A recursive dimension-growing method for computing robotic manipulability polytope

In this paper, the general problem of mapping an n-dimensional polytope Q to an m-dimensional polytope P by P=AQ with n>m is studied. It is well-known that some vertices of Q are mapped to internal points of P, and it is very time consuming to detect them when their number is large. A computationally efficient recursive algorithm based on dimension-growing has been developed which is capable of successively removing the internal points of each intermediate polytope when they are first detected, hence eliminating their further growth into additional internal points in subsequently intermediate polytopes. The method can be applied to compute the robotic manipulability polytope based on the mapping x˙=Jq˙. It is shown that substantial reduction in computation time can be achieved for higher DOF redundant robot manipulators. Examples including the 8-DOF ARMII robot are presented and comparisons to the conventional method are made