I. Introduction
Giving robots the ability to perform functional movements and to exert forces effectively on the external environment is a fundamental task in robot design. The most straightforward strategy is to use the fully actuated method with each robot joint driven independently by the actuators. In principle, fully independent actuation offers the widest possibilities, limited only by the robot kinematics. However, this design is difficult to effectively integrate and control in many situations such as multifingered dexterous hands and micromobile robots. The other alternative is underactuated mechanism, with fewer actuators than the degrees of freedom (DOFs), offloading some of control to the physical structure. The design of the underactuated mechanism is to embed mechanical intelligence [1] into the transmission, thereby giving the mechanical system the ability to passively adapt to the external environment in both motion and force. Usually, to keep the mechanisms from incoherent motion, it is embedded with passive elements, such as mechanical limits, clutches, and springs. Among them, mechanical compliance is of particular concern, because it can conform passively to the external environment and improve the stability and robustness of transmission. Because of its mechanical adaptability [2], bioimitability [3], and simple control, underactuated compliant mechanisms (UCMs) have been widely used in design of robots such as walking robots [4]–[6], flapping-wing aerial robots [7]–[9], and rehabilitation robots [10]–[12]. Especially in robotic and prosthetic hands [13]–[16], the underactuated hands do not only achieve enveloping grasp, but also are expected to perform dexterous functions like human hands, such as precision grasp [17] and in-hand manipulation [18]. In underactuated robots, the underactuation and compliance transform the control complexity based on sensing driven into the design complexity based on mechanical adaptation.