Planning tracking motion insusceptible to unknown disturbances using sensitivity measure

In the present paper, we show a novel motion planning method, which finds an arm trajectory that is insusceptible to unknown disturbances in the direction where task accuracy is required. First, we show that the sensitivity of the ende-ffector to unknown disturbances is measured by the direction of singular vectors and the condition number of a matrix which represents the input-output relation of the robotic arm system. We propose a motion planning method for tracking tasks, which finds the arm posture not only so that the maximum singular vector points toward the direction of a desired end-effector´s path but so that the condition number becomes larger. We show by simulations and experiments that the end-effector can track the desired path as closely as possible even though disturbances are applied to the robotic arm.