Semi-smooth and variational methods for real-time dynamic optimization

Project Abstract/Statement of Work:

Model Predictive Control’s capability to enforce safety constraints online makes it a strong candidate for autonomous vehicle control. Deploying real-time optimization (RTO) and Model Predictive Control (MPC) on real systems is dependent on the availability of fast and reliable methods for solving the underlying optimal control problems (OCPs), which may be constrained and/or nonlinear, at each sampling instance. This is a significant technical challenge as onboard computing power is limited and sampling rates for automotive and robotic systems are typically in the range of 10 – 1000 Hz. General purpose optimizers may not be able to meet these requirements and hence it is necessary to exploit structure inherent to RTO problems in developing solvers tailored for real-time applications.

An important class of optimization problems are convex quadratic programs (QPs). The optimal control problem arising from MPC for systems with linear dynamics and quadratic cost functions can be written as a convex quadratic program. In addition, many methods for nonlinear optimization, in particular sequential quadratic programming and its real-time variants, require the solution of a sequence of convex QPs. As a result, the ability to efficiently solve QPs is a key enabling technology for RTO. Research Objective

The research objective is to develop, implement, and validate novel and effective numerical methods for solving real-time optimization problems in support of TRI’s Guardian thrust. In particular, the algorithms developed in the proposed research will support TRI in applying MPC to control of vehicle dynamics as part of their autonomous vehicle development programme. The PIs research group is developing optimization techniques based on semismooth calculus and variational methods which combine the best aspects of Active Set and Interior Point methods. In particular, these techniques can exploit both sequential and internal structure of the associated problems. The implementation of MPC at kHz sampling rates using FBRS, an early version of these methods, has been experimentally demonstrated for an engine control application. In addition, a preliminary version of the FBRS algorithm has been successfully implemented and demonstrated on TRI’s autonomous vehicle by TRI.