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MODEL-FREE CONTROL FRAMEWORK FOR MULTI-LIMB SOFT MATERIAL ROBOTS

VISHESH VIKAS1, PIYUSH GROVER2AND BARRY TRIMMER1

1NEUROMECHANICS AND BIOMIMETIC DEVICES LAB, TUFTS UNIVERSITY AND 2MITSUBISHI ELECTRIC RESEARCH LAB, CAMBRIDGE

INTRODUCTION

Soft body robots have potential for search and ex-

ploration during disaster relief operations. Soft

deformable materials promise versatility, adapt-

ability and impact resistance. However, control of

modular, multi-limbed soft robots for terrestrial

locomotion is challenging due to the continuum

nature of soft materials and robot-environment

interaction. Traditionally, robot control is usually

performed by modeling kinematics using exact

geometric equations and ﬁnite element analysis.

An alternative model-free control framework ad-

dresses following challenges

1. Generic - control exists in task space, not actu-

ator space, thus, independent of type of actua-

tor, soft material properties, etc.

2. Adaptability - allows learning for change in

surface of locomotion. Does not directly model

robot-environment interaction.

3. Modeling - indirect modeling by identifying

key factors that dominate robot control, e.g.

friction manipulation, and discretize them.

CONTROL FRAMEWORK

The model-free approach to control of soft robots

does not directly model the robot. It can be sum-

marized as a four-step process

1. Discretization: Discretizing the key factors

that dominate robot-environment interaction.

In process, deﬁning ﬁnite robot states.

2. Visualization: Use graph theory for providing

mathematical representation of periodic con-

trol patterns and locomotion gaits.

3. Learning : Rewards are weighted displace-

ment and orientation change for robot state-

to-state transitions. Learn rewards speciﬁc to

locomotion surface.

4. Optimization: Optimization of reward depen-

dent locomotion task (translation or rotation)

cost function is an Integer Linear Program-

ming (ILP) problem.

EXAMPLE ROBOT AND MODEL-FREE CONTROL

Step 1: DISCRETIZATION Step 2: VISUALIZATION

Friction manipulation mechanisms dominate control by inﬂuencing the robot-

environment interactions.

•Node NK≡State dec2bin(K −1)

•Arc (Ai): transition from one state to another

•Simple cycle (ci∈ R56): periodic cycles of state

transitions and act as linear basis for ﬁnding

locomotion gaits.

ci,j =1 if ciincludes arc Aj

0otherwise

•Circulation:L=

K

P

i=1

xici, xi∈ {0,1,2, ..}

Step 3: LEARNING AND GRAPH THEORY Step 4: OPTIMIZATION

•State transition reward (Rj∈ R3×1) : weighted result, some

translation (∆x, ∆y) and rotation (∆θ), of transition from one

robot state to another. This is unique to surface of locomotion

and is learned.

•Simple cycle cost J(ci) =

56

P

j=1

ci,j ·Rj

•Locomotion (L): deﬁned as circulation i.e. integer sum of sim-

ple cycles.

•Locomotion cost: J(L) =

K

P

i=1

xiJ(ci)=[Jx, Jy, Jθ]T

•For translation in +Xdirection

max

xi∈(Z+)PJx

s.t. len(L)≤lmax and

Jy∈[−y−, y+], Jθ∈[−θ−, θ+]

•Integer Linear Programming problem

with linear constraints!

ADAPTABILITY: LOSS OF LIMB

No need for re-learning state transition rewards.

CONCLUSION AND FUTURE RESEARCH

•Graph theory analogy: Facilitates mathemati-

cal deﬁnition of periodic control (simple cycle)

which are instrumental in deﬁning locomotion.

•Speed of locomotion: Dependent on speed at

which a robot can transition from one state to

another as control exists in task space.

•Optimization problem: Integer linear program-

ming problem with linear constraints. Can be

quickly solved using standard linear solvers for

small to medium size graphs.

-Complex locomotion gaits: Optimization for large

angular displacements and time constraint (ac-

tuator speciﬁc) will result in complex gaits.

-Way point navigation: Curvilinear path following

for way point navigation can be achieved by up-

dating the cost function.

-Intelligent learning: State transition rewards

(arc weights) can be learned intelligently for

new unstructured environment and dynami-

cally changing environment scenarios.

REFERENCES

[1] R. Diestel. Graph Theory. Springer, 4th edition.

[2] D. B. Johnson. Finding all the elementary circuits of a directed graph. SIAM Journal on Computing, 4(1):77–84, 1975.

[3] G. Optimization et al. Gurobi optimizer reference manual. URL: http://www. gurobi. com, 2012.