Trajectory Optimization

As a graduate student research assistant (GSRA) at the University of Michigan, I perform research within the Multidisciplinary Design Optimization Laboratory (MDO Lab). Initially I primarily investigated aerodynamic shape optimization of multi-element airfoils. However, I quickly became interested in optimal control theory. As a big F1 fan, I always wonder what types of tools are used to connect the inputs and outputs of aerodynamics, vehicle dynamics, powertrain (and more) analyses. All these disciplines need to come together at some point in order to help the engineer make decisions based on the metric that truly counts — the lap time.

I implemented a vehicle model with load transfer, non-linear tires, active aerodynamics, and four-wheel drive. Using OpenMDAO and Dymos I transform the equations of state into a nonlinear programming problem (NLP), that is solvable by a wide array of optimizers (IPOPT in my case). The result of this is an optimal trajectory (based on minimizing lap time) on any given track. This includes the ‘racing line’, but also optimal deployment/recuperation of the four in-hub electric motors and optimal usage of the adjustable rear wing flap (DRS-like). In addition, vehicle parameters such as the wheelbase, center of gravity/center of pressure location, roll stiffness, etc. can be optimized in tandem with the trajectory. This makes a tool like this such a valuable asset in the engineering design process, as trade-offs can be established rapidly.

A research paper on this topic is currently under evaluation.