Force Control

Niklas Fiedler

May 23, 2019 Intro Controller Overview PID-Controller Force Control

OutlineI

1 Intro

2 Controller Overview

3 PID-Controller

4 Force Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Bibliography

Mainly based on the following works: Modern Robotics - Mechanics, Planning, and Control (Kevin M. Lynch and Frank C. Park) Introduction to Robotics - Mechanics and Control (John C. Craig) Force Control in Robotics (Luigi Villani)

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Sense - Plan - Act

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Sense - Plan - Act

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Force Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Acting based on which input?

On/Off Position Velocity Force Temperature Combination of multiple variables

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

1 Intro

2 Controller Overview

3 PID-Controller

4 Force Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Controller

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Controller

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Control Systems in Robots

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Open Loop Control

Controlling independent of process variables

timer stepper motors

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Control System Application

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Closed Loop Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Closed Loop Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Bang-Bang Control

switches between two states hysteresis

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

1 Intro

2 Controller Overview

3 PID-Controller

4 Force Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID Controller Application

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID Controller Application

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID-Controller

Proportional Integral Derivative Controller most widely used controller concept originally developed for ships first formulation in 1922

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID-Controller

closed loop control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID-Controller

https://en.wikipedia.org/wiki/PID_controller#/media/File:PID_en.svg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Proportional Term

Pout = Kpe(t)

Pout linearly proportional to the error e(t)

correction controlled by gain Kp output of a proportional controller solely usable

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Effect of Kp

https://upload.wikimedia.org/wikipedia/commons/a/a3/PID_varyingP.jpg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Integral Term

Z t Iout = Ki e(τ)dτ 0

Iout grows with the error summed up over time

controlled by gain Ki grows faster if the error is reached slowly output of a integral term solely usable used to handle load in the movement

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Effect of Ki

https://upload.wikimedia.org/wikipedia/commons/c/c0/Change_with_Ki.png

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

P vs PI

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Derivative Term

de(t) D = K out d dt

Dout linearly proportional to the change of the error e(t)

controlled by gain Kd output of a derivative term NOT solely usable used to reduce overshoot

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Effect of Kd

https://en.wikipedia.org/wiki/PID_controller#/media/File:Change_with_Kd.png

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Proportional (or P-) Controller

Pout = Kpe(t)

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PI-Controller

Z t PIout = Kpe(t) + Ki e(τ)dτ 0

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID-Controller

Z t de(t) PIDout = Kpe(t) + Ki e(τ)dτ + Kd 0 dt

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

PID-Controller

https://en.wikipedia.org/wiki/PID_controller#/media/File:PID_en.svg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

1 Intro

2 Controller Overview

3 PID-Controller

4 Force Control

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Raw Force Control

basically the same as position control forces instead of positions abstraction which is unusual in real applications the environment has to provide resistance forces in each direction

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Raw Force Control

without feedback: T τ =g ˜(θ) + J(θ) Fd

g˜(θ): gravitational force

Fd : desired wrench

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Force Measurement

Usually, force is measured by force/torque sensors

measuring occurring force on six axes mounted at the actuator of the robot generally noisy output

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Raw Force Control

with feedback (PI-Controller):    Z  T   τ =g ˜(θ) + J(θ) Fd + KfpFe + Kfi Fe(t) dt  | {z }  proportional term | {z } integral term

g˜(θ): gravitational force

Fd : desired wrench velocity damping can be added for practical use

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Position/Force Control Application

https://www.kuka.com/-/media/kuka-corporate/images/industries/case-studies/schwingenmontage/

flexfellow_mrk_header.jpg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Position/Force Control Application

http://www.metalworkingworldmagazine.com/files/2013/10/Fig_09.jpg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Force Control Motivation

object manipulation performing tasks on a surface contact with stiff surfaces dynamic environments (collaboration with humans)

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Force Control

Controlling the force applied to the environment in combination with the pose active compliance

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Force Control

http://www.metalworkingworldmagazine.com/files/2013/10/Fig_09.jpg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Force Control

http://www.metalworkingworldmagazine.com/files/2013/10/Fig_09.jpg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Force Control

http://www.metalworkingworldmagazine.com/files/2013/10/Fig_09.jpg

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Force Control Formula

Niklas Fiedler Force Control Intro Controller Overview PID-Controller Force Control

Hybrid Position/Force Control: the easy way

setting a maximal effort in each joint applicable to reach a position stopping the movement when the effort is reached measuring the applied effort without a force/torque sensor

Niklas Fiedler Force Control Image Sources

http://www.electricshopping.com http://www.appliance-world.co.uk https://www.electronicsb2b.com https://make-create.org

Niklas Fiedler Force Control PD vs PID

Niklas Fiedler Force Control