Uncertainty and Compliance of Robot Manipulators with Applications to Task Feasibility

The uncertainty and compliance of a robot manipulator used to perform a task are 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 also studied. Manipulators are modeled as having rigid links and compliant joints, following experimental results. It is shown that given any symmetric positive semidefinite compliance, a robot manipulator of the above type can be constructed that will realize this compliance at some point in its work space. 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. The results developed here have direct application to several areas of robotics: determining whether a robotic task is feasible in the presence of uncertainty and joint compliance, 1. This is called two-point contact in Whitney (1982). 2. That is, errors resulting from both the end-effector and task position uncertainties. 3. The symbol ( )ᵀ denotes the transpose. 4. The half-size of a box is half the length of the box in a specified coordinate direction. 5. Also called the set-sum. 6. The effective compliance refers to the compliance at the peg tip resulting from the compliance of the robot or some other support, choosing work space locations for a robotic task, and the design and selection of robot manipulators.