The design of a planar robotic manipulator for optimum performance of prescribed tasks

The application of a general optimization methodology, previously proposed by the authors, is extended here to the design of a three link revolute-joint planar manipulator performing more practical and complicated prescribed tasks. In particular a tool moving task and a spray painting task are considered. Both the minimisation of average torque and energy usage required for execution of the tasks are addressed and the optimization is carried out with the link lengths and base coordinates taken as the five design variables. In addition to simple physical bounds placed on the variables, the maximum deliverable torques of the driving motors represent further constraints on the system. Joint angle constraints, not previously considered but of great practical importance, are also imposed in this study. This results in significantly more challenging optimization problems than those previously tackled. The complications arising from lockup and nonassembly are handled by specially devised procedures. The optimization is carried out via penalty function formulations of the constrained problems to which the Snyman unconstrained trajectory optimization algorithm is applied in a special way. For bath tasks and far both objective functions, with the full complement of constraints imposed, feasible designs with low objective function values are obtained by using, in each case, four different infeasible designs as starting paints for the algorithm.