In various industrial robotic applications, the effective traversal of a manipulator amidst obstacles and its ability to reach specific task-points are imperative for the execution of predefined tasks. In certain scenarios, the sequence in which the manipulator reaches these task-points significantly impacts the overall cycle time required for task completion. Moreover, some tasks necessitate significant force exertion at the end-effector. Therefore, establishing an optimal sequence for the task-points reached by the end-effector’s tip is crucial for enhancing robot performance, ensuring collision-free motion and maintaining high-force application at the end-effector’s tip.

To maximize the manipulator’s manipulability, which serves as a performance index for assessing its force capability, we aim to establish an optimal collision-free task sequence considering higher mechanical advantage. Three optimization criteria are considered: the cycle time, collision avoidance and the manipulability index. Optimization is accomplished using a genetic algorithm coupled with the Bump-Surface concept for collision avoidance. The effectiveness of this approach is confirmed through simulation experiments conducted in 2D and 3D environments with obstacles employing both redundant and non-redundant robots.

The manipulability index suggested by Yoshikava is an important tool for the design of mechanisms and their control. It represents a quantitative measure of the functionality and the ability for realizing some tasks or groups of tasks. This index is some kind of performance measure and should be taken into consideration in the design phase of a mechanism and also in the design of control algorithms.

In this paper two important properties of the manipulability index are investigated. The first part of the present work demonstrates that manipulability of a mechanism is independent of task space coordinates. In the second part, a proof of the independency of the manipulability index on the first DOF is given.

This invariance is important for simplification of the mechanism's Jacobian matrix and gives excellent insight into the dependences of configuration space coordinates on this index. Moreover, it proves that the manipulability index is determined only by relative positions of the mechanism itself and by the mechanism's geometry.

Finally, the properties of the manipulability index are illustrated by some examples for fundamental open kinematical chain structures.