- This paper comes from the perspective of generating gaits for computer graphics
- Deals with both 2-D and 3-D skeletons
- Uses a parameterized system to develop a number of types of gaits, which can walk stably down steps, declines, and react successfully to pushes
- Says there are 4 major ways to approach walking:
- Use passive walking as a starting point
- ZMP Control
- Parameter search
- Developing feedback laws based on insights into balance and locomotion (what is used in this paper)

- For control, they use a finite state machine which they call a pose control graph
- Each state is made of target angles w.r.t parent links for all joints
- All joints drive toward their target angles using proportional derivative (PD) controllers
- Transitions occur either after a fixed amount of time, or when contact changes
- The torso, and hip however arent expressed relative to another part of the body, but rather the environment
- The hip’s target angle is set as a linear function of the center of mass position and velocity

- “The seminal work of Raibert, Hodgins, and colleagues contains key insights into producing robust hopping ad running gaits. At the heart of this research is a three way decomposition of control of hopping and height… torso pitch, and… hopping speed. Swing foot placement provides the basic mechanism for controlling balance from stride to stride.”
- The work here is different from the above by performing continuous adaptations using both the position and velocity of the center of mass
- There is also an approach that is based on an inverted pendulum
- They say that policy search methods have not been successful in making a robust walking algorithm
- A number of citations. Theres one by Tedrake (Stochastic Policy Gradient Reinforcement Learning on a Simple 3D Biped)

- Each state in the FSM has its own target pose, the targets are generally exaggerated versions of the desired pose to allow the PD to transition to what is actually desired
- There is explicit mechanics to deal with hip movement
- They do a manual search for good parameterization
- <not finishing the paper, doesn’t seem so relevant>

### Optimizing Walking Controllers. Wang, Fleet, Hertzman. Siggraph 2009

- Extends the above work, but uses CMA (which is a generalization of cross-entropy) to perform parameter optimization, which was done by hand in the above work.
- Says that the gait generated in the above does not look realistic in that the motions look too much like marching (overuse of knee, underuse of ankle)
- CMA is used in another paper from 2009 to fill in steps between keyframing
- The search space is 184 dimensional
- The reward function is partially defined by the user and partially based on a-priori knowledge about human walking
- CMA is initialized with a hand tuned controller
- They compare the gaits after optimization with Mocap data and they are in error bounds, whereas the hand tuned results from the above paper are characteristically very different
- Walks up a grade of up to 12 degrees