Control Algorithms Development for Locomotion of a Humanoid Robot

Centre for Mechanical Technology and Automation

Institute of Electronics Engineering and Telematics

TEMA

IEETA http://www.mec.ua.pt/robotics

Control Algorithms Development for Locomotion of a Humanoid Robot

Milton Ruas1

Filipe M. T. Silva1

Vítor M. F. Santos2

1 Department of Electronics and Telecommunications2 Department of Mechanical Engineering

University of Aveiro, PORTUGALUniversity of Aveiro, PORTUGAL

UNIVERSITY OF AVEIRO, PORTUGALCentre for Mechanical Technology and AutomationInstitute of Electronics Engineering and Telematics

Overview Introduction Humanoid Platform: Overview

Actuation Element: the Servomotor Experimental Setup Speed Control Open and Closed Loop Performance Torque Measurement Algorithms Application on the Humanoid Balance Control

Conclusions and Open Issues


Introduction Project ’s Motivation

Develop a humanoid platform for research on control, navigation and perception

Offer opportunities for under & pos-graduate students to apply engineering methods and techniques

The utopia of Man to develop an artificial being with some of its own capabilities…

Objectives Describe how an external microprocessor can read the

shaft position and current consumption of RC servomotors Improve servo’s performance towards a control system

that provides variable velocity and compensates for load variations

Implement an example of local control based on force sensors present in both feet


Humanoid Platform Complete humanoid model

22 degrees of freedom Weight - 5 kg Height - 60 cm Max. width - 25 cm Foot print - 20 8 (cm2)

Actuation Servomotors with transmission belts

Sensors Servos’ internal potentiometers Sensitive foot Accelerometers Gyroscopes


Control System Architecture

Distributed control system A network of controllers connected

by a CAN bus Master/multi-slave arrangement:

• 8 slave units for joints actuation and sensors reading

• 1 master unit for interface between main unit and slaves

Asynchronous communications Between master and slaves: CAN

bus at 833.3 Kbit/s Between master and high level

controller: currently serial RS232 at 115200 baud

Main ControlMain Control

RS23RS2322MasteMaste

rr

CAN CAN BUSBUS

1

23 1

2

3

1

2

31

2 1

2

3

1

2

3

1

2

3

1

2

SlaveSlavess


Local Control

Power resistor (0.47)

16:1 multiplexer

CAN connector

Piggy-back socket

PIC Cristal oscillator

CAN driver

PIC

Unit CAN Address

PWM plugs

Servo fuse

Fuse status LED

Piggy-back board 2

Piggy-back board 1

Connector to sensor

CAN bus Power plug

Power regulator Reset button

RS232 plug

Connector to sensor

Each slave controller is made of a PIC 18F258 device with I/O interfacing

All slave units: Connect up to 3 servomotors Have a common base (a piggy-

back unit can add I/O sensors)


The Servomotor

1-2 ms 20 ms

PWM

PWM: Period: 20ms (50 Hz) Duty cycle: 1-2 ms

Why servomotors? Small and compact Relatively inexpensive Position control included

Servomotor parts: DC motor Gearbox Controlling electronics Position feedback mechanism

Characteristics Motion excursion: 180º Position control: digital signal, PWM

Some constraints: Doesn’t offer velocity control Doesn’t consider the external load


Experimental Setup Main goals

To study the servomotor’s performance with high loads and/or velocities

Improve the system’s behaviour by software compensation

Only one physical intervention: Connection of an extra output wire to the

servo internal potentiometer Servomotor

Feedback position y(t)

Applying position u(t)

Computer

CAN bus

RS-232

Master unit

Slave unit


Servo’s Parameters Measurement Potentiometer outputs shaft

position (feedback signal)

Different voltage “grounds” for external measurement and internal controller can produce measuring fluctuations

For high loads/fast motions a pulse above the position voltage is added: Fixed amplitude Synchronized to PWM Pulse width related with current

consumption!

Position and current measured from the same output: Position: minimal value Current: pulse width For high current draining, position

reading can be inhibited!

Input PWM pulse

Motor position

(variable)

“current” pulse

Amplitude fixed at

maximum

20 ms

Pulse width proportional to torque/current

τg = Ka.I = m.g.L.cos(Θ)


Programming Issues Each slave unit controls up to 3 servos. Actuation:

Each servo has associated to it a variable to store its PWM width

μC Timer2 interrupts compares a counter to each variable to apply PWM fall-down

Potentiometer signal

PWM

Potentiometer reading Interrupts (Timer 0)

ADCconversion

start

ADCreading

PWM for actuation

High frequency interrupts forPWM fall down (Timer 2)

Interrupt for PWMrise up (Timer 1)

5V

20 ms

1 to 2 ms

ADC starts conversion

Converted voltage is processed

Select next Servo (change MUX input)

Timer 0 generates an interrupt

ADC finishesconversion and

generates an interruptConversion Time: 40μs

Processing Time:10μs

MUX stabilization + Acquisition time:70μs

Sensing Timer0 interrupts used to measure

feedback data Servo output sensing is multiplexed in

time (120μs*3).


Velocity Control Application of a position step

Servo drives to the commanded position at maximum speed

User cannot directly control velocity!

How to control velocity with only position control? Trajectory planning!

Slope input Application of successive “small” step Amplitude and time delay of each step defines

the average speed Existence of speed discontinuities!

