A Configuration Manifold Embedding Model for Dynamic Control of Redundant Robots

Abstract

This paper presents a configuration manifold embedding model that provides a new approach to dynamic model reduction and adaptive control of redundant robotic systems. The proposed model is developed based on a geometrical and topological analysis of configuration manifolds (C-manifolds) hidden behind every robotic dynamic system that commonly obeys the Lagrange equation. With a detailed study of the C-manifold immersion and embedding into Euclidean space, we show that for a redundant robotic system, a subtask decision by choosing a certain null solution is technically equivalent to the C-manifold embedization. A direct adaptive control strategy is then developed based on the C-manifold embedding model for a specific application to model reduction and control of redundant robotic systems with both main tasks and subtasks represented in Cartesian space. It is also demonstrated that making only a kinematics model for a redundant robot can do the dynamic control job. Finally, a computer simulation study shows the effectiveness of this adaptive control algorithm.

A gauge-invariant formulation for constrained robotic systems using square-root factorization and unitary transformation

“…On the other hand, the zero-input response of a mechanical system isv = −Γv. Substituting the latter equation in the time-derivative of (12) gives…”

Analytical Mechanics With Quasi-Velocities

“…Alternatively, the dynamics of a multibody system can be formulated in terms of the vector of quasi-velocities, i.e., a vector whose Euclidean norm is proportional to the square root of the system's kinetic energy. It is known that this formulation can lead to simplification of the equations of unconstrained MBSs [9,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]33]. In short, the square-root factorization of the mass matrix is used as a transformation to obtain the quasi-velocities, which are a linear combination of the velocity and the generalized coordinates [22,25,33,34].…”

Notes on vibration control of a micro/macromanipulator mounted on a flexible structure

“…Control of robotic arms has been studied. Many subjects related to this aspect are studied, such as the ways in which the performance of direct drive serial robots changes with system size [43]; a fuzzy-Gaussian neural network controller applying a Gaussian function as an activation function [44]; a composite control law for end-effector path tracking with a FSMS [45]; a configuration manifold embedding model that provides a new approach to dynamic model reduction and adaptive control of redundant robotic systems [46]; a solution for the problem of control of the robotic manipulators mounted onto a free flying platform in space [47]; and an overwhelming controller-based implicit system inversion scheme to control a hydraulically driven planar (three degrees of freedom) parallel manipulator [48].…”