Trajectory Optimization with Optimization-Based Dynamics

TL;DR

This paper introduces a bi-level trajectory optimization framework that encodes system dynamics as a constrained optimization problem, enabling efficient handling of complex systems with constraints and non-smooth behaviors.

Contribution

The authors develop an optimization-based dynamics representation with an interior-point method and implicit differentiation, facilitating trajectory synthesis for complex systems within a bi-level optimization framework.

Findings

Successfully modeled diverse systems including acrobot, cart-pole, and rocket landing.

Achieved efficient trajectory optimization using iterative LQR.

Demonstrated constraint handling and non-smooth behavior management.

Abstract

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 an interior-point method for efficient evaluation of constrained dynamics and utilize implicit differentiation 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.