Maintain Biped Balance Through Inverted Pendulum Model

I used this project as my undergraduate Senior Design project. By analytically solving for an inverted pendulum, I made a character able to sustain up to 100n of continuous force without losing balance purely through the application of torques on the ankle. I also used this project as a stepping stone to my implementation of SIMBICON, which I started as part of this project.

As an interesting experiment, I implemented a "seaweed" simulation using force-constrained particles in my Baraff-Witkin-inspired Particle Simulator, where the linear constraints were the "bodies" of the seaweed and the particles would be where I would apply torques, with the objective of having each particle directly over the next lower particle. Coupled with a simple 3D Stam-style fluid sim, where force is added by dragging the mouse across the screen and then applied to the particles by interpolating their position within the grid, and collision between the constraint "seaweed bodies", the resultant behavior is quite believable unless the fluid forces get high enough to force the simulation to go unstable (I used RK4 integrator for this particular sim).