Tham khảo tài liệu 'control problems in robotics and automation - b. siciliano and . valavanis (eds) part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Underactuated Mechanical Systems Mark w. Spong Coordinated Science Laboratory University of Illinois at Urbana-Champaign USA In this chapter we discuss the control of underactuated mechanical systems. Underactuated mechanical systems have fewer control inputs than degrees of freedom and arise in applications such as space and undersea robots mobile robots flexible robots walking brachiating and gymnastic robots. The Lagrangian dynamics of these systems may contain feedforward nonlinearities non-minimum phase zero dynamics nonholonomic constraints and other properties that place this class of systems at the forefront of research in nonlinear control 22 15 . A complete understanding of the control of these systems is therefore lacking. We will discuss the application of geometric nonlinear control as well as methods based on passivity and energy for stabilization and tracking control. We will survey some of the existing results and point to open research problems. 1. Introduction A mechanical system may be underactuated in several ways. The most obvious way is from intentional design as in the brachiation robot of Fukuda 31 the passive walker of McGeer 23 the Acrobot 5 or the Pendubot 39 . Underactuated systems also arise in mobile robot systems for example when a manipulator arm is attached to a mobile platform a space platform or an undersea vehicle 45 A third way that underactuated systems arise is due to the mathematical model used for control design as for example when joint flexibility is included in the model 35 . It is also interesting to note that certain control problems for fully actuated redundant robots are similar to those for underactuated robots 7 . The class of underactuated mechanical systems is thus rich in both applications and control problems. The class of underactuated mechanical systems is far too broad to survey in a single chapter. For fully actuated systems there are a number of control results that apply to the entire class such as .
