Underactuated robotics: A review <s> UR walking mechanism <s> The nonlinear dynamic control for a novel one-legged hopping robot in flight phase is investigated. The proposed planar hopping robot is composed of single leg, a body, and a tail. The leg of the robot is structured by two links connected by an elastically passive joint with articulated form. The body of the robot is designed as an inertia wheel that the mass center is coincident to the hip joint. Though there are an articulated type leg and a tail such that the suggested one-legged hopping robot cannot be effectively approximated by the famous Spring Loaded Inverted Pendulum (SLIP) model system, the dynamics of the robot is considerably simplified since the novel design for the body. Considering the nonholonomic constraints of the hopping robot in flight phase due to angular momentum conservation, the problem of stabilizing the posture of the hopping robot in flight phase is investigated. By converting the dynamics to a chained form, an exponentially stabilizable control is proposed based on the integrator backstepping procedure. Some numerical simulations show the performance of the control. <s> BIB001 </s> Underactuated robotics: A review <s> UR walking mechanism <s> The researches on two-wheeled self-balancing robots have gained momentum in recent decade around the world. This paper describes the kinematics model of a two-wheeled self-balancing autonomous mobile robot. After mechatronics system design of the robot is completed, the analysis of the whole kinematics model can be divided into two wheels and a body. Then the velocity decompositions of robot wheel and body are analyzed respectively. After the left and right wheel kinematic model is established based on above velocity decomposition method, and the kinematic model of self-balancing robot’s body is also calculated by this method. The whole kinematics model of the two-wheeled self-balancing robot system is then established. The effectiveness of the kinematics model is testified by the simulation analysis on ADAMS and experimental validation. <s> BIB002 </s> Underactuated robotics: A review <s> UR walking mechanism <s> In this study, a walking manner of a spatial compass-like biped robot with underactuated ankles is presented. This biped robot has 3 degrees of freedom with only one actuator. The hip joint is equipped with a constraint mechanism to lock the angle when it retracts to a desired value. With the Poincare shooting method, a limit cycle of 3D walking gait on level ground is obtained. This limit cycle is unstable by checking the Jacobian of the Poincare map. We use this limit cycle as a reference trajectory and then introduce a method based on discrete transverse linearization to transform the reference trajectory tracking problem to a stabilization problem of a discrete periodic linear system. Thus, the classical discrete-time linear quadratic regulator is recalled to solve the stabilization problem. That is, a stable walking control law is obtained for the proposed 3D robot with a constraint mechanism. <s> BIB003 </s> Underactuated robotics: A review <s> UR walking mechanism <s> Abstract In order to overcome the drawbacks of traditional gait training methods, gait rehabilitation robotized systems have been developed to provide a consistent, labor-saving and efficient treatment. However, the high cost of these systems makes them impracticable for home healthcare. This paper deals with the conceptual design and dimensional synthesis of cam-linkage mechanisms for gait rehabilitation. First, a two degrees of freedom seven-bar crank-slider mechanism is selected as the original mechanism, of which the displacement of the slider is formulated as a function of the crank angle to achieve the target trajectory by using the inverse kinematics. A cam is then designed to reduce the mobility of the mechanism to one. Moreover, a constant speed motor is sufficient for the control of the mechanism. For the dimensional synthesis, a goal function is proposed based on the kinematic performance criteria and constraints, and the genetic algorithm is employed for global searching. Two target trajectories are used for the dimensional synthesis of the mechanism. The results show the generated trajectories match well with the desired ones, which illustrates the feasibility of the methodology. <s> BIB004
All mobile robots have a common component, namely, wheels, tracks, legs, and other devices that support the robot to move. These devices, such as wheels, tracks, or legs, are called the walking mechanism of a robot system. Due to different applications, different mobile robots have different working environments and overall structures. In order to achieve smooth and accurate motion of the robot, a suitable walking mechanism needs to be selected. At present, there are four commonly used walking mechanisms: a foot-type walking mechanism, a crawler-type walking mechanism, a wheeled walking mechanism, and a mixing walking mechanism. The foot-type walking mechanisms. Walking mechanism is a kind of mechanism used by walking robot. The movement of walking robot is to imitate the movement of human or animal. It could walk on the flat and uneven ground. It could even cross obstacles, up and down steps, and adapt to the environment. It has a relatively high degree of intelligence. It has mobility that other mobile robots could not achieve, which has unique superior performance. The nonlinear dynamic control for a novel one-legged hopping robot in flight phase is investigated. BIB001 Based on humanoid robots, Wang et al.  developed an adaptive feedforward control strategy to stabilize underactuated biped robots that walk on compliant ground. However, the study of walking robots is extremely challenging for designers and producers. Tang et al. BIB003 presented a walking manner of a spatial compass-like biped robot with underactuated ankles. This biped robot has three DOFs with only one actuator. The hip joint is equipped with a constraint mechanism. Lock the angle when it retracts to a desired value. Shao et al. BIB004 proposed a new method for synthesizing gait cam linkages. It could be used as a joint mechanism for URs. The main difficulty lies in the coordinated control of each leg joint, the attitude control of the fuselage, the steering mechanism and steering control, the effective transmission of power, and the mechanism of the traveling mechanism. There are many types of foot robots, which could be generally divided into two-legged robots and multi-legged robots. The crawler-type walking mechanisms. Track-type walking gears are widely used to improve the ability of the wheels to adapt to soft ground and uneven ground. The crawler mode is also called the cyclic track mode. The greatest feature is that the circular loop track crawler is wound around a number of wheels, so that the wheel does not directly contact the road surface. And the road surface state Figure 7 . Commonly used mechanism of UR. UR: underactuated robot. could be buffered, so that it could walk on various road surfaces. The robot adopts the crawler walking mode, which has the following advantages: 1. It could climb a higher step due to the action of the angle of attack. 2. The crawler has a strong driving force, and it is suitable for moving on the step. 3. It could rotate in place. Therefore, it is suitable for moving in a narrow house. 4. It is stable due to low center of gravity. Tracked walking mechanisms are widely used in various construction machinery and military vehicles. The shortcoming of the crawler-type walking mechanism is that the turning is not as flexible as the wheel type. When the direction needs to be changed, the track driving mechanism on one side is decelerated or braked to realize the turning, or the reverse driving is to realize the in situ rotation of the vehicle body. However, this would cause the track to slide laterally relative to the road surface. It increases the energy consumption of the robot body and damages the road surface. The wheeled walking mechanisms. The wheeled operating mechanism replaces sliding friction by rolling. Its main feature is high efficiency. Sun et al.  proposed a new type of transformable wheel-legged mobile robot that could be applied on both flat and rugged terrains. The wheeled travel mechanism is ideal for moving on flat roads. It has the characteristics of accurate positioning, lightweight, and simple production. Most wheeled mechanisms are non-holonomic motion constrained drive systems. There are many types of wheeled movements, which are divided into single-wheel, two-wheel, and multi-wheel robots according to the number of wheels. At present, the most commonly used robots are three-wheel or four-wheel movement. In some special applications, there are also five or more robots, but the robot's walking mechanism and control are complicated. BIB002 The kinematics model of a two-wheeled self-balancing autonomous mobile robot is shown in Figure 8 .