Guaranteeing task prioritization for redundant robots given maximum number of tasks and singularities

This paper evaluates the effectiveness of a proposed task-prioritization scheme for redundant robots. The scheme has an advantage of a non-inverse computation of the projection matrix. This feature is important because the projection matrix for redundant robots is singular all the time, except when the Jacobian is zero. The evaluation is based on how task prioritization is managed through singularities, despite carrying out maximum load of task requirements. In particular, the redundant robot should be able to: (1) utilize the lost degree of freedom in the world space for the newly prioritized singularity-escape task in the null space, (2) set this new task as the highest-priority task in the null space, and (3) maintain the hierarchy of task prioritization of the previously assigned tasks. To proceed with the evaluation, we first established the maximum number of prioritized tasks that a given redundant robot can accommodate. Then we assigned this maximum number of tasks on the robot, forced it to assume a singular configuration, and evaluated its task prioritization performance. This scenario is very useful when singularity cannot be avoided during task execution, e.g., avoiding obstacles in the null space such that the robot is forced to assume a singular configuration while fully loaded with prioritized tasks.