Trajectory Optimization with Optimization-Based Dynamics

Trajectory Optimization with Optimization-Based Dynamics

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

Code is available here.

Related Papers

PDF Trajectory Optimization with Optimization-Based Dynamics
Taylor Howell, Simon Le Cleac'h, Sumeet Singh, Pete Florence, Zac Manchester, and Vikas Sindhwani
arXiv (Submitted)


Taylor Howell
Robust feedback motion planning and optimization through contact
Simon Le Cleac'h
Game-theoretic optimization and optimization through contact
Zac Manchester
Assistant Professor
Last updated: 2021-12-11