The influence of joint angle constraints on the optimum design of a planar robot manipulator following a complicated prescribed path

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 a complicated prescribed task. In particular the end effector follows a “figure-of-eight” path. The minimization of average torque required for execution of the task is 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, which are severe for this problem, are also imposed. This results in a challenging optimization problem. Two different approaches are used in the application of torque and joint angle constraints. The complications arising from lock-up and nonassembly are handled by specially devised procedures. The optimization is carried out via a penalty function formulation of the constrained problem to which Snymanʹs unconstrained trajectory optimization algorithm is applied in a special way. Without joint angle constraints feasible designs with low objective function values are obtained. With the imposition of joint angle constraints the method yields good, but compromised, solutions.