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### Sources

Three Layer Evolutionary Approach

Local perceptions, such as “bald head” or “long beard”

Encoded behaviors or internal states

Time intervals

Evolve Behaviors

Evolve Motions

Evolve Perceptions

Motions as timed sequences of encoded actions, for instance RFRFLL

Global perceptions, possibly encoded such as “narrow Corridor” or “beautiful Princess”

Behaviors such as “go forward until you find a wall, else turn randomly right or left

Evolve in hierarchy

- Together or separately
- Feedback from model or from real world
- First evolve motions and encode them.
- Then evolve behaviors.
- Finally develop perceptions.

Go to the end of the corridor and then look for food

If you see a beautiful princess go to her and bow low.

If you see a dragon escape

Evolve in hierarchy

avoid obstacles

Execute optimal motions

Save energy

Look for energy sources in advance

Execute actions that you enjoy

What if robot likes to play soccer and sees the ball but is low on energy?

Optimizing a motion

Parking a Truck

Solving this analytically would be very difficult

Question; How to represent the chromosomes?

Here you see several snapshots of a “movie” about parking a truck, stages of the solution process.

Another example

Learning Obstacle Avoiding

Input and output data are some form of MV logic

how- How would you represent chromosomes?
- Design Crossovers?

Robot can move freely but has to avoid obstacles

This can be like the lowest level of behaviors in subsumption or other behavioral architecture for all your robots

Remember the goal when you create the fitness function

The key to success is often in fitness function

Evolutionary Methods

- Optimization problems:
- Single objective optimization problems
- Multi-Objective optimization Problems

More examples of problems in which we use evolutionary algorithms and similar methods.

- Search Problems (Path search)
- Optimal multi-robot coordination
- Multi-task optimization
- Optimal motion planning of robot arms (Trajectory planning of manipulators )
- Motion optimization (optimization of controller parameters - morphology in different control schemas)
- PID (PI)
- Fuzzy
- Neural
- Hybrid (neuro-fuzzy)
- Path planning and tracking (mobile robots)
- Optimal motion planning of robot arms
- Trajectory planning of manipulators
- Vision – computational optimization

What are these “other algorithm”?

- Evolutionary Algorithms - Related techniques:
- Ant colony optimization (ACO)
- Particle swarm optimization
- Differential evolution
- Memetic algorithm (MA)
- Simulated annealing
- Stochastic optimization
- Tabu search
- Reactive search optimization (RSO)
- Harmony search (HS)
- Non-Tree Genetic programming (NT GP)
- Artificial Immune Systems (AIS)
- Bacteriological Algorithms (BA)

You can try them in your homework 1 if GA or GP is too easy for you.

Using them gives you higher possibility of creating a successful superior method for a new problem

GA-operators

- Selection
- Roulette
- Tournament
- Stochastic sampling
- Rank based selection
- Boltzmann selection
- Nonlinnear ranking selection
- Crossover
- One point
- Multiple points
- Mutation

Read in Auxiliary Slides about these methods. Or invent your own operators for your problem.

Your design parameters to be decided

- Genotype length
- Fixed length genotype
- Variable-length genotype
- Population
- Fixed population
- Variable population
- Species inside population
- Geometrical separation

Drawbacks of GA

- time-consuming when dealing with a large population
- premature convergence
- Dealing with multiple objective problems

Solutions

- Niches
- Islands
- Pareto approach
- Others

More examples of using GA in robotics

Trajectory Planning Problems

GA and Trajectory Planning

- GA techniques for robot arm to identify the optimal trajectory based on minimum joint torque requirements (P. Garg and M. Kumar, 2002)
- path planning method based on a GA while adopting the direct kinematics and the inverse dynamics (Pires and Machado, 2000)
- point-to-point trajectory planning of flexible redundant robot manipulator (FRM) in joint space (S. G. Yue et al., 2002)
- point-to-point trajectory planning for a 3-link (redundant) robot arm, objective function is to minimizing traveling time and space (Kazem, Mahdi, 2008)

Projects last years

Optimal path generation of robot manipulators

- Control Schema
- Robotic arm – kinematic model
- Controller type
- Objective function - optimal path
- Optimization algorithm (method)
- GA use smooth operators and avoids sharp jumps in the parameter values.

