CELL-TO-CELL MAPPING METHOD FOR TIME-OPTIMAL TRAJECTORY PLANNING OF MULTIPLE ROBOT ARM SYSTEMS

This paper presents the results obtained by applying the cell-to-cell mapping method to solve the problem of the time-optimal trajectory pla nning for coordinated multiple robotic arms handling a common object a long a specified geometric path. Based on the structure of the time-op timal trajectory control law, the continuous dynamic model of multiple arms is first approximated by a discrete and finite cell-to-cell mapp ing on a two-dimensional cell space over a phase plane. The optimal tr ajectory and the corresponding control are then determined by using th e cell-to-cell mapping and a simple search algorithm. To further impro ve the computational efficiency and to allow for parallel computation, a hierarchical search algorithm consisting of a multiple-variable opt imization on the top level and a number of cell-to-cell searches on th e bottom level is proposed and implemented in the paper. Besides its s implicity, another distinguishing feature of the cell-to-cell mapping method is the generation of all optimal trajectories for a given final state and all possible initial states through a single searching proc ess. For most of the existing trajectory planning methods, the plannin g process can be started only when both the initial and final states h ave been specified. The cell-to-cell method can be generalized to any optimal trajectory planning problem for a multiple robotic arms system .