bio-inspired locomotion control of hexapods alessandro rizzo

Bio-inspired locomotion control of hexapods

Alessandro Rizzo

Outline

• Bio-inspired robotics

• CNN-based Central Pattern Generators (CPG)

• CPG and sensory feedback– The VLSI CNN-based CPG chip

• High-level control

• HexaDyn and future works

BIO-INSPIRED ROBOTS

Synergies from various disciplines (robotics, neuroscience, biology, ethology)

Robotic animal models to a major understanding of biological behaviors

Biological inspiration to build efficient robots

REFLEXES IN THE STICK INSECT

Stepping reflex (A) Elevator reflex (B) Searching reflex (C)

Stepping reflex (A) Elevator reflex (B) Searching reflex (C)

Local reflexes improve rough terrain locomotion in a hexapod robot

Cosa hanno in comune questi animali e il robot?

CPG: a paradigm for bio-inspired locomotion control

• Animals move according to a pattern of locomotion

• This pattern is due to the pattern of neural activities of the so-called CPG

• This paradigm can be used to control a legged robot

Basic definitions for gait analysis

• Transfer phase (swing phase, return stroke)

• Support phase (stance phase, power stroke)

• Cycle time T

• Duty factor i

• Leg phase i

• Leg stride • Leg stroke R

• Stroke pitch

• Effective body length

• Gait matrix

• Gait formula

• Dimensionless foot position

• Dimensionless initial foot position

• Kinematic gait formula• Event

• Singular gait• Regular gait• Symmetric gait• Support pattern• Periodic gait

• Stability margin• Front stability margin (rear stability

margin)• Gait stability margin• Stability margin normalized to stride

Stability

Anatomy/Structure

Gait

Gait

skip

Locomotion Patterns – Alternating tripod

5.0Stance T

Ti

T

Tstance (L1) TRIPOD GAIT

Duty Factor (df)

5.0321 RLR 0321 LRL Leg phases

The swing (flexion phase) depends on the mechanics of the limb

Locomotion Patterns – Medium Gait

T

Tstance (L1) MEDIUM GAIT

8

5Stance T

Ti Duty Factor (df)

5.031 LR 031 RL Leg phases

75.02 L 25.02 R

Locomotion Patterns – Tetrapod Gait

T

Tstance (L1)

3

2Stance T

Ti Duty Factor (df)

Leg phases

TETRAPOD GAIT

3/13 L

01 L3/22 L

6/53 R6/12 R2/11 R

3/1ipsi2/1contra

CPG: a paradigm for bio-inspired locomotion control

• Animals move according to a pattern of locomotion

• This pattern is due to the pattern of neural activities of the so-called CPG

• This paradigm can be used to control a legged robot

The Central Pattern Generator

CPG

Environment

Effector Organs

Higher Control

Sensory feedback

Reflex Feedback

Cen

tral

Fee

dbac

k

• Definition: A neural circuit that can produce a rhythmic motor pattern with no need for sensory feedback or descending control

• Proof of existence: remove sensory feedback, descending control and elicit motor pattern

• CPG have been demonstrated in all animals to date for rhythmic movements that are essential for survival

• Feedforward controlThe motor system

• Action potential (spike)• Beating, Bursting, Silent state• Frequency coding• Synapses: chemical, gap junctions

Neurons and motor-neurons

Neural Control of Muscles

vertebrates

arthropods

Motor-neuron Muscle fiber

…

…

Motor-neuron Muscle fiber

…

…

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Flexor Extensor Pair Block

antagonistic pair: flexor – extensor

flexor – extensor modeled by a CNN-based motor unit called CNN neuron

more…

A CPG-based control system• The CPG is realized by a network of coupled nonlinear

oscillators through CNNs• Q: How to design a CNN network generating a given

pattern?• A: Exploit the analogy with the biological case

(synapses, motor-neurons…)• A: Reduce the complexity of the problem

1,21,1

2,1

3,1 3,2

2,2

1,21,1

2,1

3,1

2,2

3,2

A CPG-based control system• Ring of N neurons: each neuron is connected to its

neighbor with an excitatory (or inhibitory) synapse in a well defined direction (clockwise or counterclockwise)

