Generating Control Policies for Autonomous Vehicles Using Neural ODEs

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.

Tasks

Reproductions