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Advanced Robotics
Published in Vadim Utkin, Jürgen Guldner, Jingxin Shi, Sliding Mode Control in Electro-Mechanical Systems, 2017
Vadim Utkin, Jürgen Guldner, Jingxin Shi
A large number of control problems for mechanical systems are based on controlling the position or location of a mass using a force or a torque as the input variable. Instead of the pure regulation problem of driving the output location to a specified value, the position of the mass often is required to follow a prescribed trajectory. Levels of complexity may be added by introducing sets of masses with coupled dynamics, to be controlled by sets of force/torque inputs. The standard “fully actuated” case then features one control force/torque input associated with each primary mass and additional forces/torques arising from static and dynamic coupling between the different masses. A typical example is a robotic arm or robot manipulator with n links connected by n joints with force/torque-generating actuators. Usually, an end-effector tool is mounted at the tip of the last link for manipulating objects according to the specific robot application. The case of less control inputs than primary masses is called underactuation and requires extra consideration. Examples were given in Chapter 4.
Modelling and control of a knuckle boom crane
Published in International Journal of Control, 2022
As all cranes, knuckle cranes are nonlinear systems with underactuated dynamics. The problem of controlling underactuated systems has been a topic of great interest in different industrial fields (Li et al., 2017; Moreno-Valenzuela & Aguilar-Avelar, 2018; Scalera et al., 2020; Yan et al., 2019; S. Yang & Xian, 2020; Zhang et al., 2020). The condition of underactuation refers to a system having fewer actuators (input variables) than degrees of freedom (number of independent variables that define the system configuration). This implies that some of the states of the system cannot be directly commanded, which highly complicates the design of control algorithms. In particular for a knuckle crane (as for any crane), the non-actuated variable are the swing angles of the payload, whereas the four actuated variables are the three main rotation (i.e. luff, slew, and jib movements) and the length of the cable. While in the past few years, several solutions have been proposed for the control of boom cranes control, the control problem of a knuckle crane is still an opening and challenging problem.
Zero dynamics analysis and adaptive tracking control of underactuated multibody systems with flexible links
Published in International Journal of Control, 2021
Zehui Mao, Gang Tao, Bin Jiang, Xing-Gang Yan
Underactuated mechanical systems have less control inputs than degrees of freedom, which have the advantages of lighter weight, cheaper cost, and less energy (Lai, Wang, Wu, & Cao, 2016). Underactuation is purposely introduced in some systems, such as aircraft, underwater vehicles, and humanoid robots, for which the control problem has attracted much attention (Huang, Wen, Wang, & Song, 2015; Jafari, Mathis, Mukherjee, & Khalil, 2016; Lai, Zhang, Wang, & Wu, 2017; Wang, Yang, Shen, Shao, & Wang, 2018; Wu, Luo, Zeng, Li, & Zheng, 2016; Zhang & Wu, 2015). However, most of the existing results attempt to stabilise only a subset of the system's degrees of freedom, which reduces the complexity of the control problem associated with underactuated mechanical systems (Pucci, Romano, & Nori, 2015). The stability problem of the left subset that has no concern with the system's degrees of freedom, has not been fully studied. Therefore, the study on the control design and stability problem of the underactuated mechanical systems is of both theoretical challenges and practical importance.
Periodic motion planning and control for underactuated mechanical systems
Published in International Journal of Control, 2018
Zeguo Wang, Leonid B. Freidovich, Honghua Zhang
A systematic periodic motion planning and periodic motion control design method is proposed in this paper. It could be applied to underactuated mechanical systems with arbitrary underactuation degree. The idea originates from the fact that any continuous periodic function could be decomposed into an infinite uniformly converging Fourier series and, therefore, it can be arbitrarily accurately approximated by a trigonometric polynomial. Hence, the reference trajectory of each state of the system is assumed to be a truncated Fourier series. Moreover, this reference trajectory should satisfy differential constraints imposed by passive dynamics equations. Therefore, a numerical optimisation search is implemented to find the parameters to minimise the error, which is given by passive dynamics equations. An almost feasible periodic motion is defined in this way. The obtained reference trajectory does not satisfy the equations precisely but a feedback controller can be used to force the closed-loop system's feasible trajectories into a small neighbourhood of the desired approximately feasible motion.