Generating Control Policies for Autonomous Vehicles Using Neural ODEs

Houston Lucas, Richard Kelley

Keywords: robotics, ODE, BVP

TL;DR: Boundary Value Problems are useful, but sometimes slow to solve, this paper demonstrates a method for faster solutions.

Abstract:

The problem of robot control often requires solving a system of
ordinary differential equations (ODEs). Traditionally this has been
accomplished by using iterative ODE solvers. These solvers start with
an initial guess, which is iteratively improved to converge to a
correct solution. However, traditional solvers can be slow and do not
combine well with other systems since they are not differentiable. In
response, some researchers have proposed using neural networks in an
end-to-end system that directly maps perceptual inputs to control
actions. Because of their differentiablity, end-to-end approaches can
be composed with other modules more readily than traditional ODE
solvers. However the end-to-end approach no longer carries the
guarantee that the solution obeys the required dynamics.
We propose a framework for using Neural ODE to
combine the flexibility of the end-to-end approach with the guarantees
of traditional solvers. In our approach a neural network is used to
provide the initial guess to a differentiable ODE solver. The ODE
solver then yields a solution trajectory. We use this trajectory to
improve the guesses of the neural network. This
framework allows the neural network to learn initial guesses that are
close to the correct solution, improving overall system performance
while ensuring that dynamics constraints are always satisfied. We
demonstrate the utility of this framework in the case of robot
control, where we use it to solve a family of boundary value problems
that are essential for steering an autonomous vehicle to a goal state.