1. Evolving CPPNs to Grow Three- Dimensional Physical Structures Joshua E. Auerbach Josh C. Bongard GECCO 2010 – Portland, Oregon Evolving CPPNs to Grow Three-Dimensional Physical Structures Dept of Computer Science

2. Evolving CPPNs to Grow Three-Dimensional Physical Structures Motivation It is easy to create robots that can perform simple actions in structured environments But as the task and environmental complexity increase, simple solutions no longer suffice: V. Braitenberg. Vehicles: Experiments in Synthetic Psychology. MIT Press, 1984.

3. Evolving CPPNs to Grow Three-Dimensional Physical Structures Motivation Often in Evolutionary Robotics a control strategy is evolved for an existing morphology. But, this limits and biases the actions that the robot can perform. Evolving morphology allows for discovering body plans appropriate for the machine’s task environment instead of being artifacts of human design biases or copies of animal body plans only appropriate for that animal’s ecological niche.

4. Evolving CPPNs to Grow Three-Dimensional Physical Structures

5. Our Approach We use Compositional Pattern Producing Networks (CPPNs) as our encoding. CPPNs are able to capture appropriate geometric symmetries, and have shown promise for encoding control policies for legged robots. K. O. Stanley. Compositional Pattern Producing Networks: A Novel Abstraction of Development. Genetic Programming and Evolvable Machines Special Issue on Developmental Systems 8 (2): 131–162, 2007. J. Clune, B. Beckmann, C. Ofria, and R. Pennock. Evolving Coordinated Quadruped Gaits with the HyperNEAT Generative Encoding. In Proceedings of the IEEE Congress on Evolutionary Computing: 2764–2771, 2009.

6. Our Approach Evolving CPPNs to Grow Three-Dimensional Physical Structures Root sphere Priority Queue CPPN Point Cloud x y z output Above threshold? Yes No bias Φ 1,θ 1,Φ 2,θ 2,r,d

7. Evolving CPPNs to Grow Three-Dimensional Physical Structures Our Approach Once a structure is grown from a CPPN it is placed in a physical simulator (ODE). CPPNs are evolved using CPPN-NEAT for maximum displacement due to gravity. K. O. Stanley. Compositional Pattern Producing Networks: A Novel Abstraction of Development. Genetic Programming and Evolvable Machines Special Issue on Developmental Systems 8 (2): 131–162, 2007.

8. Evolving CPPNs to Grow Three-Dimensional Physical Structures Our Approach This sphere-based construction was devised to leverage the ability of CPPNs to operate at different “resolutions”

9. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Sample Structures (evolved for max displacement due to gravity)

10. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Sample Structures (evolved for max displacement due to gravity)

11. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments Eight experiments, each experiment consists of 30 independent runs

12. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

13. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

14. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

15. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

16. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

17. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

18. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results – Experiments

19. Evolving CPPNs to Grow Three-Dimensional Physical Structures Results - Experiments

20. Evolving CPPNs to Grow Three-Dimensional Physical Structures Conclusions CPPN-NEAT is capable of evolving three dimensional physical structures with non-trivial properties Additional inputs which provide the CPPN with information about the growth trajectory and environment are beneficial - Can yield more fit individuals - Resulting CPPNs more robust to changes in growth resolution Can improve runtime performance by using lower resolution structures early in evolutionary runs