This paper discusses a motion coordination method that has shown great promise in both simulation and application. Essentially, the method uses closed-form reverse position analysis to satisfy the placement constraints on the robotís hand and numerical optimization to resolve the redundancy. The numerical optimization generates configuration options and, based on a six DOF substructure of the robotís geometry, closed-form reverse position analysis ensures the options satisfy the placement constraints. This process explicitly identifies configuration options within the robotís null space. A decision making process based on multiple performance criteria chooses one option as the next set-point for the robotís servo controllers. Crane, Duffy, and Carnahan (1991) have also shown the use of closed-form reverse position analysis to solve 6
DOF substructures within a redundant robot, though they leave the decision making to a human operator.
Constraint tracking acts as a filter to eliminate options not satisfying the positional and orientational
equality constraints, on the placement of the robotís EEF. Concatenation of the geometric transformations
associated with each of these constraints generates the transformation the placement of the robotís hand must
satisfy. The formulation of the transformation for the closed-form position analysis proceeds as follows:
This section discusses two methods of generating configuration options. The first method systematically
generates options within a local hypercube about the robotís current configuration. The second method bases
the configuration options on a simulated annealing algorithm and thus incorporates randomness.
Perturbing the joint displacements a small amount, AO, from their current values generates a set of local
configuration options: where s is an arbitrary sweep vector with all elements equal to Ī1 or 0. The vector
of current displacement values, 0, is the base point for the perturbations.
All other E with elements equal to combinations of Ī1 and 0 generate points on the faces, edges, and vertices of an n-dimensional hypercube
with n equal to the number of joints involved in the exploration.