To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and design parameter uncertainties. Inner approximations of the solutions to the interval linear systems can be used to describe the common capabilities of a robotic manipulator corresponding to the considered sets of values. In this work, several classes of problems are considered. For each class, reliable and efficient polytope, n-cube, and n-ball inner approximations are presented. The interval approaches usually proposed are inefficient because they are too computationally heavy for certain applications, such as control. We propose efficient new inner approximation theorems for the considered classes of problems. This allows for usage with real-time applications as well as rapid analysis of potential designs. Several applications are presented for a redundant planar manipulator including locally evaluating the manipulator's velocity, acceleration, and static force capabilities, and evaluating its future acceleration capabilities over a given time horizon.
翻译:为了可靠地模拟真正的机器人特性,间线性方程系统可以描述考虑数组值的问题的种类。 这样可以很容易地考虑到典型的复杂性, 如一组联合状态和设计参数不确定性。 对间线性系统解决方案的内部近似可以用来描述与考虑的数组值相对应的机器人操纵者的共同能力。 在这项工作中,会考虑若干类问题。 对于每一类,会提出可靠和高效的多管、 n-cube 和 n-ball 内心近似。 通常提出的间隔方法效率低下, 因为它们对于某些应用程序( 如控制) 来说过于计算过重。 我们为所考虑的各类问题提出了高效的新内部近近近光标。 这可以用于实时应用和快速分析潜在设计。 有几个应用程序用于冗余的平面操纵器, 包括本地评估操纵者的速度、 加速和静态力能力, 以及评估其在特定时间范围内的未来加速能力 。