Designing Dynamic Machines With Large-Scale Root Finding

Abstract

Achieving high-performance dynamic behavior in a robot requires careful design of morphology. However, searching for a global optimum morphology in an intensely nonlinear design space is difficult, especially if stochastic seeding is used. In contrast to optimization, we encode design requirements into a polynomial system with a huge number of isolated roots. Each root describes an alternate robot morphology in the design space. Following this, the computation of nearly all isolated roots constitutes design space exploration. Previously, these systems were intractable, due to the heavy burden of degenerate roots. We relieve this burden by using the finite root generation (FRG) method to enable the discovery of nearly all isolated roots for a certain six-bar design problem for the first time. The FRG synthesis method enables the design of a transmission function from motor dynamics to a loaded end effector to influence the overall dynamic behavior. In an example, we formulate synthesis equations which were previously intractable, obtain 1 528 608 isolated roots (estimated 99.0%), and find 3764 physical designs. Design options are compared according to their sensitivity to joint errors.