Dynamic Rolling Control of 5R Closed Kinematic Chain with Passive Joints

The purpose of this study is to develop a simple but useful robot with passive joints. As an example of such a robot, this paper presents dynamic rolling of a 5R closed kinematic chain, only two of whose joints are actuated.When it rolls, it has one DOF for its absolute orientation besides two DOFs for its shape. The absolute orientation is independent of the constraint for forming the closed kinematic chain. If its unactuated joints were actuated, the closed form would be over-actuated but the absolute orientation could not be driven directly. We show that the absolute orientation is subject to an acceleration constraint, not a velocity constraint. Therefore, the formulation of the dynamics of the rolling motion makes it possible to control the absolute orientation. The shape and orientation of the robot cannot be controlled simultaneously. This paper proposes a control strategy switching the shape and orientation controllers. The orientation controller reduces a negative acceleration caused by gravity which acts on the robot. We verify the control strategy by computer simulations and experiments.