• The behavior of this kind of network for a suitable valuable of the synaptic weight is a well-defined pattern (traveling wave)• The oscillators are synchronized• The phase lags between adjacent oscillators are

constant1,21,1

2,1

3,1

2,2

3,2

Slow gait

R1

L2

R3L1

R2

L3

UNIVERSITY OF CATANIA, DEES, SYSTEM AND CONTROL GROUP

P. Arena, L. Fortuna, M. Frasca

Fast Gait

L3

R2

L1

R1

R3

L2

Locomotion pattern CNN Waveforms (SC circuit)

Examples of locomotion patterns with Multi-Template Approach CNN

Design of CNN-based CPG

From Reaction-Diffusion Equations to inhibitory/excitatory connections

Skip this section


• The biological paradigm– Pattern of neural activities

– Pattern of rhythmic movements

• Application in the bio-inspired robotics: the CPG controls the locomotion of an hexapod robot

CPG

Environment

Effector Organs

Higher Control Sensory feedback

Reflex Feedback

Cen

tral

Fee

dbac

k

CNN realizationMotor System

RD-CNN as CPG for an hexapod robot

• Reaction-diffusion equation

• CNN implementation of the nonlinear medium

• Autowaves (slow-fast dynamics)– Reorganization of the

slow part when the pattern is switched into another one

• Turing patterns in the higher control level

The design of CPG in which also chemical synapses are involved is considered in the followingThe design of CPG in which also chemical synapses are involved is considered in the following

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• Equations & Parameters

• Behavior

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The Neuron Model - Slow-Fast CNN Neuron

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Poincaré-Bendixson theorem:• This theorem is a powerful tool to establish the existence ofperiodic orbits in 2D flows.• It states that if R is a closed region that does not contain fixed points for the vector field x=f(x) and a trajectory C confined in R does exist, then R contains a closed orbit (and either C is itself the closed orbit or spirals toward to it).

Existence of a periodic orbit

Leg Controller

a1

a22 DOF leg

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PEP

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• Control of a 2 DOF leg: 1 CNN neuron

CNN neuronCNN neuron

• MxN Two-layer CNN cell equations

• Neighbourhood

• PWL Output

Cellular Neural Networks - Two-layer CNN equations

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• Scheme of a CNN layer

• Chemical Synapse

The Synapse Model - Chemical Synapse for the Slow-Fast Neuron

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• Simplified Chemical Synapse (excitatory and inhibitory)

• Simplified Delayed Chemical Synapse (excitatory and inhibitory)

function

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CNN Multi-Template Approach - Guidelines

Guidelines• Create a ring of N neurons

• Add the n-N neurons by using synchronisation via “coupling” or synchronisation via “duplicating”

• Choose the synaptic weights

Guidelines• Create a ring of N neurons

• Add the n-N neurons by using synchronisation via “coupling” or synchronisation via “duplicating”

• Choose the synaptic weights

Definitions:• N = number of pattern steps • n = number of legs• ring of N neurons = each neuron is connected to its neighbor with an excitatory (or inhibitory) synapse in a well defined direction (clockwise or counterclockwise)

Definitions:• N = number of pattern steps • n = number of legs• ring of N neurons = each neuron is connected to its neighbor with an excitatory (or inhibitory) synapse in a well defined direction (clockwise or counterclockwise)

• Inhibitory synapses: (a) connections on the layer: A11… (b) connections between layers: A21... (delayed synapses)

• The behavior can depend on initial conditions

• In the case (b) [“delayed synapse”] patterns with traveling waves in a well defined direction are obtained

(a) (b)

Rings of N Slow-Fast Neurons

Adding the n-N neurons

• Synchronisation via “coupling”

• Synchronisation via “duplicating”

Neuron B’ and neuron B have the same synaptic inputs

Neuron B and neuron B’ are synchronised because they belong to rings that have the same number of cells and share a neuron

B

C A

B’B

C A

...... ... ...

B

C A

B’

C’

MTA-CNN: An Example - The Caterpillar Gait

Guidelines (1)• Create a ring of N neurons

Guidelines (1)• Create a ring of N neurons

Scheme of the locomotion pattern: Caterpillar for six legged robots (right and left legs move in synchrony)

N=3

R3L1

R2

L1

L2

L3

R2

R3

R1Two layer 3x2 CNN

Hexapod1,21,1

2,1

3,1 3,2

2,2

Guidelines (2)• Add the n-N=3 neurons by using synchronisation via “coupling” or synchronisation via “duplicating”

Guidelines (2)• Add the n-N=3 neurons by using synchronisation via “coupling” or synchronisation via “duplicating”

