Abstract
A set of new iterative solutions to the inverse geometric problem is presented. The approach is general and does not depend on intersecting axes or calculation of the Jacobian. The solution can be applied to any manipulator and is well suited for manipulators for which convergence is poor for conventional Jacobian-based iterative algorithms. For kinematically redundant manipulators, weights can be applied to each joint to introduce stiffness and for collision avoidance. The algorithm uses the unit quaternion to represent the position of each joint and calculates analytically the optimal position of the joint when only the respective joint is considered. This sub-problem is computationally very efficient due to the analytical solution. Several algorithms based on the solution of this sub-problem are presented. For difficult problems, for which the initial condition is far from a solution or the geometry of the manipulator makes the solution hard to reach, it is shown that the algorithm finds a solution fairly close to the solution in only a few iterations.
Highlights
Motion control is performed in operational space or joint space (Khalil and Dombre, 2002)
The transformation from operational to joint space is obtained by solving the inverse kinematic problem, which finds the joint velocities from the desired end-effector velocities
The transformation from operational space to joint space is obtained by solving the inverse geometric problem, i.e. to find the joint positions from the desired end-effector position/orientation
Summary
Motion control is performed in operational space or joint space (Khalil and Dombre, 2002). Some joint space control scheme, independent of the task, can be designed The disadvantage of this approach is that the inverse geometrics is a time-consuming problem to solve. When kinematic redundancy is present, the inverse geometric approach allows for optimising a general secondary criteria, and does not depend on finding a suitable inverse of the Jacobian, such as the Moore-Penrose generalised inverse, as for the inverse kinematic problem. Another advantage of the inverse geometric approach is that each joint can be controlled more directly and ISSN 1890–1328 doi:10.4173/mic.2008.3.1 c 2008 Norwegian Society of Automatic Control. A combination of the algorithms presented may give good and reliable performance for difficult problems and reasonably good convergence close to the solution
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