Adaptive Control Schema – Track Control error function between outputs of a real system and mathematical model

- What we optimize?
- Which parameters must be optimized?
- How many objectives (single –objective or multiobjective)?
- Collision free? (How to model collision in GA?)

- A three-joint robotic manipulator system has three inputs and three outputs.
- The inputs are the torques applied to the joints and the outputs are the velocities of the joints
- No ripples

- For n-DOF we will have n inputs ui, i=1…n, (ui↔ i)
- Controller
- PID (PI)
- Neural network (multilayer perceptron, recurrent NN, RBF based NN)
- Fuzzy
- Neuro-Fuzzy (hybrid)

- NN: We must to adapt the weights and eventually the bias

The chromosome:

- Adapt the weights

FUZZY LOGIC

- Fuzzy Logic
- Aggregation of rules
- defuzzification
- free-of-obstacles workspace (Mucientes, et. al, 2007)
- wall-following behavior in a mobile robot

Learning FUZZY LOGIC Controllers

- Learning of fuzzy rule-based controllers
- Find a rule for the system

Step 1: evaluate population;

Step 2: eliminate bad rules and fill up population;

Step 3: scale the fitness values;

Step 4: repeat NI iterations for Step 4 to Step 9

Step 5: select the individuals of the population;

Step 6: crossover and mutate the individuals;

Step 7: evaluate population;

Step 8: eliminate bad rules and fill up population;

Step 9: scale the fitness values.

Step 10: Add the best rule to the final rule set.

Step 11: Penalize the selected rule.

Step 12: If the stop conditions are not fulfilled go to Step 1

Encoding fuzzy controls

- The chromosome encode the rules:
- Sn is constant in this application but it can be also variable to be optimized
- wall-following behavior of the robot
- the robot is exploring an unknown area
- moving between two points in a map
- Requirements
- maintain a suitable distance from the wall that is being followed
- to move at a high velocity whenever the layout of the environment is permitting
- avoid sharp movements (progressive turns and changes in velocity)

Path-based robot behaviors

- The requirements are “encoded” in Universes of discourse and precisions of the variables
- right-hand distance (RD)
- the distances quotient (DQ), based on left-hand distance
- Orientation
- linear velocity of the robot (LV)
- Linear acceleration
- Angular velocity
- Path of the robot (simulated environments)

Fast, reliable, no harm to robot or to environment

- This is useful for out PSU Guide Robot
- Do not harm humans
- Do not harm robot

Fixed points: the desired Cartesian path Pt is given the problem is to find the set of joint paths P in order to minimize the cumulative error between desire and real path during trajectory

Pk is the kinematic model

- Free end points case

Find the set of joint paths, next smooth it

Minimize the cumulative error

Weighted Global Fitness

- fitness function (minimization)
- Global fitness: Linear function of individual objectives

Fot – excessive driving (sum of all maximum torques), fq – the total joint traveling distance of the manipulator, fc - total Cartesian trajectory length, tT - total consumed time for robot motion

- Penalty function
- Population initialization (probability distribution)
- Random uniform
- Gaussian

example

Drug Delivery Problem

Drug delivery using microrobots (Tao, et. al, 2005)

- (GA)–based area coverage approach for robot path planning.
- Drawbacks of most currently available drug delivery methods are that the drug target area, delivery amount, and
- release speed are hard to be precisely controlled.
- It is very difficult or impossible to eliminate side effects.
- Open issues
- actively control the delivery process
- Access to appropriate areas that cannot be reached using traditional devices
- Current Issues
- On-line path planning (solve unexpected obstacles problem)
- Optimal path planning (efficiency, path planning)

microcontroller is used to guide the robot movement

- GA-based approach uses fine grid cell decomposition for area coverage
- Because the robot will move cell by cell, the start point of chromosomes has to be changed dynamically whenever the robot reaches the center of a cell
- The end point of a chromosome is not fixed and needs to be determined by applying GA operators.
- The robots may move from the center of a cell to its 8 adjacent cells along 8 directions.
- some obstacles are unknown before drug delivery (the robot discover these obstacles during the motion)

- Deleting the path
- Crossover operator

- Travel further
- Delete
- Reverse delete
- Stretch
- Shortcut
- The algorithm keep mind the visited nodes
- Extension to operational research?

