Nonlinear Attitude Control of Planar Structures in Space Using Only Internal Controls

An attitude control strategy for maneuvers of an interconnection of planar bodies in space is developed. It is assumed that there are no exogeneous torques and that torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero. The control strategy utilizes the nonintegrability of the expression for the angular momentum. Large angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is summarized

The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page

A coordinate-free approach to instantaneous kinematics of two rigid objects with rolling contact and its implications for trajectory planning

This paper adopts a coordinate-free approach to investigate the kinematics of rigid bodies with rolling contact. A new equation of angular velocity of the moving body is derived in terms of the magnitude of rolling velocity and two sets of geometric invariants belonging to the respective contact curves. This new formulation can be differentiated up to any order. Furthermore, qualitative information about trajectory planning can be deduced from this equation if the characteristics of rolling objects and the motion are taken into consideration

Steering nonholonomic systems in chained form

The authors introduce a nilpotent form, called a chained form, for nonholonomic control systems. For the case of a nonholonomic system with two inputs, they give constructive conditions for the existence of a feedback transformation which puts the system into chained form, and show how to steer the system between arbitrary states. Examples are presented for steering a car and a car with a trailer attached: other examples can be found in the areas of space robotics and multifingered robot hands. The present results also have applications in the area of nilpotentization of distributions of vector fields on R^n

Planar reorientation maneuvers of space multibody systems using internal controls

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77104/1/AIAA-11411-971.pd

A qualitative test for N-finger force-closure grasps on planar objects with applications to manipulation and finger gaits

This paper presents a force-closure test function for an n-finger grasp on a planar object with friction. All n-finger grasps can be represented by an n-dimensional contact space. The critical conditions of the test function are used to define force-closure curves which are the boundaries of force-closure sets in the contact configuration space. We show that the force closure sets can be decomposed into subsets in which m (m < n) fingers satisfy force closure. We also prove that m = 6 is an upper bound on the order of the force closure subsets. These subsets are required for planning finger gait maneuvers which are force-closure in all phases of the gait. The characteristics of these subsets are discussed, and an algorithm to enumerate them is given. The application of the test function and the contact configuration space formulation to multifinger object manipulation and finger gait planning is demonstrated by an example

A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact

This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame

Nonholonomic motion planning: steering using sinusoids

Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given

Nonholonomic control systems: from steering to stabilization with sinusoids

The authors present a control law for globally asymptotically stabilizing a class of controllable nonlinear systems without drift. The control law combines earlier work in steering nonholonomic systems using sinusoids at integrally related frequencies, with the ideas in recent results on globally stabilizing linear and nonlinear systems through the use of saturation functions. Simulation results for stabilizing a simple kinematic model of an automobile are included