This paper deals with the ball-plate manipulation problem considered as a typical but complicated model of a driftless nonholonomic system. Due to a strong nonlinearity of the ball-plate system, a state equation of the kinematic model cannot be transformed into a chained form, which is known to be effective in constructing a feedback control law for some driftless nonholonomic systems. To address this problem, we utilize a time-state control form, a kind of canonical form which covers a broader class of systems than the chained form. This form is first applied to two separate subproblems, position control, in which the planar position of the ball is controlled but not the orientation, and orientation control, in which the orientation is controlled without changing the positional relation between the ball and the plates. It turns out that there exists a linearly uncontrollable subspace in the transformed subsystem, which turns into controllable by a change of coordinates. This implies that the system has the structure of a system with two generators. We propose a control strategy using iterative changes of coordinates, ensuring convergence in the neighborhood of the origin. Finally, we unify the subproblems into simultaneous control of position and orientation, i.e., the whole configuration of the system. The important idea in the simultaneous control is the coordinate transformation, which enables us to avoid a singular point. Results of simulations show that the proposed method achieve robustness to a measurement noise and perturbation of radius of the ball.

An alternative coordinated motion control architecture for robot arms manipulating an object is proposed. The motion and the internal force of the object are resolved in the motion of each arm. Each arm's control is based on the virtual internal model so as to operate in coordination even if geometric errors exist in the robot arms and the object. The virtual internal model is a reference model driven by sensory information implemented in the controller. The proposed architecture keeps the state of the system bounded even if breakage of the manipulated object occurs. The control algorithm is experimentally applied to the coordinated motion control of two planar robot arms, each of which has three degrees of freedom. The results illustrate the validity of the proposed control architecture.>

The authors propose an alternative coordinated motion control architecture for robot arms manipulating an object. The motion and the internal force of the object are resolved into the motion of each arm. Each arm is controlled, on the basis of the virtual internal model, so that they operate in coordination even if geometric errors exist in the arms and the object. The virtual internal model is a reference model driven by sensory information implemented in the controller. The proposed architecture maintains the stability of the system even if breakage of the manipulated object occurs. The control algorithm was experimentally applied to the coordinated motion control of two planar robot arms, each of which has three degrees of freedom. The results illustrate the validity of the proposed control architecture.>