R3L1

R2

R3L1

R2

L3 R1

L2

R3L1

R2

L3 R1

L2

1

2

1 1

22

Synchronisation by duplicating synapses 1 and 2. Thus, neuron R2 is synchronised with L2

Synchronisation by duplicating synapses 1 and 2. Thus, neuron R2 is synchronised with L2


Guidelines (3)• Choose the synaptic weights

Guidelines (3)• Choose the synaptic weights

R3L1

R2

L3 R1

L2

R3L1

R2

L3 R1

L2

• Firing Sequence

• CNN Implementation: synaptic connections are established by the feedback templates, these templates depend on the cell position (i.e. they are space-variant)

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Simulation Results (SPICE)


L2 R2

L1 R1

L3 R3

Other locomotion patterns have been implemented (the fast gait, the medium gait and the slow gait)

To change a locomotion pattern a new set of template should be loaded, while the network structure is not varied

R3L1

R2

L3 R1

L2

R3L1

R2

L3 R1

L2

R3L1

R2

L3 R1

L2(a)

(b)

(c)

Changing the locomotion pattern

Conclusions

• A new approach for the design of CNN based CPG to control artificial locomotion has been presented

• It includes a model of chemical synapses• A neighborhood of r=1 is always used• Each leg is always driven by the same cell in all

the gaits• Several locomotion patterns have been

successfully implemented on a hexapod robot

CPG and feedback

• Observation: The feedback is fundamental for animal (and legged robot) locomotion

• How to implement sensory feedback?

CPG & Feedback from Sensors

CPG

Environment

Effector Organs

Higher Control

Sensory feedback

Reflex Feedback

Cen

tral

Fee

dbac

k

Focus of this work is how to include the sensor feedback in the CNN-based CPG

++

Wheels

• Direct coupling sensor/motor

• The speed of the motor is changed according to the output of the sensor

• Excitatory/inhibitory connections

• “+” increase the speed• “-” decrease the speed

• Behavior of the vehicles

Braitenberg vehicles

Sensors

++ --

Braitenberg vehicles attracted by light

-- ++

Braitenberg vehicles – photophobic behavior

The principles underlying Braitenberg

vehicles are used to implement feedback

in CNN-based CPG

--

• To this aim the dynamical behavior of the CNN cells controlling the mid legs is changed by acting on the bias parameter

• Control of direction: including sensor feedback in the CPG for obstacle avoidance as in Braitenberg photophobic vehicle

CNN based CPG: obstacle avoidance

Dynamics of the CNN cell

i2=0.34 i2=0.35 i2=0.36

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• Continuous line

• Diamonds: Numerical data

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10)(

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Period of oscillations T versus bias values

• The hexapod is equipped with two sensors (measuring the distance from an obstacle)• Feedback from sensors is included in the CNN-based CPG

--

CNN-based CPG with sensor feedback

R1L1

R2

L3 R3

L2

SRXSLX

obstacle

obstacle

Control Scheme

CNN CPG(MATLAB)

HEXAPOD(VISUAL NASTRAN)

antennae output

Simulation tools• The CPG is implemented in MATLAB• A dynamical simulator of the hexapod robot is provided by VisualNastran

Video

Results

Signals from CPG

The CNN-based CPG Chip

Analog CoreCNN-based CPG

Digital Control

cTC

C

2

1

Control of the oscillation frequency

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Clock frequency

Switched Capacitors Implementation

Feedback signals in the CNN-based CPG Chip

CNNSC

OSC

SENSORSA/DDIGITAL

CONTROL

1

2

4

3

1 Switched Capacitors Clock2 Bias control signal3 Topology (connections) control signal4 Frequency clock adjust signal

• Speed control (clock frequency)• Direction control (bias of the middle CNN cells)• Choice of the gait (choice of the connections)

Experimental results

• Oscillation frequency

• Speed control

• Locomotion patterns

• Direction control

Single cell behaviour

fc=100Hz

fc=10kHz

Frequency range 100mHz-3MHz

Large variations of the clock frequency allows the control of the stepping frequency

Speed control

Small variations of the clock frequency allows the control of the gait speed

Measured period and simulated period of oscillations

Locomotion patterns

1 Switched Capacitance Clock2 Bias control signal3 Topology (connections) control signal

Cell

ANALOGOUTPUTS

Set ofConnections

Cell

Cell Cell

Cell Cell

DIGITALINPUTS

2

2

2

2

22

3

SC CLOCK 1

Fast Gait

R1L1

R2

L3 R3

L2

fc=1kHz

fc=100Hz

Direction control

R1L1

R2

L3 R3

L2

SRXSLX

High-level control• A CNN based Biomorphic Adaptive Robot

• Attitude control through CNNs

• Attitude control through Motor Maps

• Wave-based control of navigation

High-level control

• A CNN based Biomorphic Adaptive Robot




Skip

A CNN based Biomorphic Adaptive Robot

CNNTuring Pattern

sensors IR (sensors status)