3ª order polynomial x(t)=a0+a1t+a2t2+a3t3

Total period defines speed Null initial and final speed Finite initial and final acceleration


Open Loop Performance Step response: -45º → +45º

Steady state error varies with the load (around 8 degrees for 1129g)

Response delay varies with the load Servo executes a fast and continuous

motion to the final position Unstable position readings with the

maximum load!

Ramp response: Δt=100ms Δx=5º T=1.8s Steady state error still present Transient response improved

Static analysis Steady state error depends of

gravitational terms


Low-Level Control Objectives

Eliminate steady state error Reduce response time lag … using software solutions

An external controller is implemented using: Servo’s own potentiometer for feedback Incremental algorithm of a digital PID controller


Integral Control Ramp:

-45º → +45º Δt=100ms, Δx=5º, T=1.8s

Open loop vs. closed loop (KI=0.2) Steady state error eliminated Time lag reduced

Ramp: -90º → +50º Δt=40ms, Δx=5º, T=1.12s

KI=0.06 vs. KI=0.10 (KP=0.04) Time delay reduced Overshoot arises


PID Control Ramp response

-90º → +50º Δt=40ms, Δx=5º, T=1.12s

KP=0.04 VS KP=0.30 (KI=0.10) Overshoot eliminated No interference with time delay

Polynomial response (T=1s): Increasing KP… Overshoot is reduced Time delay diminishes Establishment time increases

Adding Derivative component: Transient state smoothed Overshoot and time delay remains

unchanged Sensitive to noise


P+I+D Terms Integrator term

Eliminates steady state error Improves time lag Deteriorates overshoot

Proportional term Reduces overshoot Improves time delay Deteriorates establishment time

Derivative term Smoothes transient response Very sensitive to noise


Servo’s Torque Measurement For a Humanoid platform, the load

seen by each actuator can vary rapidly and substantially

For each task it is required to apply an adequate set of control parameters to ensure good performance

Two approaches can be followed: Parameters determination and manual

application from the main unit for each task Local parameter automatic adaptation,

through torque analysis

Torque estimation can be done from current measurement (τ=K*I)


Humanoid Locomotion The robot is able to stand, lean on sides, for/backward


Humanoid Locomotion Load weight: 2.1Kg


Humanoid Locomotion

0 2 4 6 8-60

-50

-40

-30

-20

-10

0

10

time (s)

Hip

po

sitio

n (

de

gre

es)

Open Loop

Ki=0.10, Kp=0.80

Expected trajectory

0 2 4 6 8-80

-60

-40

-20

0

20

40

time (s)

Kn

ee

po

sitio

n (

de

gre

es)

Ki=0.10, Kp=0.80

Open Loop

Expected trajectory

0 2 4 6 80

10

20

30

40

50

60

70

time (s)

Fo

ot p

osi

tion

(d

eg

ree

s)

Open Loop

Expected trajectory

Ki=0.10, Kp=0.80

Flexion movement

Foot roll jointFoot roll joint

Kn

ee join

tK

nee join

tH

ip join

tH

ip join

t


Humanoid Locomotion Lateral movement

0 1 2 3 4 50

5

10

15

20

25

30

35

time (s)

Fo

ot p

osi

tion

(d

eg

ree

s)

Open Loop

Expected trajectory

Ki=0.15, Kp=0.20

Foot tilt jointFoot tilt joint


Balance Control Our goal is to balance Humanoid’s body using

Force sensors Force sensors on each foot are used to…

measure ground reaction forces calculate the location of the Center of Pressure (CoP)

4 Extensometers used as force sensors!

Sensor’s outputAmplifier

Sensor’s outputAmplifier


Balance Control Control Law: Δq = K·JT·e

Δq: velocity to apply to the leg joints K: constant JT: transposed Jacobian of the CoP

• For lower velocities CoP≈CoM e is the error between the desired and the

actual CoP

Velocity application: pos(n)=pos(n-1)+Δq

knee

z

footroll

z

foottilt

z

knee

y

footroll

y

foottilt

y

knee

x

footroll

x

foottilt

x

CoMCoMCoM

CoMCoMCoM

CoMCoMCoM

J

Senso

r 1

Senso

r 2

Senso

r 3

Senso

r 4

y

x

FootFoot

4

1

4

1

sensorsensor

sensorsensorsensor

F

rF

CoM


Balance Control Application Pression on each force sensor


Balance Control Application Changing support plane sloping


Plane Sloping Change Balance through the yy axis


Balance Control Application Introducing perturbations


Conclusions Procedures were presented to measure servos’

position and torque with a servomotor… without velocity control whose speed and steady-state error is dependent of motor load

Methods were described on how… to introduce velocity control through trajectory planning to correct time lag and steady-state error through an external

controller using position reading as feedback …all this without hardware interventions!

Nevertheless, controller needs to be updated to maintain efficiency: To build an adaptive PID controller whose parameters are based

on torque estimation is the next objective to pursue

A special case of local control was presented: Leg’s balance was implemented with very reactive responses!


Future Perspectives

Use torque estimation to compensate inertial variations on the joints;

Improve materials quality used to sense the reaction forces for the balance control;

Combine position/velocity control with balance control;

Substitute the main controller unit (PC) with an embedded motherboard based on a PC104, nano-ITX or similar;

Participate in the next edition of Robocup in 2007 – Humanoid League!

Control Algorithms Development for Locomotion of a Humanoid Robot

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