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.

Highlights

  • T HERE are no simple tools for designing machines that exhibit some desired dynamic behavior

  • We propose a scheme for design space exploration powered by the recent finite root generation (FRG) algorithm, a method for obtaining most isolated roots to a system of equations

  • The method is based in homotopy continuation and is used for obtaining most isolated roots, both real and complex, to large kinematic synthesis systems

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Summary

INTRODUCTION

T HERE are no simple tools for designing machines that exhibit some desired dynamic behavior. From the standpoint of new design capabilities, the finite, isolated roots that we compute are used to perform design exploration for mechanisms that produce a prescribed transmission function from its motor’s dynamics onto the path of its end effector. This allows us to explicitly prescribe torque/force ratios between the motor and load at different points in the configuration space. In a related work [7], this mechanism was prototyped and tested

Mechanism Synthesis
Design Principles for Legged Robots
Homotopy Continuation
DYNAMIC MOCK-UP
Specifying Mechanism Characteristics
Equations of Motion
Mock-Up Example
SYNTHESIS EQUATIONS
Formulation
FINITE ROOT GENERATION
Reformulation of Synthesis Equations
Constructing Start Systems
Cognate Structure
Computational Work
APPLICATION TO LEG MECHANISM
SENSITIVITY ANALYSIS
Findings
VIII. CONCLUSION
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