MEDM Package For Walking Robot

General Outline Organized for any multi-legged robot

Hexapod, Quadruped, Biped, … Explicit Dynamic Calculation Gait Planning

New algorithm for rhythmic gait Trajectory Planning

Optimal trajectory subject to maximum speed

respected to stable motion Graphical interface

Graphical gait showing

Over 2500 lines code

Organized simply to coordinate for any Walking Robot Compliance structure added

Linked to Simmechanic toolbox

Optimized trajectory added

Over 2500 lines code Minimum possible required codes added

All modules writing as function for providence

Organized for any walking robot Simply coordinating for a arbitrary walking robot structure:

• Add how many legs with arbitrary configuration• Replaced “D-H” recipes with new one “Direct Configuration” as become more user-friendly.

Dynamic

Kinematic

Dynamic

Method

Install coordinate frames

• Method

Explicit Dynamic formulation:

•

Based on Lagrangian

formulation:

Install coordinate

frames

Algorithm

Explicit Dynamic

3 10 1

m m

nnmTn

R LT

: Ci i

i i i

WEd L LEq Q

dt q q q

Install frame

Kinematic FormulaDirect output to LaTeX

0

cos cos sin cos sin cos sin sin cos cos sin sin

sin cos cos cos sin sin sin cos cos cos cos sin

sin sin sin cos cos

bR

Kinematic

Explicit Dynamic

Input Output

T T Tv v a aM q J MJ J R IRJ

1

1 1

2 2ij

njkik

ij ij C kk j i

MMC M C q

q q

jacobian ,

jacobian ,

jacobian ,

jacobian ,

v G

a

f force

torq

J X q

J q

J WE f

J WE

, , ,fM q q C q q q G q J q q J q q f d

Minimum slippage possibilityForce distribution methodQuadratic ProgrammingNimbly walkingMaximum Speed respected to stable and

non-slipping motion

Trajectory Planning

Stability

MHS (Measure height of system)ZMP (Zero moment point)FML (Force moment line)

MHS Criterion

1

1

1

1

i= 1,2, , 1i ii

i i

nn

n

p pa n

p p

p pa

p p

. . i= 1,2, ,iii vi iI M a n

1 . 0

1 . 0

iii

ii

M a

M a

i= 1,2, ,iMin n

. . i= 1,2, ,c m ih Min n

. .

. .

. i= 1,2, ,nom

c m i

i nomc m nom

h Minn

Minh

Graphical Gate Planning

Linked to Simmechanic

Conclusion

MDEM suitable for:modeling compliant walker robotsChecked new stability criterions Implemented new algorithm controls Implemented online stability controls

The End

MEDM Package

Type: Package Version: 1.5.0v Product name: MEDM Date modified: 12/01/2009