Other applications using evolutionary algorithms

- Autonomous mobile robot navigation - Path planning using ant colony optimization and fuzzy cost function evaluation (Garcia, et. al, 2009).
- Legged Robots and Evolutionary Design
- Optimal path and gait generations (Pratihar, Debb, and Gosh, 2002) – 0/1 absence or presence of rule
- six-legged robot
- collision-free coordination of multiple robots (Peng and Akela, 2005)

What if you want to optimize two parameters at the same time?

Pareto Optimization

What is better this or this?

- We want to optimize both functions f1 and f2

Biobjective means two objectives to reach

- We have x and y, two objectives here

Pareto solutions for different algorithms

Pareto Front

Pareto front

- The single objective optimisation problem (SOP) conduct to a minimization (or maximization) of one cost function, less or more complex, that is a single objective is taken into account.
- Conversely, the multi-objective optimization problem takes into account two or more objective that has to be minimized (or maximized) simultaneously.
- Some objectives can be in competition, so a simultaneous minimization is not possible, but only a trade-off among them.
- Some time, the number of objectives can be high, like 16 objectives or more that make the multi-objective optimization problem (MOP) and interesting and challenging area of research

Example of Pareto Optimization of two parameters

Optimization of Airplane Wings

* In most of the design space the red method is better than the blue method* It is good to use many Pareto methods and modify parameters

- Two objectives: Maximize lift, and minimize drag

Multi-Pareto

- We optimize many parameters,
- We may switch between subsets of them.
- Subsets can have two elements each.

General multiobjective optimization problem

- The multiobjective optimization problem could be generally formulated as minimization of vector objectives Jt(x) subject to a number of constraints and bounds:

Pareto-optimal set

- In the case of competing objectives a trade-off is involved such a problem usually has no unique solution.
- Instead, we can admit a set of solutions, equally valid non-dominated as a set of alternative solutions known as Pareto-optimal set
- In what follows we assume without loss of generality that all the function objectives must be minimized.
- If we have a maximization case fi we simply minimize the function -fi.
- For any two points that are usually named candidate solutions V1,V2, V1 dominates V2 in the Pareto sense (P-dominance) if and only if the following condition hold

The Pareto set

- The Pareto set is the set of PO (Pareto-Optimal) solution in design domain and the Pareto Front (PF) is the set of PO solutions in the objective domain.
- The most popular way to solving the MOP (Multi Objective Optimization Problem) is to reduce the minimization problem to a scalar form by aggregating the objectives in weighted sum, with the sum of weights constant:
- The weighted sum method has a serious drawback, the method usually fail in the case of nonconvex PF.

Nice properties

- GA can provide an elegant solution for tradeoff among different minimization of cost function for each variable versus total cost or other variable.
- Non-convex solutions
- “Immigrants”, possible solution for jump from local minima.
- Dealing with many variables (e.g. 16 variables)

Multi-Robots

- Pareto optimal multi-robot coordination with acceleration constraints (Jung and Ghrist, 2008)
- collection of robots sharing a common environment
- each robot constrained to move on a roadmap in its configuration space
- each robot wishes to travel to a goal while optimizing elapsed time considering vector-valued (Pareto) optima
- all illegal or collision sets are removed.

Conclusions

- GA is not a universal panacea to optimization problems.
- Coding the problem into a genotype is the most important challenge!
- The best selection schema of individuals for crossover operator is difficult to be chosen apriori(tournament selection seems to be more promising)
- A number of parameters are determined empirically:
- Size of population
- pc and pm even often values inspired from biology are given
- Other parameters in hybrid or more sophisticated GA

Good properties

- One of the most important element in the design of a decoder-based evolutionary algorithm is its genotypic representation.
- The genotype-decoder pair must exhibit efficiency, locality, and heritability to enable effective evolutionary search
- locality, and heritability:
- small changes in genotypes should correspond to small changes in the solutions they represent,

and

- solutions generated by crossover should combine features of their parents

DragosArotaritei

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