Evo star2012 Robot Base Disturbance Optimization with Compact Differential Evolution Light

Robot Base Disturbance Optimization with
Compact Differential Evolution Light
Giovanni Iacca, Fabio Caraffini,
Ferrante Neri, Ernesto Mininno
University of Jyväskylä
Faculty of Information Technology
evo* 2012 - Málaga, Spain
April 13th
2012

#giovanni_iacca @evostar_2012_málaga
Outline

Memory Issues in Computational Intelligence

Compact Differential Evolution Light (cDElight)

Robot Base Disturbance Optimization

Simulation Results

Conclusions


Computational Intelligence Optimization is good!

Why, Master?

Because its methods are efficient and robust!

Only that? What else, Master?

In addition to that, they often don't require any information
about the problem at hand, my son.

Oh, cool! But is there any drawback?

Well, actually most of them use plenty of hardware resources
and are computationally expensive.

Mmm...

So, what if we need to perform an
optimization on board of an embedded
system with limited hardware?


Single Solution Algorithms
- Simulated Annealing (SA)
- Single Particle Optimization
- Some Local Search Algorithms (e.g. Hooke-Jeeves)

Compact Optimization
- compact Genetic Algorithm (cGA)
- compact Differential Evolution (cDE)


Estimation of Distribution Algorithm (EDA)

Does not use a population of individuals → low memory footprint

Makes use of a statistic model of the population:
Multivariate Gaussian with decision variables normalized in [-1,1]

Convergence: shrinkage of the Gaussian over the best (“elite”)

Sampling introduces beneficial randomness
compact Differential Evolution (cDE)

Probability Vector (PV)
PV update rule
(offspring vs elite)


DE can be straightforwardly
encoded into a compact algorithm
without losing the basic working
principles (instead of cGA)

Survivor selection scheme
(one-to-one spawning logic)

Persistent vs non-persistent elitism

Parameters: F, Cr, Np
Original implementation
(cDE rand/1/bin)

Mutation Light: only one solution is sampled (instead of 3)
→ →
compact Differential Evolution light (cDElight)

Statistic independence

Truncated Gaussian ~ Gaussian
Under the following
assumptions/approximations:
Limited computational overhead!

Exponential Crossover Light: ad hoc xover exp instead of xover bin
Exponential Crossover (standard) Exponential Crossover Light
only one
random number
multiple
random numbers
→

Computational Overhead
(vs cDE)
Computational Overhead
(vs different algorithms)
~1/3 computational
overhead - O(n)
Tests performed on a single core Pentium 2.8 GHz PC, with the sphere function (Java implementation) for
different dimensions (2:100). The algorithm overhead is computed on 10000 fitness evaluations.
memory-saving
population-based

Trajectory plan: given a task, generate a trajectory (pos, vel, acc) for each joint so that
1) the end effector execute the task, 2) the trajectory is smooth, 3) kinematic/dynamic
constraint are satisfied, 4) the trajectory is optimal according to some criteria


Point-to-point problem:
define inter-knot points and
interpolate
(linear interpolation, spline, etc.)

Motion control: define the
torques to be applied

Free-floating
environment
Mutual disturbance between base and end-effector:
FB
= N-1
FE
↔ FE
= NFB
Fitness function: minimize the integral over
time of the norm of the acceleration vector
on the base

Simulation Results

Matlab/Simulink implementation

{pos, vel, acc} x 2 knots x 3 joints = 18 variables

5th
order spline to model q(t), continuity condition on {pos, vel, acc}

4 different memory-saving optimization algorithms

Parameter setting suggested in original papers

30 runs x 10000 fitness evaluations

Wilcoxon Rank-Sum Test (confidence level 0.95)

Simulation Results
Compact Differential Evolution (cDE)
Intelligent Single Particle Optimization (ISPO)
Non-Uniform Simulated Annealing (nuSA)
Without optimization (beginning of learning period)
With optimization (end of learning period)

Conclusions

Some industrial applications are plagued by limited hardware

Compact algorithms, e.g. cDE, due to their compactness and
robustness are well suited for this kind of applications

We proposed a more efficient cDE (cDElight)

cDE proven to be successful on a complex space robotic
application

Possible alternatives and future works: different compact
frameworks (e.g. cBFO, cPSO), memory-saving MC

Thank you! ¡Muchas gracias! Grazie!
Questions?

Evo star2012 Robot Base Disturbance Optimization with Compact Differential Evolution Light

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