非ホロノミック拘束下における三次元物体把持のシミュレータ構築 [in Japanese] Construction of a Simulator for 3-D Object Pinching by Two Robot Fingers under Nonholonomic Constraints [in Japanese]
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This paper proposes a method for constructing a simulator of pinching a 3-D object by a pair of robot fingers under the gravity effect, holonomic constraints, and a differential equation of non-holonomic constraints expressing rotational motion of the pinched object. A noteworthy difference of modeling of motion of a 3-D object from that of a 2-D object is that the instantaneous axis of rotation of the object is fixed in the 2-D case but that is time-varying in the 3-D case. This difference appears as non-holonomic constraints. A further difficulty 3-D physical interactions between two robot fingers and a rigid object is that spinning motion may arise around the opposing axis connecting the two contact points between fingertip's and the pinched object. The proposed simulation method deals with the case after such spinning motion ceases. Non-occurrence of such spinning motion induces a further non-holonomic constraint. It is shown that Lagrange's equation of motion of the overall system can be derived without violating the causality that governs such non-holonomic constraints. In the mathematical model, holonomic constraints and Euler-Lagrange equations are mutually related. Therefore, this paper aims at ordering these conditions and proposing the algorithm to carry out numerical simulation of the overall system motion without violating the principle of causality of time. Then, results of the simulation are shown to verify the validity of the proposed control input called"blind grasping"based on opposable forces between the thumb and another finger (index or middle finger) without use of any object kinematics or any external sensing.
JRSJ 25(2), 280-288, 2007-03-01
The Robotics Society of Japan