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Summary: A cart‐pendulum system is a nonlinear underactuated mechanical system with two degrees of freedom. This paper addresses the motion trajectory design and tracking control problems for this underactuated system. First, a friction‐like control law is designed for the system. Then, the characteristics of the closed‐loop control system are analyzed. Second, a new method of constructing an optimal trajectory for the system is developed. Then, a tracking control law is designed to quickly track the constructed trajectory. It guarantees that the motion control of the cart‐pendulum system is achieved along a reference trajectory. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results. This study constructs an optimal trajectory for the cart‐pendulum system in its whole motion space and solves the motion control objective by tracking the constructed trajectory. It has many advantages compared with other motion control methods, eg, the optimal motion control objective of the system is achieved by a single control law; and the motion process and transient characteristics (eg, the settling time) of the control system can be accurately predicted. [ABSTRACT FROM AUTHOR]

A translational oscillator with a rotational actuator (TORA) is an underactuated mechanical system with two degrees of freedom. This paper presents a new method to solve the global stabilisation control problem for this underactuated system. First, a set of suitable state variables is chosen for the TORA. It transforms the system into a cascade affine nonlinear system. Then, a positive-definite Lyapunov function is constructed based on the structural characteristics of the system. A control law is designed to guarantee that the derivative of the Lyapunov function is non-positive. Finally, the global stability of the closed-loop control system is analysed using the Lasalle invariance principle. The condition on the control parameters is presented to globally stabilise the TORA at the origin. The effectiveness and robustness of the method are verified by a numerical example. [ABSTRACT FROM AUTHOR]

An underactuated wheeled inverted pendulum (UWIP) is a nonlinear mechanical system that has two degrees of freedom and has only one control input. The motion planning problem for this nonlinear system is difficult to solve because of the existence of an uncontrollable manifold in the configuration space. In this paper, we present a method of designing motion trajectory for this underactuated system. The design of trajectory is based on the dynamic properties of the UWIP system. Furthermore, the tracking control of the UWIP for the constructed trajectory is also studied. A tracking control law is designed by using quadratic optimal control theory. Numerical simulation results verify the effectiveness of the presented theoretical results. [ABSTRACT FROM AUTHOR]

This paper concerns the global stabilization of an underactuated spring-coupled three-link horizontal manipulator (STHM), which is an underactuated mechanical system (UMS) with two actuators and three degrees of freedom (DOF). A new control method is developed that asymptotically stabilizes the STHM at the origin using the position measurements of the manipulator only. First, we introduce a homeomorphic coordinate transformation for the STHM system. This changes the stabilization of the STHM into that of the transformed system. Next, we analyze the characteristics of the transformed system. After that, we construct an equivalent-input-disturbance- (EID-) based control system to globally stabilize the transformed system at the origin. Finally, a numerical example demonstrates the validity of the presented method. Our method only uses the position measurements of the STHM to design stabilizing controller. It reduces the cost of the whole control system and avoids the influence on the system’s control performance imposed by velocity noises. In addition, the analysis and control method of this paper is easy to extend to the global stabilization of other n -DOF ( n ⩾ 3 ) UMSs. [ABSTRACT FROM AUTHOR]