Speaker
David Christopher Bickford
Title
Path Following and Stabilization of an Autonomous Bicycle
Abstract
We investigate the problem of designing a control system for a modern bicycle so that the bicycle is stable and follows a path. We propose a multi-loop control architecture, where each loop is systematically designed using linear control techniques. The proposed strategy guarantees that the bicycle asymptotically converge to paths of constant curvature. A key advantage of our approach is that, by using linear techniques, analysis and controller design are relatively simple.
We base our control design on the nonlinear (corrected) Whipple model of a bicycle. The inner-loop control consists of a forward-speed controller as well as a lean and steer controller. We design the forward speed controller using classical control and the lean and steer control using optimal state-feedback control. When following a constant-curvature path, a vehicle has a constant yaw rate. Using this knowledge, we design the outer-loop path-following control by finding a map that converts a yaw rate into appropriate lean angle and steer angle references for the inner loop. Using a linear approximation of the inner loop and with the linear map, a classical feedback controller for yaw-rate tracking is designed. In addition to yaw-rate control, we introduce linear controllers that act on the difference in the yaw angle of the bicycle and the closest point on the path, and the distance of the bicycle to the path to guarantee asymptotic convergence the bicycle converges to the path.
We highlight some problems that can arise when the bicycle is started far from the path. To overcome these problems we develop the concept of a virtual path, which is a path that when followed returns the bicycle to the actual path. We also recognize that, in practice, typical paths do not have constant curvature, so we construct more practical paths by joining straight line segments and circular arc segments, representing a practical path similar to a path that would be encountered when biking through a series of rural roads.