Dissertation Information for Tina Shou-Mei Cheng Fu
- Tina Shou-Mei Cheng Fu
- (Alias) Tina C. Fu
- Library and Information Science
- University of Wisconsin, Madison (USA) (1988)
- Jane B. Robbins
- Douglas L. Zweizig
- Darlene Weingand
- Dennis Dresang
- Wayne A. Wiegand
MPACT Status: Fully Complete
Title: A linear programming approach for proximity analysis and collision avoidance of polyhedral objects
Abstract: This dissertation investigates a different approach to the problem of obstacle detection and on-line motion planning for a mobile robot. The robot and the obstacle are considered as polyhedral objects in two-dimensional space. The on-line planning is achieved by a hybrid control strategy, which alternatively activates a global control to lead the system to the goal and a perturbed control to avoid any impending collision. The global controller is required to have at least global stability to ensure convergence. The perturbed controller accesses batch files for the detection information in order to determine when it should be activated.
The batch files, which contain proximity information for all possible relative configurations between the robot and the obstacle, can be obtained off-line based on the initial relative configuration only. A linear programming problem can be formulated to serve this purpose. By realizing that any movement of a rigid object can be decomposed into a pure translation and a pure rotation, the linear programming problem can be decomposed into two sub-problems, one of which deals with the relative translation and the other is for the relative rotation. The former can be solved via parametric linear programming to obtain the first kind distance function. A solution procedure is also developed for the latter to obtain the second kind distance function. The composition of the two distance functions serves as the batch files. The sensitivity analysis of the detected proximity is easily obtained by the nature of the composition of the two distance functions.
Algorithms are developed for implementing the proposed approaches. Some examples are used for demonstration and show the potential advantages of the proposed hybrid control strategy.