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Model-free control framework for multi-limb soft material robots

  • June 2015
DOI:10.13140/RG.2.1.2209.6486
  • Conference: 7th International Symposium on Adaptive Motion of Animals and Machines
Authors:
Vishesh Vikas at University of Alabama
Vishesh Vikas
Piyush Grover at University of Nebraska at Lincoln
Piyush Grover
Barry Andrew Trimmer at Tufts University
Barry Andrew Trimmer
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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
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[3] G. Optimization et al. Gurobi optimizer reference manual. URL: http://www. gurobi. com, 2012.
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Gurobi optimizer reference manual
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