Ranbots

Ranbots
Alvaro Cassinelli, Assistant Professor
Ishikawa-Komuro Lab, University of Tokyo
Emmanuel Fort, Associate Professor
Institut Langevin ESPCI ParisTech, University Paris
Diderot
Control N degrees of freedom with a unique actuator
(1 DOF) introducing noise into the others DOF through
mechanical coupling… then, reduce the noise intensity
as it get close to the target in phase-space.
Tokyo, 2009

Ishikawa Komuro Lab http://www.k2.t.u-tokyo.ac.jp/
How? (a) First, a simple, unique actuator introduces noise into every DOF of the
system (through mechanical coupling). Noise can be generated by the robot itself,
or be just modulated noise from the external environment.
(b) Then, noise intensity is reduced as the system get close to the target in phase-
space. This is done by sensing an external “excitation” field that decreases in
intensity when the configuration is close to the target. This excitation field is
especially tailored so as to accelerate convergence.
Why? The rationale is that it may be easier to build (many/directional)
sensors than directional actuators producing thrust in particular directions.
Sensors can be directional, but there is only one (or few) simple actuators that
make the system move randomly (in phase space).
I. Ranbot idea
What? A method to steer a micro-robot by modulating the intensity of mechanical
noise (internally generated or acquired from the external environment). More
generally, a method to control a complex mechanical system using a (single) simple
actuation mechanism.

Applications
• Locomotion for low complexity or micro-robots: make a random move,
with a jump proportional to a designed "excitation" field. The closer to
the goal, the less large the jump. Robot will sway towards the "less
exciting spot“. This excitation field can be anything: temperature,
pressure, chemical concentration, but also synthetic (light & sound
fields).
Although time-inefficient, this process can be useful in
a handful of situations:
• Cheap control of a complex mechanical system (when time is
not critical). The only difference, is that the “jump” is done in
phase space.
• Finally, it is interesting to note that the “actuator” may just need
to control the gain of a dumping system for external noise
sources (ex: molecular collisions).

Example: Thousands of cheap micro-robots, the shape of “high-bounce balls”, launched on the surface of Mars, each containing
a handful of simple, isotropic sensors (temperature, humidity, etc). Say we want to “steer” them towards the poles (to explore the
planet cold poles). Then the strength of their jump will just be a function of temperature. Now, there can be many thousands or
millons of them: given that the process is very likely ergodic, we can be sure some of them will reach the pole quite quickly…
Perhaps after a hundred or thousands years, some of these robots would concentrate near the pole - in the meanwhile they can
be used as “moth” sensors for weather logging. The robots could gather energy for only one or two bounces a day (solar energy,
using the 3d solar cells embedded on the material). This is to compare with a complex and fragile unique land-rover robot.
Ranbots for cheap space exploration?

x
x
Although the DIRECTION of jump is
equiprobable, the change in magnitude
results in a non-compensated drift
Intuition: why this should work…
l(0)
l(3)
t
t+dt
Notes:
• even if this model is discrete and 1d, it cannot be treated easily using generating functions (to compute <x> and
<x2>(n) for instance as it is done in the case of the simple random walk on Z) because we cannot use the binomial
distribution for the length after n steps.
• this can be studied however by building the transition matrix of a random markov chain
1D and with
discrete +/-
flight steps

Inspiration…
...Later experiments showed that this is was a consistent biais
unrelated to the proposed mechanism!

Ishikawa Komuro Lab http://www.k2.t.u-tokyo.ac.jp/Ishikawa Komuro Lab http://www.k2.t.u-tokyo.ac.jp/
Simulations Start
End
Null excitation
• one jump/iteration
• the direction of the jump is random, i.e.
equidistributed on [0-360[ deg.
• the length of the jump is deterministic, and
directly proportional to the excitation field
I modeled a RANDOM WALK with
the following properties:
This differs from the drunkard’s walk or Levy-flight in a fundamental way: the steps
(taken as random variables) are no longer independent!
Therefore, the process very likely does not converges to a Wiener process (typical of
Brownian motion).

