A spatial operator algebra for manipulator modeling and control

A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed

Spatial operator approach to flexible multibody system dynamics and control

The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects

THREAD: A programming environment for interactive planning-level robotics applications

THREAD programming language, which was developed to meet the needs of researchers in developing robotics applications that perform such tasks as grasp, trajectory design, sensor data analysis, and interfacing with external subsystems in order to perform servo-level control of manipulators and real time sensing is discussed. The philosophy behind THREAD, the issues which entered into its design, and the features of the language are discussed from the viewpoint of researchers who want to develop algorithms in a simulation environment, and from those who want to implement physical robotics systems. The detailed functions of the many complex robotics algorithms and tools which are part of the language are not explained, but an overall impression of their capability is given

Spatial operator algebra framework for multibody system dynamics

The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed

Classification using set-valued Kalman filtering and Levi\u27s decision theory

We consider the problem of using Levi\u27s expected epistemic decision theory for classification when the hypotheses are of different informational values, conditioned on convex sets obtained from a set-valued Kalman filter. The background of epistemic utility decision theory with convex probabilities is outlined and a brief introduction to set-valued estimation is given. The decision theory is applied to a classifier in a multiple-target tracking scenario. A new probability density, appropriate for classification using the ratio of intensities, is introduced

Modeling & control of a space robot for active debris removal

Space access and satellites lifespan are increasingly threatened by the great amount of debris in Low Earth Orbits (LEO). Among the many solutions proposed in the literature so far, the emphasis is put here on a robotic arm mounted on a satellite to capture massive debris, such as dead satellites or launch vehicle upper stages. The modeling and control of such systems are investigated throughout the paper. Dynamic models rely on an adapted Newton-Euler algorithm, and control algorithms are based on the recent structured H infinity method. The main goal is to efficiently track a target point on the debris while using simple PD-like controllers to reduce computational burden. The structured H infinity framework proves to be a suitable tool to design a reduced-order robust controller that catches up with external disturbances and is simultaneously compatible with current space processors capacities

Spatial operator algebra for flexible multibody dynamics

This paper presents an approach to modeling the dynamics of flexible multibody systems such as flexible spacecraft and limber space robotic systems. A large number of degrees of freedom and complex dynamic interactions are typical in these systems. This paper uses spatial operators to develop efficient recursive algorithms for the dynamics of these systems. This approach very efficiently manages complexity by means of a hierarchy of mathematical operations