Nonlinear and Geometric Controllers for Rigid Body Vehicles

Nonlinear;control;quadrotors;rigid body;feedback linearization;lie groups;lie algebra;geometric

Akhtar, Adeeladvisor:Waslander, Steve ; affiliation1:Faculty of Engineering ; Waslander, Steve ;

University of Waterloo

关键词: Nonlinear;    feedback linearization;    lie algebra;    rigid body;    lie groups;    geometric;    control;    quadrotors;    Doctoral Thesis;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/14006/7/Akhtar_Adeel.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

In this thesis we investigate the motion control problem for a class of vehicles C V , which includessatellites, quadrotors, underwater vehicles, and tailsitters. Given a globally represented model ofC V , and a curve, the motion control problem entails following the curve using control inputs. Inthis thesis the motion control problem is viewed under two settings, 1) as a local path followingproblem, 2) as a geometric trajectory tracking problem. We provide solutions to both problemsby designing controllers based on the concept of feedback linearization.In the local path following problem, the C V class of vehicles is represented by a local chart.The problem is solved in a monolithic control setting, and the path that needs to be followed istreated as a set to be stabilized. The nonlinear model under study is first dynamically extendedand then converted into a fully linear form through a coordinate transformation and smooth feed-back. This approach achieves path invariance. We also design a fault tolerant local controller thatensure path following and path invariance in the presence of a one rotor failure for a quadrotor.The second major problem addressed is the geometric trajectory tracking problem, which istreated in an inner-outer loop setting. Specifically, we design a controller class for the attitude dy-namics of the C V class of vehicles. The novel notion of Lie algebra valued functions are definedon the Special Orthogonal group SO(3), which constitutes a family of functions. This familyof functions induces a novel geometric controller class, which consists of almost globally stableand locally stable controllers. This class is designed using the idea of feedback linearization, andis proven to be asymptotically stable through a Lyapunov-like argument. This allows the systemto perform multiple flips. We also design geometric controllers for the position loop, which aredemonstrated to work with the attitude controller class through simulations with noisy sensordata.