Trajectory Tracking Control for Nonholonomic Mobile Manipulators

In the paper we present new control algorithms for a special class of mobile manipulators, namely for nonholonomic mobile manipulators. A mobile manipulator is defined as a robotic system composed of a mobile platform and a manipulator mounted on the platform equipped with non-deformable wheels. Such a combined system is able to perform manipulation tasks in a much larger workspace than a fixed-base manipulator. Taking into account the type of mobility of their components, there are 4 possible configurations: type (h, h) with both the platform and the manipulator holonomic, type (h, nh) a holonomic platform with a nonholonomic manipulator, type (n/i, h) a nonholonomic platform with a holonomic manipulator, and finally type (nh, nh) both the platform and the manipulator nonholonomic. The notion doubly nonholonomic manipulator was introduced in [13] for the type (nh,nh). The rigid manipulator can be a holonomic or a nonholonomic system depending on its construction. In our considerations we focus on the latter two types of mobile manipulators, namely the mobile manipulator with nonholonomic platform only (nh, h) and the doubly nonholonomic mobile manipulator. The problem of design of a control law for rigid robotic manipulators received much attention in late eighties and nineties of the last century. The algorithms were divided into two classes: the computed-torque algorithms, which came from the theory of linearization, see e.g. [8,14] and the passivity-based algorithms, which explored the passivity property of mechanical system, see e.g. [10,11]. So far in all considerations authors assumed that the every degree of freedom had independent linear engine direct drive. Recently, a new approach to the problem of robot drive has been proposed. In [7] Nakamura, Chung and S0rdalen presented a new nonholonomic mechanical gear, which is able to transmit velocities from the inputs to many passive joints (i.e. without actuators). In [7] the prototype of the nonholonomic manipulator was introduced and discussed. The nonholonomic constraints of the gear appear due to the rolling contact without slipping between balls of gear and special supporting wheels in the robot joints. Because the construction of the nonholonomic