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Advanced Examples and Ideas

Advanced Examples and Ideas. Evolutionary Programming. Neural Net. EXPERT SYSTEM. Fuzzy System. Neuro -Fuzzy System. UNIVERSAL SEARCH SYSTEM. Three Layer Evolutionary Approach. Local perceptions, such as “bald head” or “long beard”. Encoded behaviors or internal states. Time intervals.

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Advanced Examples and Ideas

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  1. Advanced Examples and Ideas

  2. Evolutionary Programming Neural Net EXPERT SYSTEM Fuzzy System Neuro-Fuzzy System UNIVERSAL SEARCH SYSTEM

  3. 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

  4. 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

  5. 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?

  6. Optimizing a motion Parking a Truck

  7. Find the control Solving this analytically would be very difficult

  8. Question; How to represent the chromosomes? Here you see several snapshots of a “movie” about parking a truck, stages of the solution process.

  9. t is time u

  10. Another example Learning Obstacle Avoiding

  11. Similar to Braitenberg Vehicle but has 8 sensors

  12. 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

  13. Remember the goal when you create the fitness function The key to success is often in fitness function

  14. Number of collisions • Time of learning When you train longer you decrease the number of collisions

  15. Applications and Problems

  16. General GA Schema

  17. Evolutionary Methods • Optimization problems: • Single objective optimization problems • Multi-Objective optimization Problems • Combine with other approaches.

  18. More examples of problems in which we use evolutionary algorithms, neuro-fuzzy, 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

  19. 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

  20. 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.

  21. Your design parameters to be decided • Genotype length • Fixed length genotype • Variable-length genotype • Population • Fixed population • Variable population • Species inside population • Geometrical separation

  22. Drawbacks of GA • time-consuming when dealing with a large population • premature convergence • Dealing with multiple objective problems Solutions • Niches • Islands • Pareto approach • Others

  23. More examples of using GA in robotics Trajectory Planning Problems

  24. 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

  25. 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.

  26. 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?)

  27. EXAMPLE: Combining kinematics, control, evolutionary and neural

  28. Three join Manipulator • 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

  29. Design of robotic controllers • 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)

  30. Use of Neural Networks • NN: We must to adapt the weights and eventually the bias The chromosome: • Adapt the weights

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

  32. 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

  33. 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)

  34. 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)

  35. 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

  36. 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

  37. 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

  38. example Drug Delivery Problem

  39. 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)

  40. 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)

  41. Expandable chromosomes • Deleting the path • Crossover operator

  42. New mutation operators • Travel further • Delete • Reverse delete • Stretch • Shortcut • The algorithm keep mind the visited nodes • Extension to operational research?

  43. 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)

  44. What if you want to optimize two parameters at the same time? Pareto Optimization

  45. Pareto Evolutionary Methods

  46. What is better this or this? • We want to optimize both functions f1 and f2

  47. Biobjective means two objectives to reach • We have x and y, two objectives here Pareto solutions for different algorithms Pareto Front

  48. 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

  49. Example of Pareto Optimization of two parameters Optimization of Airplane Wings

  50. Two objectives: Maximize lift, and minimize drag

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