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.

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PDF Trajectory Optimization with Optimization-Based Dynamics
Taylor Howell, Simon Le Cleac'h, Sumeet Singh, Pete Florence, Zac Manchester, and Vikas Sindhwani
Robotics and Automation Letters


Taylor Howell
Model-predictive Control and Differentiable Simulators for Contact
Simon Le Cleac'h
Boston Dynamics AI Institute
Zac Manchester
Assistant Professor
Last updated: 2021-12-11