Robot trajectory planning using the curvature theory of ruled surfaces
Abstract
This dissertation is concerned with the curvature theory of a rigid body moving in three-dimensional space. While the theory is applied to robot trajectory planning, the results also provide insight into rigid body motion in general. The motion of a robot end-effector in space has six degrees of freedom, in general, and six independent parameters are required to describe the position and orientation of the end-effector. The robot trajectory, describing the motion of a robot end-effector, is represented in this dissertation by a ruled surface and an additional parameter, referred to as the spin angle. This is believed to be a more efficient approach than the conventional matrix representation which shows redundancy of parameter. A method of robot trajectory planning is proposed based on the curvature theory of ruled surfaces. The curvature theory of general and special ruled surfaces are studied. The special ruled surfaces, referred to as developables, are the cylindrical surface, cone, and tangent surface. The curvature theory is used to determine the differential properties of the motion of a robot end-effector. The differential properties of the robot end-effector motion are then related to the time-dependent properties of the motion which are essential in the robot trajectory planning. In many practical applications, a robot trajectory can not be represented by a closed-form parametric expression of a ruled surface. In this case, a geometric modeling technique, based on the Ferguson curve model, is used to generate a ruled surface. This method is incorporated into the robot trajectory planning.
Degree
Ph.D.
Advisors
Pennock, Purdue University.
Subject Area
Mechanical engineering
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.