IR fixed-action patterns


P. Arena, L. Fortuna, M. Frasca, L. Patané

A CNN based Biomorphic Adaptive Robot

Front Sensor

Right SensorLeft Sensor

CNNROBOT



LEGO roving robot Obstacle

Obstacle position, CNN patterns and fixed-action patterns

ObstaclePosition

CNNPattern

Fixed-actionPattern

ObstaclePosition

CNNPattern

Fixed-actionPattern



video

C:\mattia\VideoBiorobots\CNN_biomorphic_adaptive_robot2.avi

Reactive Deliberative

Predictive capabilities (World model accuracy)

Speed of response

Our robotFuturedevelopments

Perception through CNNs

High-level control

• A CNN based Biomorphic Adaptive Robot




Skip

Rexabot II: features of the control system

• Locomotion control– A CPG built of CNN neurons controls the

locomotion– The CPG is constituted by 6 leg controllers

(each leg has its own network of CNN neurons controlling its kinematics)

• Attitude control– Simple bio-inspired principles– P.I.D. controllers

Structure of the robotThe hexapod robot prototype Aluminum carrying

structure 3 servomotors for each 3

DOF leg (PWM driven) Attitude sensor: 2-axis

accelerometer (ADXL202) 38x40x20cm

The hexapod robot prototype Aluminum carrying

structure 3 servomotors for each 3

DOF leg (PWM driven) Attitude sensor: 2-axis

accelerometer (ADXL202) 38x40x20cm

Leg Controller: from 2dof legs to 3dof legs

a1

a22 DOF leg 3 DOF leg

a1

a2

AEP

PEP

X

H

stanceswing

A

C

D

B

115.0

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)1(

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iysyxdt

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x2

x1

1,11,1B1,1

• Control of a 2 DOF leg: 1 CNN neuron• Control of a 3 DOF leg: a network of CNN neurons• The two CNN neurons are connected using chemical

synapsesCNN neuronCNN neuron

Design of the Leg Controller

a1

a2 3 DOF legIdeal kinematics Actual kinematics

9.05

5.02

,13

,12

,21

I

II

I

yq

yq

yq

Directkinematics

Specifications:• stance• swing

• An ideal kinematics is assumed by keeping into account the specifications of the stance and swing phases

• A network of CNN neurons able to furnish the joint signals is designed

1,11,1B

+y2,I

-y1,II

Circuit Implementation• The discrete components circuit

implementation is based on operational amplifiers blocks to realize the sum blocks and the saturation nonlinearities

1,1B1,1

+y2,I

-y1,II

• Alternating tripod gait: legs are organized in two tripods (L1,R2,L3) and (R1,L2,R3) that alternatively stay on ground

• The leg controllers are connected using synapses as in figure

• Other locomotion pattern can be considered


Attitude Control - Simple principlesAttitude Control - Simple principles

Euler Angles: Roll-Pitch-Yaw roll pitch yaw

Roll and pitch angles are controlled by using simple principles: adding an offset on the angle between the femur and the tibia (-joint) and subtracting the same offset on the angle between the femur and the coxa (-joint) changes the roll and pitch attitude of the hexapod

Attitude Control - Pitch controlAttitude Control - Pitch control

x

y

zAbsolute reference y1

x1

z1

11

00

11

P

Add a negative offset at the angle of the front legs Subtract the same offset at the angle of the front legs Subtract the same offset at the angle of the hind legs Add the same offset at the angle of the hind legs

L1 R1

R2 L2

L3 R3

Attitude Control - Roll controlAttitude Control - Roll control

11

11

11

R

Act on the contralateral legs in an opposite way

L1 R1

R2 L2

L3 R3

x

y

zAbsolute reference

x1

z1

y1

Attitude Control of the Hexapod Robot: PID controllersAttitude Control of the Hexapod Robot: PID controllers

Nonlinear control of attitude control based on P.I. controllers (1 P.I. for each leg) and saturation blocks A 2-axis accelerometer sensor CNN implementation

