“…In general, this approach solves a large optimization problem that minimizes a performance criterion while satisfying kinematic and dynamic constraints. The task-based design optimization has been widely applied to manipulators [22,5,28] and parallel manipulators [17,7,30] for reaching desired workspace and avoiding joint singularities. However, there exist only a few studies on under-actuated robots, such as pipe-cleaning robots [15], stair-climbing mobile robots [16], virtual creatures [29,10], or quadrupeds [12] due to complexity of required models.…”