Dynamic equivalence conditions and controller scaling laws for robotic manipulators

Abstract

In many engineering disciplines, it is standard practice to construct prototype models of the actual system, for the purposes of testing and analysis. Traditional examples of this practice are the shipbuilding and the aeronautics industries. A prototype gives the engineer physical insight about the system, and allows the engineer to determine dynamic effects not contained in the theoretical model of the system. In addition, by constructing a smaller prototype, a cost savings can be achieved since a smaller quantity of material is required.

As the twenty-first century approaches, the use of large robotic manipulators is increasing. Long flexible manipulators are being used to clean out underground tanks containing hazardous materials. Large robots are being used in mining, and in forestry to prune and harvest trees. In soace, the Canadarm is already being used on the space shuttle, and soon more manipulators will be used on the international space station. Looking into the future, robots that will be designed and tested on Earth, will be sent to the Moon, and even to Mars, which have different gravitational environments than the Earth.

In order to quantitatively scale the results obtained on the prototype model tot he actual large manipulator, the dynamic equivalence conditions for robotic manipulator systems must be determined. With such a dynamically equivalent prototype, the dynamic behaviour of the prorotype can be directly scaled to predict the behaviour of the actual system.

In this dissertation, the scaling conditions for rigid and flexible robotic manipulators are determined. The robots examined are of the broad class of manipulators are determined. The robots examined are of the broad class of manipulators with n links, p actuators, any link topology, and having unconstrained motion. The dynamic equivalence dconditions are defined by nondimensional groups, which can be found by applying dimensional analysis to the manipulator dynamics. Robot motion is achieved by implementing controllers on the joint atuators. Scaling laws are required for the controllers, so that a control scheme designed on the prototype can be scaled and implemeneted on another dynamically equivalent robot. In this thesis, scaling laws for linear and nonlinear controllers are developed and presented.

The theoretical scaling laws are illustrated by application to several sample manipulator systems. The examples include rigid and flexible manipulators, linear and nonlinear control strategies, and friction effects.

The thesis concludes with a summary of the main results. The major contributions of this work are identified, and avenues for future research are proposed.