Geometric Design of Robotic Systems Using Computational Algebraic Geometry

Eric Lee, Rutgers University

This project studies the computational design of spatial mechanism and robotic systems. Designers of robotic systems are often caught in a dilemma whether to design a new mechanical system for moving a rigid body through specified locations or to use a generic, off-the-shelf multi-axis robot to perform the task. In many cases, the off-the-shelf robots are preferred. However, off-the-shelf robots are very expensive. In addition, for repetitive tasks, which are usually the case, the use of multi-axis robots is highly unjustified as several of the axes remain under-utilized because of the kinematic redundancy. On the other hand, if the designer decides to design and build a new system, the computational design algorithms either do not exist or are very complicated. Therefore, there is a need to develop design methodologies for spatial, task oriented robotic systems.

One of the most important spatial, task oriented robotic system design problems is the Rigid Body Guidance Problem. This is the calculation of the geometric parameters of a mechanical system so that it guides a rigid body in a number of specified spatial locations. This project focuses on the development of practical computational design algorithms for the spatial rigid body guidance problem with serial manipulators. One of the biggest computational challenges is that the geometric constraint equations are a set of highly nonlinear algebraic equations and usually have a large number of solutions. The methods for solving these equations come from computational commutative algebra and algebraic geometry. They include symbolic methods (e.g. resultants, sparse resultants and Gröbner Basis) and numerical methods (e.g. polynomial continuation).

In this presentation, I will present some of the most important results and the future research direction of robotic mechanism design.

Abstract Author(s): Eric Lee