Underactuated robotics: A review <s> Introduction <s> Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a starting point to design swing up control algorithms. Analysis of the resulting zero dynamics as well as analysis of the energy of the system provides an understanding of the swing up algorithms. Simulation results are presented showing the swing up motion resulting from partial feedback linearization designs. > <s> BIB001 </s> Underactuated robotics: A review <s> Introduction <s> This paper focuses on the state-of-the-art of control problems in robotics. Beyond its tutorial value, the work aims at identifying challenging control problems that must be addressed to meet future needs and demands, as well as at indicating preliminary solutions to the identified problems. Various topics are covered starting from the closest issues related to industrial robotics, such as force control, multirobots and dexterous hands, to the most advanced issues related to underactuated and nonholonomic systems, as well as to teleoperation, haptic interfaces and visual servoing. <s> BIB002 </s> Underactuated robotics: A review <s> Introduction <s> Stratospheric airship is a new kind of aerospace system which has attracted worldwide developing interests for its broad application prospects. Based on the trajectory linearization control (TLC) theory, a novel trajectory tracking control method for an underactuated stratospheric airship is presented in this paper. Firstly, the TLC theory is described sketchily, and the dynamic model of the stratospheric airship is introduced with kinematics and dynamics equations. Then, the trajectory tracking control strategy is deduced in detail. The designed control system possesses a cascaded structure which consists of desired attitude calculation, position control loop and attitude control loop. Two sub-loops are designed for the position and attitude control loops, respectively, including the kinematics control loop and dynamics control loop. Stability analysis shows that the controlled closed-loop system is exponentially stable. Finally, simulation results for the stratospheric airship to track typical trajectories are illustrated to verify effectiveness of the proposed approach. <s> BIB003 </s> Underactuated robotics: A review <s> Introduction <s> Summary ::: ::: This article considers the problem of directing a family of underactuated ships to formation tracking a set of closed orbits and achieve attitude synchronization. It shows that our previous concentric compression design can be extended to deal with a general kind of non-convex, closed curves and the coordinated motion of underactuated ships. The condition of nonzero total linear speed of each ship is ensured by a potential function. Under the bidirectional communication topology, asymptotical stabilization is proved with the help of the invariance-like theorem and the extension of Barbalat's lemma. Theoretical results are proved by the numerical examples. Copyright © 2014 John Wiley & Sons, Ltd. <s> BIB004
According to the International Federation for the Theory of Machines and Mechanisms terminology, the degree of freedom (DOF) of a mechanism is the number of independent generalized coordinates that completely defines the configuration of a system at any instant of time. By comparing the DOF and the number of actuators, mechanisms could be categorized in three types: fully actuated mechanisms, redundantly actuated mechanisms, and underactuated mechanisms. The number of actuators of the underactuated mechanism is less than its DOF. In terms of mechanism, the underactuated robot (UR) is a kind of robot with underactuated mechanism. From the perspective of control, URs refer to a class of robots with independent control input less than the DOF of the system. Under normal circumstances, the robot has underactuated characteristics in the following situations 1-5 : 1. Inspired by human motion, it is used for bionic robots to achieve efficient and beautiful movements, such as gymnastics robots and so on. 2. In order to make certain structures simple and efficient, the flexibility of the system is increased and the use of underactuated joints could greatly reduce weight and cost, such as two propeller satellites, flexible-link robots, and so on. 3. The robot system itself has some dynamic constraints that make it a UR, such as aircrafts, underactuated stratospheric airships, BIB003 underactuated submarines, BIB004 and so on. BIB002 . In some emergency situations, if the drive motor fails and could not be replaced, it is practical to treat the joint at the drive motor into an underactuated joint to meet the requirements of emergency, such as surface ships and so on. Shanghai Key Laboratory of Intelligent Manufacturing and Robotics, School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China 5. More complex low-order nonlinear systems have been artificially created to study the control of high-order UR systems, such as two-stage inverted pendulum (IP), bat system, rotating pendulum, and so on. Although UR is more complex than full-drive robot, UR has a number of advantages, such as energy savings, material savings, space savings, and so on. In some specific cases, if there is precise drive control, UR could achieve higher efficiency and better flexibility even with a lot of DOF (e.g. biped walking robots, robots, etc.). Therefore, UR has high research value both in control theory and practical applications, which could be summarized as follows: 1. Enhance application value. The sources of UR are very wide. In reality, some common systems (e.g. surface ships and helicopters) are underactuated systems. Research on these systems has been carried out very early. Therefore, by studying a class of systems, not only could these research results be applied to other similar systems but also other systematic research results could be introduced into the underactuated system to promote progress in various studies. 2. Saving natural resources. Compared with full-drive robots, UR has fewer drives while maintaining the same DOF, thus reducing mass, volume, and energy consumption. Reduce costs while conducive to sustainable development. It is ideal for applications where quality, volume, energy, and cost are critical, such as aerospace systems. 3. Enhance system security. When a drive unit of the all-drive robot is damaged, it becomes a UR. If the original control strategy is still adopted, the original control target would not be realized. Of course, this problem could also be solved by redundant drives, but redundant devices could also fail and increase costs. Therefore, if the corresponding underactuated control algorithm could be designed to partially replace the original work and ensure the normal operation of the system, it is safer to ensure system security without any burden, which is a better choice. 4. Improve theoretical research. As a special nonlinear system, UR has its unique characteristics and research value. Due to the lack of the number of drive sources, the control difficulty is greatly increased. In terms of control strategy, UR is very different from all-drive robot. Most control strategies could be applied to all-drive robot systems. For example, precise feedback linearization control and passive control. However, for UR, there is almost no uniform control strategy except for the partial feedback linearization (PFL) control method. BIB001 Therefore, from the perspective of theoretical research, the study of UR has a strong theoretical significance. UR has its own unique advantages and values, but it needs to achieve breakthroughs or unprecedented innovations in both theoretical and practical techniques. At present, research on UR has become a frontier research topic in the field of robotics. Due to the flexibility and versatility of UR, it is difficult for UR to be comprehensively and systematically classified. In this article, the purpose of studying UR is to find a comprehensive classification method and summarize the underactuated mechanisms and control methods in common use. In order to further explore and research UR in the future, this article would study the UR from the following main aspects: classification of UR, common mechanisms of UR, and control methods of UR. Main sections of this article are shown in Figure 1 .