Optimal Gait and Form for Animal Locomotion. Wampler, Popovic. Siggraph 2009.

1. Discusses a fully automatic method for generating gaits and morphologies for legged locomotion
   1. Given a shape, it will determine an effective gait for locomotion
   2. It can also adapt a bodies morphology to be optimized for a particular locomotion task
2. They do not require shaping (an initial gait proposal)
3. Method combines derivative-based and derivative free search, with the first probably suited for fine-grained optimization and the latter for dealing with discontinuities
4. Show the approach with bodies that have 2, 4, and 5 legs
5. There are a number of references here worth checking out (mostly in section 2)
6. Simulation is more physically accurate than my stick figures as it simulates elasticity that results from actual muscles, also more accturately models skeleton and muscle activiation
7. Models active and passive forces
8. Reward function attempts to encourage realistic gaits by penalizing high joint velocities, large torques, and large amounts of head movement, for example
9. Optimization is based on a variant of Covariance Matrix Adaptation (CMA)
10. The version they use, called basin-CMA, is designed to take advantage of derivatives when available as well as operate under constraints required by the skeleton and other criteria
    1. It is called basin-CMA because it operates in the basins of attraction; projects the original space into the basin
    2. There are some other tricks, such as operating in the projected space as opposed to the full space
11. The also say basin-CMA outperformed top methods on the problems from the 2006 Congress on Evolutionary Computation test set, while also being computationally cheaper
12. Separates optimization of foot placement and then does the rest of the body to match that to make the process simpler
13. Experiments are run on skeletons with 10 to 32 DOFs, fully in 3D, generally takes 50 iterations of optimizaiton
14. Very nice paper