Passivity based control of hydraulic linear arms using natural Casimir functions

This chapter discusses a modeling and passivity based control of hydraulic arms which are robotic, that is, have asymmetric cylinders. Hydraulic arms are very important components in field robotics, such as construction, agriculture, rescue , demining robotics and so on since hydraulic arms are superior to electric arms with respect to the power to weight ratio and also can keep joint forces even when the energy source (the hydraulic pump) does not work. In many cases of electric arms, the driving system (or the actuator dynamics) is simple and almost static, for example, the input torque (or velocity) is just proportional to the control input. On the other hand, in many cases of hydraulic arms, the driving system is complex and consists of compressible fluid systems, that is, nonlinear dynamical systems with unknown (or hard-to-be identified) parameters. To solve these problems, this chapter gives some results about modeling and control of hydraulic arms by applying and developing port-Hamiltonian systems and control theory.