Abstract
The article consider the test simulation of the «finite rotation and displacement» method (FRDM) when the European Robotic Arm (ERA) manipulator is passing through the singular points. The test simulation confirms the method’s efficiency when passing through singular points and shows how to control the manipulator with various manifestations of the singularity. Depending on the type of singularities manifestation the manipulator is controlled in the vicinity of the singular point by means of small changes in its configuration or by limiting and setting specific values to generalized coordinates at the software and hardware level. The FRDM method is designed to solve the inverse kinematics (IK) for sequential-structure manipulators with an arbitrary number of links connected by fifth-class kinematic pairs. The method is based on determining the exact and optimal iterative steps that provide the maximum approximation to the given parameters of the final link for each degree of mobility. The software has been developed that consists of subprograms for organizing a general solution of the IK and a particular one for a particular manipulator in the form of source data according to the algorithm of the method. The initial data are the vector model of the manipulator, the values of the structural constraints of the generalized coordinates and signs of kinematic pairs by type and class.
Highlights
Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods
The article consider the test simulation of the «finite rotation and displacement» method (FRDM) when the European Robotic Arm (ERA) manipulator is passing through the singular points
Depending on the type of singularities manifestation the manipulator is controlled in the vicinity of the singular point by means of small changes in its configuration or by limiting and setting specific values to generalized coordinates at the software and hardware level
Summary
| qi | 0 i 1 для каждого i = 1,.., n, где n – число степеней подвижности ММ, Δqi – конечный угол/смещение для i-ой кинематической пары в виде шарнира/призмы согласно теоремам 1, 2 и 3 приведенным в [14], соответствует наличию сингулярной точки для данной конфигурации ММ, что в дальнейшем называется мониторингом сингулярных точек ММ. M – число сингулярных точек на пути решения ОЗК; δqik – малые значения обобщенных координат, используемые для изменения конфигурации манипулятора при обходе k-ой сингулярной точки. Для применения метода МКПС в решении ОЗК необходимо построить в прямоугольной декартовой системе координат x0y0z0 нулевого звена математическую модель ММ, показанную в общем виде на рис. Для манипуляционного механизма ERA в прямоугольной декартовой системе координат x0y0z0 нулевого звена построим с помощью векторов модель ММ, кинематическая схема которого показана на рисунке 3.
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