XXI ICTAM, 15–21 August 2004, Warsaw, Poland BIDIRECTIONAL PATH PLANNING FOR UNDERACTUATED MANIPULATORS USING A DISCRETE-TIME APPROACH

For more than a decade underactuated manipulators have been under investigation, cf. [1]. Investigation of underactuated manipulators is of interest because both path planning and control is possible only if the nonlinear dynamic couplings between the links are taken into account. From a practical point of view, major benefits of underactuated manipulation systems are reduction of weight, costs, and energy. The advantage of reducing energy is stated in most papers (cf. [1]) but has never been subject to investigation. However, comparing motions subject to minimal energy effort as presented in [2] with motions of underactuated manipulators shows a strong relationship between both motions. At least if a discrete-time path planning approach is used for the underactuated system. Underactuated manipulators operating in the horizontal plane are of particular interest. The dynamics of these manipulators are not affected by gravitational terms. Therefore, linearization about an equilibrium point leads to a system that can not be asymptotically stabilized by smooth linear state feedback controllers nor by smooth nonlinear state feedback controllers. In contrast to the commonly used continuous-time approach a discrete-time approach, for an underactuated manipulator is proposed in [3] for the first time. The discrete-time approach presented in [3] is also used for a highly underactuated manipulator in [4]. A manipulator is called a highly underactuated manipulator if the system is equipped with no braking mechanisms and has more passive than active joints. The manipulators considered in [3] and [4] are operating in the horizontal plane. In [4] we were pointing to the problem that the iteration process that is used to calculate a feedforward control sequence, jams up in some cases. This problem has been solved by a nonlinear regularization in [4]. However, the major drawback of the nonlinear regularization is that sometimes the iteration process jams up again because the iteration process tends to converge to a region that is close to the point, where the iteration process has stuck before. In order to overcome this problem we propose a bidirectional path planning in the following.