In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined for decoupling these outputs and for their perfect trajectory tracking. The control of robotic manipulation is investigated. These are mechanical structures more complex than conventional serial-linkage arms. The robotic hand with possible inner contacts is a paradigm of general manipulation systems. Unilateral contacts between mechanical parts make the control of manipulation system quite involved. In fact, contacts can be considered as unactuated (passive) joints. The main goal of dexterous manipulation consists of controlling the motion of the manipulated object along with the grasping forces exerted on the object. In the robotics literature, the general problem of force/motion control is known as "hybrid control". This paper is focused on the decoupling and functional controllability of contact forces and object motions. The goal is to synthesize a control law such that each output vector, namely the grasping force and the object motion, can be independently controlled by a corresponding set of generalized input forces. The functional force/motion controllability is investigated. It consists of achieving force and motion tracking with no error on variables transients. The framework used in this paper is the geometric approach to the structural synthesis of multivariable systems.
In this work, a feedforward dynamic controller is devised in order to achieve H2-optimal rejection of signals known with finite preview, in discrete-time systems. The feedforward approach requires plant stability and, more generally, robustness with respect to parameter uncertainties. On standard assumptions, those properties can be guaranteed by output dynamic feedback, while dynamic feedforward is specifically aimed at taking advantage of the available preview of the signals to be rejected, in compliance with a two-degree-of-freedom control structure. The geometric constraints which prevent achievement of perfect rejection are first discussed. Then, the procedure for the design of the feedforward dynamic compensator is presented. Since the approach proposed in this work is based on spectral factorization via Riccati equation of a real rational matrix function directly related to the original to-be-controlled system, the delays introduced to model the preview of the signals to be rejected do not affect the computational burden intrinsic in the solution of the appropriate algebraic Riccati equation. A numerical example helps to illustrate the geometric constraints and the procedure for the design of the feedforward dynamic unit.
This paper investigates the geometric and structural characteristics involved in the control of general mechanisms and manipulation systems. These systems consist of multiple cooperating linkages that interact with a reference member of the mechanism (the "object") by means of contacts on any available part of their links. Grasp and manipulation of an object by the human hand is taken as a paradigmatic example for this class of manipulators. Special attention is devoted to the output specification and its controllability. An example design of a force controller using algebraic output feedback is presented at the end of this paper. In this example, a matrix representing a static output feedback is designed. The coefficients of this matrix are the weights for the sensed outputs. With the approach proposed in this paper, a robust decoupling is obtained between the output feedback and the contact forces and joint positions.