to the base spacecraft. The control objective is to stabilize the attitude of the base spacecraft while keeping the perturbations of the tether small. Analysis shows that linear equations of motion for the tethered spacecraft are not completely controllable. We study two different control design approaches: (1) we decouple the attitude dynamics from the tether dynamics and we design a linear feedback to achieve stabilization of the attitude dynamics, and (2) we decouple the controllable modes from the uncontrollable mode using Kalman decomposition and we design a linear feedback to achieve stabilization of the controllable modes. Simulation results show that, although it is difficult to control the tether, the tether motion can be maintained within an acceptable range while stabilizing the attitude dynamics of the base spacecraft.

http://www.koreascience.or.kr:80/article/JAKO200716049282363.pdf

N. Harris McClamroch

Papers

Stabilizing feedback laws for internally actuated multibody systems in space

Stabilization of wheeled vehicles by hybrid nonlinear time-varying feedback laws

Global formulations of Lagrangian and Hamiltonian mechanics on two-spheres

Space Station Attitude Disturbance Arising from Internal Motions

Attitude Control of a Tethered Spacecraft