Manipulability Index Optimization for a Planar Robotic Arm

Abstract: It is of interest to have high manipulability in robotic manipulators in order to achieve high performance. In this report, a model of a robotic arm manipulator is de ned and analyzed with focus on optimizing the manipulability. The kinematics for the robotic ma- nipulator is used to de ne quantitative measures of manipulability, manipulability indices . Analytical results for dierent manipulability indices are derived. It is shown that a common feature of the indices is that they are independent of the rst angle of the robotic arm. Using numerical optimization, the manipulability measure is optimized under dierent constraints. The manipulability measure is also used when de ning a path for the robotic arm manip- ulator with high manipulability. The path is described by polynomials in the joint space . Numerical optimization of the path is done for several examples. It is concluded that the indices give dierent measures of manipulability and are therefore suitable for dierent prob- lems. It is also shown that the manipulability can be optimized when dierent constraints are imposed and that an optimal radius for the end-eector exists. Lastly, it is concluded that a short path with high manipulability is possible to obtain using the proposed method.