ar presentation 28

Khalil Alipour

May 2015

Advanced Robotics

In the Name of God

Faculty of New Sciences and Technologies

University of Tehran

University of Tehran Advanced Robotics-Khalil Alipour2 Saturday, May 30, 2015

ContentsPart III

Chapter 9: Force and Impedance Control

Introduction Task Description Force Control of a Mass-Spring System Hybrid Position/Force Control Adding Passive Compliance Impedance Control


Part III

Chapter 9: Force and Impedance Control


Task Description

We are interested in describing contact and freedoms, so we consider only the forces due to

contact. This is equivalent to doing a quasi-static analysis and ignoring other static forces, such

as certain friction components and gravity. The analysis is reasonable where forces due to

contact between relatively stiff objects are the dominant source of forces acting on the system.

Note that the methodology presented here is somewhat simplistic and has some limitations, but it

is a good way to introduce the basic concepts involved.

Constraints of Interaction

Natural Constraints: is used to indicate that theseconstraints arise naturally from the particularcontacting situation.

Artificial Constraints: are introduced inaccordance with the natural constraints tospecify desired motions or force application.

Compliance Frame (also called a Constraint Frame) in which the task to be performed is easily described.

Jordan-SoftHighlight




Task Description

The natural and artificial constraints for two tasks.

= is due to the contact between the end-eector and a rigid environment

TwistWrench

Reciprocity

Condition

Jordan-SoftLine

Jordan-SoftLine

Jordan-SoftArrow







Task Description

Assembly strategy is a term that refers to a sequence of planned artificial constraints that will

cause the task to proceed in a desirable manner. Such strategies must include methods by which

the system can detect a change in the contacting situation so that transitions in the natural

constraints can be tracked.

Reciprocity condition is satisfied when there exists an ideal robot/environment contact task. Ingeneral, the chosen task imposes environmental constraints on six of the above variables. Theseare the natural constraints. The remaining variables can be arbitrary assigned which are calledartificial constraints. The artificial constraints should be maintained by the control system inorder to complete the task.



Task DescriptionExample: Figure (a)(d) shows an assembly sequence used to put a round peg into a round

hole. The peg is brought down onto the surface to the left of the hole and then slid along the

surface until it drops into the hole. It is then inserted until the peg reaches the bottom of the hole,

at which time the assembly is complete. Each of the four indicated contacting situations defines a

subtask. For each of the subtasks shown, give the natural and artificial constraints. Also, indicate

how the system senses the change in the natural constraints as the operation proceeds.




Task DescriptionFirst, we will attach the constraint frame to the peg as shown in Fig. (a). In Fig. (a), the peg is in

free space, and so the natural constraints are


Task Description




Task DescriptionIn Fig. (c), the peg has fallen slightly into the hole. This situation is sensed by observing the

velocity in the direction and waiting for it to cross a threshold (to become nonzero, in the idealcase). When this is observed, it signals that once again the natural constraints have changed, and

thus our strategy (as embodied in the artificial constraints) must change. The new natural

constraints are

Finally, the situation shown in Fig. (d) is detected when the force in the directionincreases above a threshold.



Force Control of a Mass-Spring System

In considering forces of contact, we must make some model of the environment upon which we

are acting. For the purposes of conceptual development, we will use a very simple model of

interaction between a controlled body and the environment.

We model contact with an environment as a springthat is, we assume our system is rigid and

the environment has some stiffness, ke.

unknown friction or cogging in the

manipulator's gearing.

Model of Environment







Steady State Analysis





Better steady state error



A practical force-control system for the springmass system.



The force-control servo as a black box.


Hybrid Position/Force Control


Hybrid Position/Force ControlIn Chapter 8, we studied the position-control problem that applies to the situation of Fig. (a).The situation of Fig. (b) does not occur very often in practice; we usually must consider forcecontrol in the context of partially constrained tasks, in which some degrees of freedom of thesystem are subject to position control and others are subject to force control. Thus, in thissection, we are interested in considering hybrid position/force control schemes.



The hybrid position/force controller for a general manipulator. For simplicity, the velocity-feedback loop has not been shown.


Adding Passive Compliance

Some devices were specially designed to introduce compliance into the system on purpose. The

most successful such device is the RCC or Remote Center Compliance device developed at

Draper Labs. The RCC was cleverly designed so that it introduced the "right" kind of

compliance, which allowed certain tasks to proceed smoothly and rapidly with little or no chance

of jamming. The RCC is essentially a spring with six degrees of freedom, which is inserted

between the manipulator's wrist and the end-effector. By setting the stiffnesses of the six springs,

various amounts of compliance can be introduced. Such schemes are called passive-compliance

schemes and are used in industrial applications of manipulators in some tasks.


Adding Passive Compliance

Two examples of Use of RCC


Impedance Control

Neville Hogan

Sun Jae Professor of Mechanical Engineering at MIT and the father of Impedance Control notion

N. Hogan, Impedance Control: An Approach to Manipulation: Part IIImplementation,

Journal of dynamic systems, measurement, and control, Vol. 107, No. 1, pp. 8-16, 1985.

In this section we discuss the notion of Impedance Control. We begin with an example (see the

next slide) that illustrates in a simple way the eect of force feedback.


Impedance Control

Example: Consider the one-dimensional system in as shown, consisting of a mass, M, on a

frictionless surface subject to an environmental force F and control input u.

Mu F

x

The equation of motion of the system is


Impedance Control

Thus, the force feedback has the eect of changing the apparent inertia of the system.

Result

The mechanical impedance is a measure of the ratio of force and velocity and is analogous toelectrical impedance as a ratio of voltage and current.

The idea behind Impedance Control is to regulate the mechanical impedance, i.e., theapparent inertia, damping, and stiness, through force feedback as in the above example.


Impedance ControlFor example, in a grinding operation, it may be useful to reduce the apparent stiness of the end-eector normal to the part so that excessively large normal forces are avoided.

Impedance Control Law

The impedance control enforces the following impedance on the robot behavior

des d p c M e K e K e F

where e is the end-effector tracking error and is as

des e x xAlso is the force/torque exerted to the end-effector due to the contact with the environment andis measured by wrist force/torque sensor.

Now, the robot task space dynamics is considered

x x x M x V G F


Impedance Control

( )des des d p c M x x K e K e F

1des des x x x d p c M x M F V G K e K e F

1 1des des des x des x x x d p c M x M M F M M V G K e K e F

1 1x des des des des x x x d p c F M M M x M M V G K e K e F

1 1T x des des des des x x x d p c

J M M M x M M V G K e K e F


The End

ar presentation 28

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