三指灵巧手内力汇交多边形存在性判别算法

Algorithm for Internal Force Concurrent Polygon Existence of Three-fingered Robot Hand

抓取内力对三指灵巧手实现稳定抓取具有重要的作用。当手指指端与物体构成有摩擦的固定点接触模型时,三指内力必须位于相应接触点摩擦扇内并交于内力汇交多边形内的一点。因此,内力优化算法的研究必须建立在内力汇交多边形存在的基础之上。基于对物体表面接触位置的几何特性分析,建立摩擦扇存在条件,每个指端接触点的内法矢与接触平面所成夹角小于接触点摩擦圆锥角。通过研究接触点摩擦扇边界线及其交点的相互位置关系,推导内力汇交多边形的存在条件,任意两个摩擦扇的边界线交点中,至少有一个位于第三个摩擦扇的严格内部,或者至少有3个边界线交点位于第三个摩擦扇边界线上。最后构建判别三指内力汇交多边形存在性的通用算法,由此可确定能实现对指端操作力起调整作用的自平衡内力。结合抓取实例说明了判别算法的有效性。

The internal forces play an important role in the stable grasping of three-fingered robot hand. Under the condition of fixed-point contact models with friction between the fingertips and the object surface, it is necessary for the three internal forces to lie in relative frictional sectors of contact points and intersect at a point within concurrent polygon. As a result, the research on optimized algorithm for internal force should be made on the basis of concurrent polygon existence. Based on the analysis of the geometrical characteristics of contact positions on the object surface, the existence condition of the frictional sectors is established. The angle between inner normal vector and relative inner normal vector of each contact point should be smaller than friction cone angle. By means of studying the relative location relationships between the frictional sector borderlines and their intersections, the existence condition of the concurrent polygon for the three internal forces is presented. All intersections of any two frictional sectors are not less than one lying in absolute inner of the third frictional sector or not less than three lying on the borderlines of the third frictional sector. At last, a general algorithm for judging the existence of concurrent polygon is founded, by which the self-balancing internal forces can be determined and used to regulate the fingertip manipulating forces. An example is given to illustrate the validity of the algorithm.