Dynamic Motion Planning Of Flexible Underactuated Manipulators

The research on light high-speed and energy-saving space robot becomes much more important and urgent than before with the further exploration of universe. Meanwhile, it is particularly important for a space robot working in outer space to have the ability to control the failed joint in the event of an actuator failure. The Underactuated Manipulators are advanced in this background. The major character is that the dimension of input space (control space) is less than dimension of configuration space. At the same time, the constraint equations of the passive joints are un-integral, so they are belong to second order nonholonomic constraints. Control of such systems is one of major topics in robotics and control engineering.In this paper, the main research object is the planar underactuated manipulators. We apply the averaging method and Poincare maps to underactuated manipulator and observe the nonlinear dynamical behaviors, and develop a feasible control method. The main contents comprise three parts:In the first section, a brief introduction to the status quo and future of the underactuated robot and flexible robot is given. And we also review the basic nonlinear concept and theorem.The second section is the main important part of this paper. In this section a 2R Underactuated manipulator of which the first joint is only actuated is to be considered. We apply the averaging method and Poincare maps to the manipulators and describe their behaviors in response to low amplitude periodic inputs. And we get three truths: (1) In the same amplitude and frequency input, the unactuated joint have a different amplitude cycle movement with various initial point. (2) With the same initial start point, the unactuated joint have a different amplitude cycle movement with various amplitude and same frequency input. (3) The phase track of (1) intersectant the phase track of (2). We develop a open loop control method for the underactuated manipulator via observe the before dynamical behaviors. The effectiveness of the method is verified by computer simulations.In the last section, we derive the dynamical model of planar two link flexible robot arm with Lagrangian approach and Assumed mode shapes. This model can help the following work about the flexible underactuated manipulators.