The whole control system is realized by CNNs

CPG-CNNAttitude Control

CNN

+

Sensor

Results

• Locomotion control– A CPG built of CNN neurons controls the

locomotion– The CPG is constituted by 6 leg controllers

(each leg has its own network of CNN neurons controlling its kinematics)

• Attitude control– Simple bio-inspired principles– P.I.D. controllers

Results - Video– The robot walking in the DEES lab

• Walk on an horizontal plane• Walk on a slope (descent)• Walk on a slope (roll)

– Attitude control when the robot is not moving

• Roll control• Pitch control

– Escaping from non-natural situations• Video





Skip

The Motor Map Controller

- (X(t) – X1(t))2 – (Y(t) – Y1(t))

2System to be

Controlled

Referencesystem

Rewardfunction

MotorMap

State variables

State variables

control signal

adaptive gain

x

+-+

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Input layerInput

Output

Neurons

Output layer

Input layer

Control

Simulation Results

Example 2 – Switching behaviour

Example 1 – Tracking of a limit cycle

Attitude control through Motor Maps

k

k

d

d

+-

-+

Motor Map

Hexapod

rewardCPG

s

1

s

1

+

Attitude control through Motor Maps





Skip

CNN Wave based Computation for Robot Navigation Planning

Paolo Arena, Adriano Basile, Luigi Fortuna, Mattia Frasca

Dipartimento di Ingegneria Elettrica Elettronica e dei SistemiUniversità degli Studi di Catania, Italy

E-mail: [email protected]

Outline

• Reaction Diffusion Cellular Neural Networks (RD-CNN)

• RD-CNN for robot navigation control

• The CNN algorithm• Experimental results (roving

robots)

Reaction Diffusion Cellular Neural Networks

Emerging computation• Pattern formation• Propagation of autowaves

uuu 2)(

ft

Reaction-diffusion equations

Reaction-diffusion CNN

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dt

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Reaction Diffusion Cellular Neural Networks

Standard RD-CNN cell

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1;1;1,1;1,1;,11;,112;1;1;1;

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Navigation control

• Robot moving in an unstructured complex environment

• Possible solution: artificial potential fields• How to solve this problem in real-time?• Wave-based computation can be useful

to solve this problem in real-time

?

RD-CNN for Robot Navigation Control

Wave-based computation

Picture of the environment Action

RD-CNN for Robot Navigation Control

• Obstacles are the source of repulsive wavefronts

• The target is the source of attractive wavefronts

• The features of the autowaves are used to drive the robot through a real-time planning of the trajectory

Action

The RD-CNN Algorithm 1

Motion Detection North

Motion Detection South

Motion Detection East

Motion Detection West

CNN autowaves

Robot Position AND AND AND AND

South North West East

• Two complementary RD-CNNs: obstacles and target are independently processed

• Motion detection templates are time-delay templates!

The RD-CNN Algorithm 1: Simulation Results

Obstacles

Target


Obstacles

The RD-CNN Algorithm 2

Threshold

CNN autowaves

AND AND AND

South

Robot

Robot

West East

• The robot is a four active pixel object

• This algorithm can be implemented on VLSI CNN chip

Instantiation on a Roving Robot

Camera on the ceiling of the laboratory

Camera on board1 2

World-centered perception

Robot-centered perception

Experimental results: world-centered perception

Trajectory of the robot

Obstacles

Experimental results: on-board camera

Experimental results: on-board camera, CACE1k

With Rodriguez-Vazquez and Carmona-Galan

Captured frame

Obstacles

Robot front wheels

Chip results

2ms

Further details

A. Adamatzky, P. Arena, A. Basile, R. Carmona-Galàn, B. De Lacy Costello, L. Fortuna, M. Frasca, A. Rodrìguez-Vàzquez, "Reaction-diffusion navigation robot control: from chemical to VLSI analogic processors", IEEE Transactions on Circuits and Systems – I: Regular papers, Vol. 51, No. 5, May 2004, pp. 926-938.

Conclusions

• Novel paradigm for real-time robot navigation control based on reaction-diffusion CNN

• Wave-based computation to calculate the trajectory for a robot moving in a complex environment

• Advantages: use of massively parallel processors, VLSI chip (fast analog processor), real-time computation

Control scheme

bio-inspired locomotion control of hexapods alessandro rizzo

Documents

motor pattern cpg

rhythmic motor pattern

welldefined pattern

given pattern

pattern of neural activities

cnnbased motor unit

cnn network

socalled cpgthis paradigm