Shape-adaptive virtual hand grasping method
Abstract: Objective: Virtual hand grasping is one of the core topics/techniques in virtual interaction, and it strongly determines the immersion. Real-time force analysis is very complex, so more rules that meet the characteristics of hand grasping are formulated, instead of complex mechanics calculations. Some existing rules focus on the included angle of two contact points’ normal vector, or the included angle of two lines that connect contact point and object’s center, but they can''t deal with some shape correctly. This paper proposes a shape-adaptive grasping method. Method: This method uses shape features and contact points of basic geometries like cube, sphere and cylinder to design grasping rules. 1) For a cube, there must be at least three contact points on the surface that are not all collinear, and one of included angles of every two contact points’ normal vector is larger than 90 degrees: First getting the positions of all the contact points. Second according to the rotation of the cube, rotating the cube and all the points so that every edge of the cube parallels to the world axis which simplifies calculation. Third determining every point’s location whether it is on the plane, edge, or vertex of the cube by the scale of the cube. Fourth calculating the normal vector of these points based on their locations. The vector’s direction is perpendicular to the plane when the point is on the plane, or is the same as the moving direction of the point when the point is on the edge or vertex. At last calculating the included angles of every two normal vectors, and determining the grasping result. 2) For a sphere, there must be at least four contact points, and the spatial relationship between these points and sphere’s center should satisfy the proposition obtained from the analysis: First getting the position of sphere’s center and all the contact points. Second using the center and every two of these points to form a plane, and then calculating whether all the other points are on the same side of this plane. At last determining the grasping result with the calculation results. 3) For a cylinder, depending on whether the contact points are all on the curved surface, a rule like sphere rule is used or not: First getting the position of all the contact point and then rotating the cylinder and all the points so that the bottom plane of the cylinder parallels to the world axis. Second projecting these points to the bottom plane of the cylinder. Third using the circle center of the bottom plane and every projected point to form a diameter, calculating whether all other projected points are on the same side of the diameter. At last determining the grasping result with the calculation results. When there are points on the top or bottom plane, cube rule is used instead. Result: It can more realistically handle the grasping of an object with curved surface. For a complex object which can be composed by multiple basic geometries, our method divides the calculation into two steps. Firstly, the object is decomposed to these three basic geometries, and then each geometry is calculated separately. Some geometries nearly meet the grasping rule, called unstable state. Secondly, our method selects every one of these unstable state geometries, gathers the information like position and normal vector of all the points to it, and then makes decisions whether the whole object is caught or not with the basic geometry rules obtained before. The calculation of the possibility of moment balance further reduces the occurrence of erroneous determinations. All the normal vectors are the opposite direction of force, but their values are uncertain. According to the proposition obtained from the analysis, the moment may balance when the normal vectors meet a specific spatial relationship just like the sphere rule: First normalizing all normal vectors, and then projecting them to a unit sphere, so there are points on the surface. Second using the points to calculate the same proposition in sphere rule. At last determining whether the moment is balanced or not. Only both rules and moment balance are satisfied, the grasping will determine success. By using unity3d software and neuron data glove, the experimental results show that the method can effectively handle the grasp of objects with curved surfaces like a ball, and complex objects like a cup. When the virtual hand touches the upper hemisphere, the ball is not caught. Only if the figures ring around the ball, it will be caught. Casually grasping the cup will not catch it. Only when the gesture is correct and the moment is balanced, the cup can be caught. Conclusion: This paper proposes a Shape-adaptive grasping method, and a calculation method that decomposing complex objects into simple basic geometries. This method effectively handles the grasp effectively, and conforms to intuitive feel.