....On realistic jump statistics (in progress)
Clearly, the magnitude of the real jump is not deterministic!
In any case, we need to model the real jump process:
• for a micro-robot, we can perhaps use the model of molecular collisions (free-path, maxwell-boltzmann
statistics for speeds).
• for macro-robots, everything depends on the jumping mechanism; the excitation field may control the
magnitude of the initial velocity of a ballistic jump (with random direction).
•Finally, it is interesting to note that one can build a Brownian-like or Levy-like process from a random walk
with properly switched swimming and tumbling modes (switching controlled by a source of noise) - this is what
I was shown by the Yuragi group at Osaka university (need references though).
Perhaps we can model the length of the jump by a normal distribution with a mean proportional
to the excitation field, and a fixed variance for instance (everything depend on how we generate
the vibration).

but ups! it takes an unexpected
long roundabout of some
hundred iterations...
however, after some thousand
iterations, the particle looks confined
to the center region and scarcely
moves...
a few hundred iterations... ...and the particle is already close
to the attraction center!
More “intelligence” needed (internal state)?
Solution: design a proper excitation field; also, perhaps the ranbot could
have an internal “temperature” that would decrease with time?
Note: that the ranbot process is very different from simulated annealing: what evolves is not
the probability of acceptance of a proposed change (sigmoid function parametrized by a
changing global temperature), but instead what changes is the reach of the neighborhood
(i.e. the proposal function) which depends directly on the energy landscape.
Problem: a very convoluted exploration!

Simulations using a grayscale field
50000 “ranbot” dots (ergodicity)
excitation=0.001*(exp(1.0*sqrt(r*r+g*g+b*b)/20)-1);

Central field
Attractive Repulsive
Note: (1) effects of discrete steps; (2) particles trapped in a ring, not in the center or the
borders of the image (which are the real global minima). Why?
click to launch video click to launch video

click to launch video
Gradient stripes
Note: Note again how the ranbots concentrate in a region around the global minima, but
have “difficulty” reaching it (exponential convergence time?)

Ishikawa Komuro Lab http://www.k2.t.u-tokyo.ac.jp/Ishikawa Komuro Lab http://www.k2.t.u-tokyo.ac.jp/
Real (macro) prototype
A central (horizontal) motor
helps randomize the jumping
direction if needed (usually
not needed).
Brightness sensor
(phototransistor+LED)
Atmega168 microcontroller
(process sensor data and
randomize actuators)
Motor vibrator
First one legged (spring-
based) ranbot – unstable…

Photosensitive Three legged Ranbot

Li-ion
battery, 3.7V
100mAh
+
-
0-1kOhm
Vf= 3v
Vcc 3.3V
3.7V on RAW pin.
(Arduino has a voltage
regulator and Vcc pin
gives a stable 3.3 V)
3.7-3.9V / 200mAh
SWITCH
Li-ion
battery, 3.7V
100mAh
-
+
(1) http://www.sparkfun.com/commerce/product_info.php?products_id=731
White LED
Motor
vibrator
(from Pin 10, PWM, 3.3V)
To ADC pin 0 (0-3.3V to 0-1024 levels)
75 ohm
NPN switching
transistor
2N 3904
~0.5 V
(saturation)
Im = 60 mA
V=~1.5V
(could go up to 3V)
Motor “central”
Motor 3
Motor 2
PWM control of motor 1
Phototransistor
(1)
(2)
(3)
(4)
PWM freq: ~500 Hz (should be made higher?)
Duty cycle: 255 levels
~0.7 V
(saturation)
10 ohm
Ranbot 1.0 Circuit
(5) http://www.datasheetcatalog.org/datasheet/fairchild/2N3904.pdf
(5)
Rechargeable
batteries
Alvaro Cassinelli 2009
Arduino Pro Mini 3.3V

• The pinout of this board matches the FTDI cable to work with official Arduino and cloned
Arduino boards. It can also be used for general serial applications.
• The major difference with this board is that it brings out the DTR pin as opposed to the RTS
pin of the FTDI cable. The DTR pin allows an Arduino target to auto-reset when a new Sketch
is downloaded. This is a really nice feature to have and allows a sketch to be downloaded
without having to hit the reset button. This board will auto reset any Arduino board that
has the reset pin brought out to a 6-pin connector.
• You can actually see serial traffic on the LEDs to verify if the board is working.
Programming/charging batteries through the USB-Serial port adapter
This way up!
(can also be used to send/receive data from the computer in real time)
FTDI Basic Breakout -
3.3V
http://www.sparkfun.com/commerce/product_info.php?products_id=8772

Motors glued to the chassis: short, rapid jumps and smooth gradient.
Video demo 1
https://www.youtube.com/watch?v=h99YcRbfYx8

Motors attached with springs: long jumps, handle larger uniform zones?
Video demo 2
Note: the photodetector averages the brightness in a small area; this means that in the borders of the stripes,
the ranbot sees a gradient.

