Ellipsoidal outer-approximation of workspace of binary manipulator for inverse kinematics solution

In this study, a binary manipulator is considered as a controlled plant. The control objective is to bring the end effector of the binary manipulator close to a given target point and orientation. One advantage of the binary manipulator is its high reliability owing to its hyper-redundancy. However, the inverse kinematics problem of the binary manipulator is a combinatorial optimization problem. The workspace of the binary manipulator is a discrete set. The number of reachable points grow exponentially with respect to the number of binary actuators. Therefore, compact representation of the workspace is necessary. This paper proposes an ellipsoidal outer-approximation of the workspace of the binary manipulator. This approximation can be calculated recursively, and it can be utilized for the inverse kinematics problem of binary manipulators. The validity of the proposed method is verified via numerical experiments.