Trajectory Optimization with Optimization-Based Dynamics

We present a framework for bi-level trajectory optimization in which system’s dynamics are encoded as the solution to constrained problem and smooth gradients of this lower-level passed an upper-level optimizer. This optimization-based representation enables constraint handling, additional variables, non-smooth behavior be abstracted away from optimizer, allows classical unconstrained optimizers synthesize trajectories more complex systems. provide path-following method efficient evaluation utilize implicit-function theorem compute representation. demonstrate by modeling systems locomotion, aerospace, manipulation domains including: acrobot with joint limits, cart-pole subject Coulomb friction, Raibert hopper, rocket landing thrust planar-push task then optimize using iterative LQR.