Singularity, uncertainty and compliance of robot manipulators

摘要

Kinematic singularities of the manipulator Jacobian are studied. For generic kinematic maps it is shown that singular points form smooth manifolds of prescribed dimension in the joint space of the manipulator. For three-joint robots, a condition for genericity using determinants is derived. The condition lends itself to symbolic computation and is sufficient for the study of decoupled manipulators. The decoupled problems, viz., orientation singularity and translation singularity, are studied in detail. A complete characterization of orientation singularities of robots with any number of joints is given. The translation singularities of the eight possible topologies of three-joint robots are also studied. A complete description of the singularities is given in the simpler cases, and the conditions on the link parameters for genericity are determined. For the more complicated cases, the singularities are studied after making certain assumptions about the link parameters. The uncertainty of a robot manipulator which is used to perform a task with a specified tolerance is considered. A formula is derived for the efficient computation of a tight bound on the uncertainty of the end-effector, given the uncertainty in the kinematic parameters of the robot. It is shown that the total uncertainty is the Minkowski difference of the manipulator uncertainty and the task position uncertainty. Simulations are performed in which the results are used to determine configurations of a robot for which the total uncertainty is within a specified tolerance. The suitability of the compliance of a manipulator for performing a planar peg-in-hole type assembly task is studied. Manipulators are modeled as having rigid links and compliant joints, following experimental results. It is shown that any symmetric positive semi-definite compliance at the end-effector can be realized by a manipulator of the above type. A new condition on the stiffness is proposed, for preventing jamming. If the peg is supported by the end-effector of a robot, we can determine configurations of the robot at which jamming can be avoided. Simulations are performed to compute the no-jam configurations of a manipulator.