Inverse kinematics of binary manipulators by the optimization method in a continuous variable space

The precise positioning of the end-effector of a binary manipulator requires many modules. In this case, most of the existing algorithms require impractically large memory size for the real-time calculation of the binary positions of all joints. To overcome this limitation, we propose a new inverse kinematics algorithm using an optimization method. The key idea of the present method is to formulate the integer-variable inverse kinematics problem as a real-variable optimization problem in which the real-valued design variables are pushed towards the permissible binary values. Since the proposed algorithm is very efficient, the inverse kinematics of three-dimensional manipulators can be solved in real time. Furthermore, some manipulation considerations such as operation power minimization can be easily incorporated into the present new formulation.