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Spacetime Constraints Revisited

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Spacetime Constraints Revisited

Joe Marks J. Thomas Ngo

Using genetic algorithms to find solutions to spacetime constraint problems in 2D

- Multimodality
- exponential number of possible solutions

- Search space discontinuities
- small changes in actuators leads to large changes in trajectory

- Traditional SC algorithms
- Initial trajectory needed to work on
- Initial trajectory is done by human hand - “coarse”
- Initial trajectory is locally optimized

- Initial trajectory needed to work on
- Genetic Algorithms
- Discovers solutions “from scratch”
- Cover global optimization problem
- Can find “novel” solutions that were not imagined

- All trajectories are described as behaviors
- Behaviors generated by parametric algorithms (nothing smart here)
- Evolutionary computation chooses behavior parameters to find optimal solutions
- can find multiple effective solutions

- Better solutions (genomes) bred further
- Worse solutions bred-out of gene pool

- Dynamics module
- simulates a physics driven world for testing creatures

- Behavior module
- generates behavior using parameterized algorithm

- Search module
- uses GA to choose values for parameters
- generates near-optimal solutions

- Most CPU intensive part of this algorithm
- Simulating simplified physics
- Based on work by Hahn
- rate of change of internal degrees of creature controlled, rather than calculating torques
- friction and slippage simulated upon contact

- Behaviors generated by stimulus-response (SR) control algorithm
- causes instinctive reflexes to conditions
- conditions are stimulus functions over senses
- reflexes are responses to conditions

- avoids traditional use of forces
- behaviors selected in search module
- no learning or planning algorithms involved

- causes instinctive reflexes to conditions

- Scalar functions based on sense variables
- state of joint angles
- force between body endpoints and floor
- vertical velocity of center of mass
- height from floor of center of mass

- Contain parameters that are determined by GA-based search module
- Stimulus functions exhibit sensitive regions
- locus of points for which function is positive
- important notion during mutation

- Change in shape in reaction to a condition
- Conducted on highest valued positive stimulus function
- Change of creature’s actual shape to a target shape
- Change kept smooth by damped motion equations

- Target shape may change during a response
- Creature must respond to another stimulus

- Response is active for several time steps

- Use of GA to pick near optimal behaviors
- Parallel processing of solutions
- each processor handles one genome solution per generation

do parallel

Randomize genome

end do

for generation = 1 to number_of_generations

do parallel

Evaluate genome

Select mate from another processor

Cross genome with mate

Mutate genome

end do

end for

- Initial parameters chosen at random
- Favorable initial gene pool formed
- hill climbing algorithm used to find good initial solutions to populate gene pool
- each solution mutated, re-evaluated four times
- mutation skewed towards multi-step solutions

- best of five solutions on each processor used
- final population is non-random, skewed

- One of the most important aspects of GA
- Net horizontal distance covered by center of mass in given time
- Sometimes this encourages “cheating”
- e.g., leap head-first rather than walking

- To encourage walking, modify criteria
- e.g., net horizontal distance covered by midpoint between two feet - i.e., use your feet!

- Only local mating permitted
- maintains diversity, handles multimodality
- mate chosen on a random walk of 10 steps
- if better solution than self found, mate is chosen
- otherwise, current solution stays single

- produces large local colonies of good genes
- larger colonies use up more processing power

- Convergence - when one colony dominates

- Linear crossover not seen as meaningful
- certain parameters should migrate as groups

- More structured, specialized crossover used
- two (of ten) SR pairs taken from self
- six (of ten) SR pairs taken from mate
- one SR pair created with stimuli and response taken from each parent, respectively
- one SR pair created with numbers taken by random from parents

- Mutation algorithm tailored for SR method
- One SR pair in genome is subject to creep
- each parameter in pair is slightly changed

- One SR pair is randomized from scratch
- but one corner of sensitive regions of new stimulus function coincides with original sense-space trajectory
- keeps new functions from either dominating or not having any effect.

- but one corner of sensitive regions of new stimulus function coincides with original sense-space trajectory

- Hardware, software used
- 4,096 processor Thinking Machines CM-2
- Code written in C*

- Creatures used
- 5 rod figures; 50 time steps; 100 generations
- Five-rod Fred
- Mr. Star-man
- Beryl Biped
- importance of adapting criteria

- 5 rod figures; 50 time steps; 100 generations
- 30 to 60 minutes of computation used