Singularities of Robot Manipulators

Abstract

Engineers have for some time known that singularities play a significant role in the design and control of robot manipulators. Singularities of the kinematic mapping, which determines the position of the end-effector in terms of the manipulator's joint variables, may impede control algorithms, lead to large joint velocities, forces and torques and reduce instantaneous mobility. However they can also enable fine control, and the singularities exhibited by trajectories of the points in the end-effector can be used to mechanical advantage.A number of attempts have been made to understand kinematic singularities and, more specifically, singularities of robot manipulators, using aspects of the singularity theory of smooth maps. In this survey, we describe the mathematical framework for manipulator kinematics and some of the key results concerning singularities. A transversality theorem of Gibson and Hobbs asserts that, generically, kinematic mappings give rise to trajectories that display only singularity types up to a given codimension. However this result does not take into account the specific geometry of manipulator motions or, a fortiori , to a given class of manipulator. An alternative approach, using screw systems, provides more detailed information but also shows that practical manipulators may exhibit high codimension singularities in a stable way. This exemplifies the difficulties of tailoring singularity theory's emphasis on the generic with the specialized designs that play a key role in engineering.

Stratifications of the Euclidean motion group with applications to robotics

“…There are three types of basic contacts between two polyhedra [20], namely face-vertex, edge-edge, and vertex-face contacts. Now, by adequately attaching flags to the two polyhedra, each contact type corresponds to the degeneration of one the three tetrahedra in (7). Therefore, the three hypersurfaces in R 3 × SO 3 (R) defining the singularity loci for flagged manipulators are the same as those defining basic contacts between polyhedra.…”

“…For a detailed formulation of kinematics mappings and their singularities, the reader is referred to [7]. Technically, singular configurations cause problems: at such configurations the derivative of does not have full rank, and hence the manipulator loses some degree(s) of constraint (or gains some degree(s) of freedom) and becomes uncontrollable.…”

Aplicação de redundância para atingir altas acelerações com manipuladores robóticos planares

“…O conceito de manipulador paralelo se deve as suas cadeias cinemáticas serem fechadas, isto é, tomando como ponto de partida a base do manipulador, é possível seguir por diferentes caminhos ao longo dos braços para atingir o end-effector 1 (Donelan, 2007). Na Fig.…”

“…1.1 é apresentado o robô Delta Par2, um manipulador paralelo que pode atingir altas acelerações chegando até 400m/s 2 com grande precisão (Company et al, 2011). Já nos manipuladores em série, a cadeia cinemática é dita aberta, uma vez que existe apenas um caminho possível da base ao end-effector (Donelan, 2007). Um exemplo de manipulador em série é representado na Fig.…”

Estudo do impacto da variabilidade geométrica no comportamento cinemático e dinâmico de manipuladores robóticos paralelos com redundância cinemática

“…Em outras palavras, dada a base do manipulador, pode-se chegar ao efetuador por mais de um caminho através de cadeias cinemáticas distintas (Donelan, 2007). A consequência dessa arquitetura são suas interessantes características já citadas.…”