Passive dynamic object manipulation: A framework for passive walking systems

In this study, we deal with passive dynamic object manipulation. During passive dynamic object manipulation, a passive object is manipulated using passive manipulators. Like other passive robotic systems, there are no actuators in these systems. The object follows a path and travels along it under the effect of its own weight, as well as, the interaction force applied by each manipulator on it. The objects are not necessarily rigid, but we manipulate passive multibody objects as well as rigid ones. Thus, for a passive walking system, we assume that the passive walker is a multibody object and is manipulated by the ground (zero degree-of-freedom manipulator). As an example, we show that a compass-gait walking model could be constructed based on a passive manipulation framework by an evolutionary procedure. First, a polygonal rigid object is selected to be manipulated by one degree-of-freedom manipulator. Then, we deal with simple two-link objects manipulating them with the same one degree-of-freedom manipulator. For each example, dynamic equations of motion are derived and the stability of the process is taken into account using analysis of Poincare map. It is also shown that the second example has chaotic behaviour for some initial conditions. Finally, the model of the compass-gait walker is constructed according to the two previous examples' results. Simulations and experiments are used to support the concept and verify the results.