Exploiting linearity to precisely control a vehicle about an unstable equilibrium

Drifting - operating a vehicle at a high sideslip angle - offers intriguing possibilities for controlling autonomous vehicles in critical situations. While drifting is a very dynamic process, occurring in a region of the state space with saturated tires and unstable equilibria, autonomous vehicles have been successfully controlled in this region. Many previous control approaches to path tracking while drifting have relied on nonlinear vehicle models. This thesis, however, demonstrates that linearized models capture the necessary dynamics for control in a large region surrounding a drift equilibrium. Furthermore, the eigenstructure moving from one equilibrium to the next is very consistent, enabling control not just around a single drift equilibrium but throughout this region of the state space. Using this linearized model, in which the longitudinal velocity is assumed to be maintained constant using the front brakes, a controller based on a linear quadratic regulator is developed. This controller uses steering, throttle, and brakes, making the system fully actuated and able to simultaneously track a velocity and sideslip profile while following a reference path. The fidelity of this linearized model and the utility of this controller are demonstrated by implementing this controller on MARTY, an electric DMC DeLorean. This linear controller accurately tracks equilibrium and quasi-equilibrium paths with centimeter-level accuracy that exceeds prior work with more complex nonlinear models and control techniques. Incorporating linear dynamics with variable speed drifting and removing the constant longitudinal velocity assumption tests the limits of this new linearized model. Additionally, incorporating wheel speed dynamics makes this controller functional for an internal combustion engine vehicle. This new fully actuated controller with variable speed linear dynamics uses a linear quadratic regulator framework and is demonstrated on Takumi, a Toyota Supra with an internal combustion engine. Experimental tracking error results again exceed previous work with nonlinear models and control techniques. While the addition of a feedforward term can minimize tracking error during transient sections of quasi-equilibrium paths, a new control framework is needed to further improve results. Accordingly, a model predictive controller is developed using the same linear model. This new control framework that optimizes the inputs over a finite horizon allows the controller to incorporate the reference trajectory and actuator constraints. By incorporating this additional information into the control framework, the input commands stay within actuator constraints even during transient portions of the reference path. This fully actuated model predictive controller is demonstrated on Takumi. This series of controllers each highlights the utility of this linearized model near unstable equilibria and demonstrates that this simple model can lead to better path tracking results than controllers developed using more complex nonlinear models

Keywords: Engineering.
Mechanical Engineering.
Advisor: Gerdes J. Christian
Kennedy Monroe
Schwager Mac