If the stripes are uniform, the robot behaves as a
brownian particle inside the stripe.
It can by chance go into the black stripe, but it can easily
go out again… It will presumably take much more time to
converge.
Importance of the gradient and size of the stripes
Goal of the model (including “parabolic” jumps instead of average “thermal” speed)
is to design the most effective shape for the trapping potential.
From my early simulations, it looks like a linear gradient is better than an
exponential or parabolic one (the latter two resemble more to “discrete” stripes: the
derivative of the “synthetic” temperature is more pronounced? - see
thermodiffusion model).
large jumps…
Smaller jumps…

Relation with other “diffusion” processes
Chemotaxis:
tumbling (disordered flagellar motion)
+ swimming (ordered flagellar thrust)
Soret effect (thermophoresis - large
particles)
Brownian motion
Brownian motion with biasing potential
“Yuragi” robots
Net force on Langevin equation
Process Model & mathematical treatment
Generating functions, markov chains, micro-
equilibrium
Net force appears on Langevin equation (Prost
papers)
Langevin equation with terms weighed by the
“activity” of the robot (state variable affected by
sensors and natural oscillation)
Thermodiffusion Statistical approach using Maxwell-Boltzmann
distribution (average speed is a function of T)
Similar to chemotaxis?
Ranbots:
tumbling (brownian collisions)
+ swimming (free path)
Similar to thermodiffusion?

- For a Maxwell-Boltzman distribution, <v> is proportional to √T, and the mean free path
is independent of T
- il reste finalement une vitesse moyenne de déplacement proportionnelle à
T^0.5gradT. Nous on aurait ensuite T fonction de l'illumination I (fonction qui est défini
électroniquement et qui reste à calibrer.
Average electronic velocity:
l : mean free path
: average speed free path
Analogy with thermodiffusion (in progress)
ATTN: in my simulations, the LEGHT of the walk is proportional to “T”; here, the initial
speed is proportional to T instead. This model is more realistic (see comments on slide
8)

Use natural occurring noise as sources of noise (ex:
brownian motion).
This can be done for instance by changing the rigidity
of the robot shell (elastic or inelastic collision).
In the case of micro or macro-robots, this can be done
using a shell made of a material that reacts to
temperature or some other environmental variable
(electric field, etc).
Interestingly, if the shell can be hardened anisotropically (thanks to a polarized electrical field for
instance), then we can use random thermal energy in the medium to directly generate thrust in one
direction (in the case of a macro-robot in the middle of a crowd, this principle will meant the use of kinetic
energy from pedestrians (bumping into the robot) to drive the robot in a specific direction). But this is not
the principle of the "ranbots".
II. Using external noise sources
This is very similar to “yuragi” principle(*)! (“yuragi”= japanese word for biological fluctuation: a
way to “switch elegantly between stochastic and deterministic behavior”)
Idea:

III. Collaborative ranbots
• Launch many ranbots;
• Each ranbot affects the global excitation field (e.g: proximity of another ranbot
decreases excitation, i.e., it works as a local target)
• Since ranbots will pass more time in low-excitation zones, these will become
even more attractive with time.
• This is an optimization method inspired on ants pheromone trails and somehow related
to “crossover” in genetic algorithms (what is transferred is the position).
Idea:
without collaboration...
... and with collaboration (slightly fastest
convergence)
• Needs more simulations on this (mathematical model may be complicated)

Conclusion
Shirai et al. robot:
Thermodiffusion (temperature is
“simulated” by the excitation field)
Ranbot:
Random jumps (no directional thrust!)Tumbling & swimming
Chemotaxis
Temporal sensing & internal
state changes
tumbling/swimming proportion
(“activity”)
Instant sensing dictates the magnitude of
the jump (this means that a good design of
the excitation field can generate an efficient
exploration - e.g., Levy-flight like).
Langevin equation with “activity”
weighting function
Statistical approach (mean free path,
thermal equilibrium)
•Both approaches do not rely on local gradient sensing.
•Both can use noise from the environment for tumbling or jumping.
•For ranbots, this need to be the only “thrust” force.
•Very likely, ranbot process is much less inefficient - but “cheaper”?

Early research (more questions than answers)
How to study convergence (<x>), and variance (<x2>) as a function of time?
Mathematical treatment of “ranbots”: micro-equilibrium?
Mathematical treatment of artificial chemotaxis:
• problem of dimension and discretization in Shirai’s markov chain simplified model
(1D, discrete) ...possible without simulations?
Importance of the shape of the “excitation” field!
• “activity” modified Langevin equation
Needs more simulations (gaussian jump, levy-flight)
Need experiments in the real world (micro/macro robots).
•For this, it is imperative to catalog the different sources of mechanical noise, and its statistics.
Importance of the statistics of the jump: gaussian or levy-flight
• both can be generated by a state machine regulating the swimming/tumbling behavior as shown in poster
Nurzaman, S.G. et al. (*) [get it!]

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