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.

中文翻译：

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设计具有大规模寻根功能的动态机器

在机器人中实现高性能动态行为需要仔细设计形态。然而，在高度非线性的设计空间中寻找全局最优形态是困难的，尤其是在使用随机种子时。与优化相反，我们将设计要求编码为具有大量孤立根的多项式系统。每个根描述设计空间中的替代机器人形态。在此之后，几乎所有孤立根的计算构成了设计空间探索。以前，由于退化根的沉重负担，这些系统难以处理。我们通过使用有限根生成 (FRG) 方法来减轻这一负担，从而首次能够发现某个六杆设计问题的几乎所有孤立根。FRG 综合方法可以设计从电机动力学到负载末端执行器的传递函数，以影响整体动态行为。在一个例子中，我们制定了以前难以处理的综合方程，获得了 1 528 608 个孤立根（估计为 99.0%），并找到了 3764 个物理设计。设计选项根据它们对接头错误的敏感性进行比较。